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Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. Estimate the standard reaction Gibbs energy of $\mathrm{N}_2(\mathrm{g})+3 \mathrm{H}_2(\mathrm{g}) \rightarrow$ $2 \mathrm{NH}_3$ (g) at $500 \mathrm{~K}$.	Substance (state) ΔfG° ΔfG° Substance (state) (kJ/mol) (kcal/mol) NO(g) 87.6 20.9 NO2(g) 51.3 12.3 N2O(g) 103.7 24.78 H2O(g) −228.6 −54.64 H2O(l) −237.1 −56.67 CO2(g) −394.4 −94.26 CO(g) −137.2 −32.79 CH4(g) −50.5 −12.1 C2H6(g) −32.0 −7.65 C3H8(g) −23.4 −5.59 C6H6(g) 129.7 29.76 C6H6(l) 124.5 31.00 The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, in their standard states (the most stable form of the element at 25 °C and 100 kPa). This implies that at equilibrium Q_\text{r} = K_\text{eq} and \Delta_\text{r} G = 0. ==Standard Gibbs energy change of formation== Table of selected substancesCRC Handbook of Chemistry and Physics, 2009, pp. 5-4–5-42, 90th ed., Lide. Moreover, we also have \begin{align} K_\text{eq} &= e^{-\frac{\Delta_\text{r} G^\circ}{RT}}, \\\ \Delta_\text{r} G^\circ &= -RT\left(\ln K_\text{eq}\right) = -2.303\,RT\left(\log_{10} K_\text{eq}\right), \end{align} which relates the equilibrium constant with Gibbs free energy. The NIST Chemistry WebBook (see link below) is an online resource that contains standard enthalpy of formation for various compounds along with the standard absolute entropy for these compounds from which the standard Gibbs free energy of formation can be calculated. Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. The standard Gibbs free energy of formation (Gf°) of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 1 bar of pressure and the specified temperature, usually 298.15 K or 25 °C). The table below lists the standard Gibbs function of formation for several elements and chemical compounds and is taken from Lange's Handbook of Chemistry. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . The Gibbs energy of any system is and an infinitesimal change in G, at constant temperature and pressure, yields :dG=dU+pdV-TdS. The Gibbs free energy is expressed as : G(p,T) = U + pV - TS = H - TS where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy. Each quantity in the equations above can be divided by the amount of substance, measured in moles, to form molar Gibbs free energy. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. Value of R Unit SI units J⋅K−1⋅mol−1 m3⋅Pa⋅K−1⋅mol−1 kg⋅m2⋅s−2⋅K−1⋅mol−1 Other common units L⋅Pa⋅K−1⋅mol−1 L⋅kPa⋅K−1⋅mol−1 L⋅bar⋅K−1⋅mol−1 erg⋅K−1⋅mol−1 atm⋅ft3⋅lbmol−1⋅°R−1 psi⋅ft3⋅lbmol−1⋅°R−1 BTU⋅lbmol−1⋅°R−1 inH2O⋅ft3⋅lbmol−1⋅°R−1 torr⋅ft3⋅lbmol−1⋅°R−1 L⋅atm⋅K−1⋅mol−1 L⋅Torr⋅K−1⋅mol−1 cal⋅K−1⋅mol−1 m3⋅atm⋅K−1⋅mol−1 The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Note that all values are in kJ/mol. Far more extensive tables can be found in the CRC Handbook of Chemistry and Physics and the NIST JANAF tables.M. W. Chase, NIST – JANAF Thermochemical Tables, 4th Edition, Journal of Physical and Chemical Reference Data, Monograph 9, 1998. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Mayer's relation relates the specific gas constant to the specific heat capacities for a calorically perfect gas and a thermally perfect gas. Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. ==References== ==External links== * Ideal gas calculator – Ideal gas calculator provides the correct information for the moles of gas involved. The value of R is then obtained from the relation :c_\mathrm{a}(0, T) = \sqrt{\frac{\gamma_0 R T}{A_\mathrm{r}(\mathrm{Ar}) M_\mathrm{u}}}, where: γ0 is the heat capacity ratio ( for monatomic gases such as argon); T is the temperature, TTPW = 273.16 K by the definition of the kelvin at that time; *Ar(Ar) is the relative atomic mass of argon and Mu = as defined at the time.	7	205	0.0245	9.73	58.2	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The enthalpy of vaporization of chloroform $\left(\mathrm{CHCl}_3\right)$ is $29.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at its normal boiling point of $334.88 \mathrm{~K}$. Calculate the entropy of vaporization of chloroform at this temperature.	J/(mol K) Enthalpy of combustion –473.2 kJ/mol ΔcH ~~o~~ Heat capacity, cp 114.25 J/(mol K) Gas properties Std enthalpy change of formation, ΔfH ~~o~~ gas –103.18 kJ/mol Standard molar entropy, S ~~o~~ gas 295.6 J/(mol K) at 25 °C Heat capacity, cp 65.33 J/(mol K) at 25 °C van der Waals' constantsLange's Handbook of Chemistry 10th ed, pp. 1522–1524 a = 1537 L2 kPa/mol2 b = 0.1022 liter per mole ==Vapor pressure of liquid== P in mm Hg 1 10 40 100 400 760 1520 3800 7600 15200 30400 45600 T in °C –58.0 –29.7 –7.1 10.4 42.7 61.3 83.9 120.0 152.3 191.8 237.5 — Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. thumb\|812px\|left\|log10 of Chloroform vapor pressure. The entropy of vaporization is then equal to the heat of vaporization divided by the boiling point: : \Delta S_\text{vap} = \frac{\Delta H_\text{vap}}{T_\text{vap}}. The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. Uses formula: \scriptstyle \log_e P_{mmHg} =\scriptstyle \log_e (\frac {760} {101.325}) - 10.07089 \log_e(T+273.15) - \frac {6351.140} {T+273.15} + 81.14393 + 9.127608 \times 10^{-6} (T+273.15)^2 obtained from CHERIC ==Distillation data== {\| border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;" Vapor-liquid Equilibrium for Chloroform/Ethanol P = 101.325 kPa BP Temp. °C % by mole chloroform liquid vapor 78.15 0.0 0.0 78.07 0.52 1.59 77.83 1.02 3.01 76.81 2.21 7.45 74.90 5.80 17.10 74.39 6.72 19.40 73.55 8.38 23.31 72.85 10.57 28.05 72.24 11.80 30.52 71.58 13.18 33.13 69.72 17.65 41.00 68.95 19.62 43.66 68.58 20.71 45.43 67.35 23.86 49.77 65.89 28.54 55.09 64.87 32.35 58.48 63.88 36.07 61.27 63.23 39.34 64.50 62.61 41.38 65.49 62.17 44.41 67.57 61.48 49.97 71.11 61.00 53.92 72.91 60.49 54.76 73.57 60.35 59.65 74.68 60.30 61.60 75.53 60.20 63.04 76.12 60.09 64.48 76.69 59.97 66.90 77.74 59.54 72.01 79.33 59.32 79.07 82.62 59.26 82.99 83.59 59.28 84.97 84.69 59.31 85.96 85.24 59.46 89.92 87.93 59.72 91.10 88.73 59.70 92.44 89.79 59.84 93.90 91.02 59.91 95.26 92.56 60.18 96.13 93.58 60.88 98.89 97.93 61.13 100.00 100.00 == Spectral data == UV-Vis λmax ? nm Extinction coefficient, ε ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? According to Trouton's rule, the entropy of vaporization (at standard pressure) of most liquids has similar values. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). Pa Critical point 537 K (264 °C), 5328.68 kPa Std enthalpy change of fusion, ΔfusH ~~o~~ 8.8 kJ/mol Std entropy change of fusion, ΔfusS ~~o~~ 42 J/(mol·K) Std enthalpy change of vaporization, ΔvapH ~~o~~ 31.4 kJ/mol Std entropy change of vaporization, ΔvapS ~~o~~ 105.3 J/(mol·K) Solid properties Std enthalpy change of formation, ΔfH ~~o~~ solid ? kJ/mol Standard molar entropy, S ~~o~~ solid ? J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? J/(mol K) Liquid properties Std enthalpy change of formation, ΔfH ~~o~~ liquid –134.3 kJ/mol Standard molar entropy, S ~~o~~ liquid ? In thermodynamics, the entropy of vaporization is the increase in entropy upon vaporization of a liquid. == Heat of vaporization == kJ/mol 1 H hydrogen (H2) use (H2) 0.904 CRC (H2) 0.90 LNG 0.904 2 He helium use 0.0829 CRC 0.08 LNG 0.0829 WEL 0.083 3 Li lithium use 136 LNG 147.1 WEL 147 Zhang et al. 136 4 Be beryllium use 292 LNG 297 WEL 297 Zhang et al. 292 5 B boron use 508 CRC 480 LNG 480 WEL 507 Zhang et al. 508 6 C carbon use WEL (sublimation) 715 7 N nitrogen (N2) use (N2) 5.57 CRC (N2) 5.57 LNG (N2) 5.577 WEL (per mole N atoms) 2.79 Zhang et al. 5.58 8 O oxygen (O2) use (O2) 6.82 CRC (O2) 6.82 LNG (O2) 6.820 WEL (per mole O atoms) 3.41 Zhang et al. 6.82 9 F fluorine (F2) use (F2) 6.62 CRC (F2) 6.62 LNG (F2) 6.62 WEL (per mole F atoms) 3.27 Zhang et al. 6.32 10 Ne neon use 1.71 CRC 1.71 LNG 1.71 WEL 1.75 Zhang et al. 1.9 11 Na sodium use 97.42 LNG 97.42 WEL 97.7 Zhang et al. 97.4 12 Mg magnesium use 128 LNG 128 WEL 128 Zhang et al. 132 13 Al aluminium use 284 CRC 294 LNG 294.0 WEL 293 Zhang et al. 284 14 Si silicon use 359 LNG 359 WEL 359 Zhang et al. 383 15 P phosphorus use 12.4 CRC 12.4 LNG 12.4 WEL 12.4 Zhang et al. 51.9 (white) 16 S sulfur use (mono) 45 CRC 45 LNG (mono) 45 WEL 9.8 Zhang et al. 45 17 Cl chlorine (Cl2) use (Cl2) 20.41 CRC (Cl2) 20.41 LNG (Cl2) 20.41 WEL (per mole Cl atoms) 10.2 Zhang et al. 20.4 18 Ar argon use 6.53 CRC 6.43 LNG 6.43 WEL 6.5 Zhang et al. 6.53 19 K potassium use 76.90 LNG 76.90 WEL 76.9 Zhang et al. 79.1 20 Ca calcium use 154.7 LNG 154.7 WEL 155 Zhang et al. 153 21 Sc scandium use 332.7 LNG 332.7 WEL 318 Zhang et al. 310 22 Ti titanium use 425 LNG 425 WEL 425 Zhang et al. 427 23 V vanadium use 444 LNG 459 WEL 453 Zhang et al. 451 24 Cr chromium use 339.5 LNG 339.5 WEL 339 Zhang et al. 347 25 Mn manganese use 221 LNG 221 WEL 220 Zhang et al. 225 26 Fe iron use 340 LNG 340 WEL 347 Zhang et al. 354 27 Co cobalt use 377 LNG 377 WEL 375 Zhang et al. 390 28 Ni nickel use 379 LNG 377.5 WEL 378 Zhang et al. 379 29 Cu copper use 300.4 LNG 300.4 WEL 300 Zhang et al. 305 30 Zn zinc use 115 LNG 123.6 WEL 119 Zhang et al. 115 31 Ga gallium use 256 CRC 254 LNG 254 WEL 256 Zhang et al. 256 32 Ge germanium use 334 CRC 334 LNG 334 WEL 334 Zhang et al. 330 33 As arsenic use 32.4 WEL 32.4 (sublimation) Zhang et al. 32.4 34 Se selenium use 95.48 CRC 95.48 LNG 95.48 WEL 26 Zhang et al. 95.5 35 Br bromine (Br2) use (Br2) 29.96 CRC (Br2) 29.96 LNG (Br2) 29.96 WEL (per mole Br atoms) 14.8 Zhang et al. 30 36 Kr krypton use 9.08 CRC 9.08 LNG 9.08 WEL 9.02 Zhang et al. 9.03 37 Rb rubidium use 75.77 LNG 75.77 WEL 72 Zhang et al. 69 38 Sr strontium use 141 LNG 136.9 WEL 137 Zhang et al. 141 39 Y yttrium use 390 LNG 365 WEL 380 Zhang et al. 363 40 Zr zirconium use 573 LNG 573 WEL 580 Zhang et al. 591 41 Nb niobium use 689.9 LNG 689.9 WEL 690 Zhang et al. 682 42 Mo molybdenum use 617 LNG 617 WEL 600 Zhang et al. 617 43 Tc technetium use 585.2 LNG 585.2 WEL 550 44 Ru ruthenium use 619 LNG 591.6 WEL 580 Zhang et al. 619 45 Rh rhodium use 494 LNG 494 WEL 495 Zhang et al. 493 46 Pd palladium use 358 LNG 362 WEL 380 Zhang et al. 358 47 Ag silver use 254 LNG 258 WEL 255 Zhang et al. 254 48 Cd cadmium use 99.87 CRC 99.87 LNG 99.9 WEL 100 Zhang et al. 100 49 In indium use 231.8 LNG 231.8 WEL 230 Zhang et al. 225 50 Sn tin use (white) 296.1 LNG (white) 296.1 WEL 290 Zhang et al. 296 51 Sb antimony use 193.43 LNG 193.43 WEL 68 Zhang et al. 193 52 Te tellurium use 114.1 CRC 114.1 LNG 114.1 WEL 48 Zhang et al. 114 53 I iodine (I2) use (I2) 41.57 CRC (I2) 41.57 LNG (I2) 41.6 WEL (per mole I atoms) 20.9 Zhang et al. 41.6 54 Xe xenon use 12.64 CRC 12.57 LNG 12.64 WEL 12.64 Zhang et al. 12.6 55 Cs caesium use 63.9 LNG 63.9 WEL 65 Zhang et al. 66.1 56 Ba barium use 140.3 CRC 140 LNG 140.3 WEL 140 Zhang et al. 142 57 La lanthanum use 400 LNG 402.1 WEL 400 Zhang et al. 400 58 Ce cerium use 398 LNG 398 WEL 350 Zhang et al. 398 59 Pr praseodymium use 331 LNG 331 WEL 330 Zhang et al. 331 60 Nd neodymium use 289 LNG 289 WEL 285 Zhang et al. 289 61 Pm promethium use 289 LNG 289 WEL 290 62 Sm samarium use 192 LNG 165 WEL 175 Zhang et al. 192 63 Eu europium use 176 LNG 176 WEL 175 Zhang et al. 176 64 Gd gadolinium use 301.3 LNG 301.3 WEL 305 Zhang et al. 301 65 Tb terbium use 391 LNG 293 WEL 295 Zhang et al. 391 66 Dy dysprosium use 280 LNG 280 WEL 280 Zhang et al. 280 67 Ho holmium use 251 LNG 71 WEL 265 Zhang et al. 251 68 Er erbium use 280 LNG 280 WEL 285 Zhang et al. 280 69 Tm thulium use 191 LNG 247 WEL 250 Zhang et al. 191 70 Yb ytterbium use 129 LNG 159 WEL 160 Zhang et al. 129 71 Lu lutetium use 414 LNG 414 WEL 415 Zhang et al. 414 72 Hf hafnium use 648 LNG 571 WEL 630 Zhang et al. 648 73 Ta tantalum use 732.8 LNG 732.8 WEL 735 Zhang et al. 753 74 W tungsten use 806.7 LNG 806.7 WEL 800 Zhang et al. 774 75 Re rhenium use 704 LNG 704 WEL 705 Zhang et al. 707 76 Os osmium use 678 LNG 738 WEL 630 Zhang et al. 678 77 Ir iridium use 564 LNG 231.8 WEL 560 Zhang et al. 564 78 Pt platinum use 510 LNG 469 WEL 490 Zhang et al. 510 79 Au gold use 342 CRC 324 LNG 324 WEL 330 Zhang et al. 342 80 Hg mercury use 59.11 CRC 59.11 LNG 59.1 WEL 59.2 Zhang et al. 58.2 81 Tl thallium use 165 LNG 165 WEL 165 Zhang et al. 162 82 Pb lead use 179.5 CRC 179.5 LNG 179.5 WEL 178 Zhang et al. 177 83 Bi bismuth use 179 CRC 151 LNG 151 WEL 160 Zhang et al. 179 84 Po polonium use 102.91 LNG 102.91 WEL about 100 85 At astatine use 54.39 (At2) GME 54.39 (At2) WEL about 40 86 Rn radon use 18.10 LNG 18.10 WEL 17 87 Fr francium use ca. 65 WEL about 65 88 Ra radium use 113 LNG 113 WEL about 125 89 Ac actinium use 400 WEL 400 90 Th thorium use 514 LNG 514 WEL 530 91 Pa protactinium use 481 LNG 481 WEL 470 92 U uranium use 417.1 LNG 417.1 WEL 420 93 Np neptunium use 336 LNG 336 WEL 335 94 Pu plutonium use 333.5 LNG 333.5 WEL 325 == Notes == * Values refer to the enthalpy change in the conversion of liquid to gas at the boiling point (normal, 101.325 kPa). == References == ===Zhang et al.=== ===CRC=== As quoted from various sources in an online version of: * David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 84th Edition. K (? °C), ? K (? °C), ? K (? °C), ? K (? °C), ? This page provides supplementary chemical data on chloroform. == Material Safety Data Sheet == The handling of this chemical may incur notable safety precautions. Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996).	258.14	+87.8	0.33333333	-0.029	24	B
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Given the reactions (1) and (2) below, determine $\Delta_{\mathrm{r}} H^{\ominus}$ for reaction (3). (1) $\mathrm{H}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^{\ominus}=-184.62 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (2) $2 \mathrm{H}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^\ominus=-483.64 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (3) $4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{Cl}_2(\mathrm{g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$	==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.18 1.293 65 KAL 33.2 1.297 65.0 SMI −239.9 13.2 kgf/cm² 0.0310 1 H hydrogen (equilibrium) LNG −240.17 1.294 12.77 atm 65.4 0.0308 1 H hydrogen (normal) LNG −239.91 1.297 12.8 atm 65.0 0.0310 1 D deuterium KAL 38.2 1.65 60 1 D deuterium (equilibrium) LNG −234.8 1.650 16.28 atm 60.4 0.0668 1 D deuterium (normal) LNG −234.7 1.665 16.43 atm 60.3 0.0669 2 He helium use 5.19 −267.96 0.227 CRC.a 5.19 −267.96 0.227 57 KAL 5.19 0.227 57.2 SMI −267.9 2.34 kgf/cm² 0.0693 2 He helium (equilibrium) LNG −267.96 0.2289 2.261 atm 0.06930 2 He helium-3 LNG −269.85 0.1182 1.13 atm 72.5 0.0414 2 He helium-4 LNG −267.96 0.227 2.24 atm 57.3 0.0698 3 Li lithium use (3223) (2950) (67) CRC.b (3223) 2950 (67) (66) 7 N nitrogen use 126.21 −146.94 3.39 CRC.a 126.21 −146.94 3.39 90 KAL 126.2 3.39 89.5 SMI −147.1 34.7 kgf/cm² 0.3110 7 N nitrogen-14 LNG −146.94 3.39 33.5 atm 89.5 0.313 7 N nitrogen-15 LNG −146.8 3.39 33.5 atm 90.4 0.332 8 O oxygen use 154.59 −118.56 5.043 CRC.a 154.59 −118.56 5.043 73 LNG −118.56 5.043 49.77 atm 73.4 0.436 KAL 154.6 5.04 73.4 SMI −118.8 51.4 kgf/cm² 0.430 9 F fluorine use 144.13 −129.02 5.172 CRC.a 144.13 −129.02 5.172 66 LNG −129.0 5.215 51.47 atm 66.2 0.574 KAL 144.3 5.22 66 10 Ne neon use 44.4 −228.7 2.76 CRC.a 44.4 −228.7 2.76 42 LNG −228.71 2.77 27.2 atm 41.7 0.4835 KAL 44.4 2.76 41.7 SMI −228.7 26.8 kgf/cm² 0.484 11 Na sodium use (2573) (2300) (35) CRC.b (2573) 2300 (35) (116) 15 P phosphorus use 994 721 CRC.a 994 721 LNG 721 16 S sulfur use 1314 1041 20.7 CRC.a 1314 1041 20.7 LNG 1041 11.7 116 atm KAL 1314 20.7 SMI 1040 17 Cl chlorine use 416.9 143.8 7.991 CRC.a 416.9 143.8 7.991 123 LNG 143.8 7.71 76.1 atm 124 0.573 KAL 416.9 7.98 124 SMI 144.0 78.7 kgf/cm² 0.573 18 Ar argon use 150.87 −122.28 4.898 CRC.a 150.87 −122.28 4.898 75 LNG −122.3 4.87 48.1 atm 74.6 0.536 KAL 150.9 4.90 74.6 SMI −122 49.7 kgf/cm² 0.531 19 K potassium use (2223) (1950) (16) CRC.b (2223) 1950 (16) (209) 33 As arsenic use 1673 1400 CRC.a 1673 1400 35 LNG 1400 34 Se selenium use 1766 1493 27.2 CRC.a 1766 1493 27.2 LNG 1493 35 Br bromine use 588 315 10.34 CRC.a 588 315 10.34 127 LNG 315 10.3 102 atm 135 1.184 KAL 588 10.3 127 SMI 302 1.18 36 Kr krypton use 209.41 −63.74 5.50 CRC.a 209.41 −63.74 5.50 91 LNG −63.75 5.50 54.3 atm 91.2 0.9085 KAL 209.4 5.50 91.2 37 Rb rubidium use (2093) (1820) (16) CRC.b (2093) 1820 (16) (247) LNG 1832 250 0.34 53 I iodine use 819 546 11.7 CRC.a 819 546 155 LNG 546 11.7 115 atm 155 0.164 KAL 819 155 SMI 553 54 Xe xenon use 289.77 16.62 5.841 CRC.c 289.77 16.62 5.841 118 LNG 16.583 5.84 57.64 atm 118 1.105 KAL 289.7 5.84 118 SMI 16.6 60.2 kgf/cm² 1.155 55 Cs caesium use 1938 1665 9.4 CRC.d 1938 1665 9.4 341 LNG 1806 300 0.44 80 Hg mercury use 1750 1477 172.00 CRC.a 1750 1477 172.00 43 LNG 1477 160.8 1587 atm KAL 1750 172 42.7 SMI 1460±20 1640±50 kgf/cm² 0.5 86 Rn radon use 377 104 6.28 CRC.a 377 104 6.28 LNG 104 6.28 62 atm 139 1.6 KAL 377 6.3 SMI 104 64.1 kgf/cm² ==References== ===CRC.a-d=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 85th Edition, online version. == Specific heat capacity == J/(mol·K) J/(g·K) 1 H hydrogen (H2, gas) use 28.836 14.304 CRC 28.836 14.304 WEL 28.82 LNG 28.84 2 He helium (gas) use 20.786 5.193 CRC 20.786 5.193 WEL 20.786 LNG 20.786 3 Li lithium use 24.860 3.582 CRC 24.860 3.582 WEL 24.8 LNG 24.8 4 Be beryllium use 16.443 1.825 CRC 16.443 1.825 WEL 16.4 LNG 16.38 5 B boron (rhombic) use 11.087 1.026 CRC 11.087 1.026 WEL 11.1 LNG 11.1 6 C carbon (graphite) use 8.517 0.709 CRC 8.517 0.709 WEL 8.53 LNG 8.517 6 C carbon (diamond, nonstd state) use 6.115 0.509 WEL 6.115 LNG 6.116 7 N nitrogen (N2, gas) use 29.124 1.040 CRC 29.124 1.040 WEL 29.12 LNG 29.124 8 O oxygen (O2, gas) use 29.378 0.918 CRC 29.378 0.918 WEL 29.4 LNG 29.4 9 F fluorine (F2, gas) use 31.304 0.824 CRC 31.304 0.824 WEL 31.3 LNG 31.30 10 Ne neon (gas) use 20.786 1.030 CRC 20.786 1.030 WEL 20.786 LNG 20.786 11 Na sodium use 28.230 1.228 CRC 28.230 1.228 WEL 28.2 LNG 28.15 12 Mg magnesium use 24.869 1.023 CRC 24.869 1.023 WEL 24.9 LNG 24.87 13 Al aluminium use 24.200 0.897 CRC 24.200 0.897 WEL 24.4 LNG 24.4 14 Si silicon use 19.789 0.705 CRC 19.789 0.705 WEL 20.0 LNG 20.00 15 P phosphorus (white) use 23.824 0.769 CRC 23.824 0.769 WEL 23.84 LNG 23.83 15 P phosphorus (red, nonstd state) use 21.19 0.684 WEL 21.2 LNG 21.19 16 S sulfur (rhombic) use 22.75 0.710 CRC 22.75 0.710 WEL 22.6 LNG 22.60 16 S sulfur (monoclinic, nonstd state) use 23.23 0.724 LNG 23.23 17 Cl chlorine (Cl2 gas) use 33.949 0.479 CRC 33.949 0.479 WEL 33.91 LNG 33.95 18 Ar argon (gas) use 20.786 0.520 CRC 20.786 0.520 WEL 20.786 LNG 20.79 19 K potassium use 29.600 0.757 CRC 29.600 0.757 WEL 29.6 LNG 29.60 20 Ca calcium use 25.929 0.647 CRC 25.929 0.647 WEL 25.3 LNG 25.9 21 Sc scandium use 25.52 0.568 CRC 25.52 0.568 WEL 25.5 LNG 25.52 22 Ti titanium use 25.060 0.523 CRC 25.060 0.523 WEL 25.0 LNG 25.0 23 V vanadium use 24.89 0.489 CRC 24.89 0.489 WEL 24.9 LNG 24.90 24 Cr chromium use 23.35 0.449 CRC 23.35 0.449 WEL 23.3 LNG 23.43 25 Mn manganese use 26.32 0.479 CRC 26.32 0.479 WEL 26.3 LNG 26.30 26 Fe iron (alpha) use 25.10 0.449 CRC 25.10 0.449 WEL 25.1 LNG 25.09 27 Co cobalt use 24.81 0.421 CRC 24.81 0.421 WEL 24.8 LNG 24.8 28 Ni nickel use 26.07 0.444 CRC 26.07 0.444 WEL 26.1 LNG 26.1 29 Cu copper use 24.440 0.385 CRC 24.440 0.385 WEL 24.43 LNG 24.44 30 Zn zinc use 25.390 0.388 CRC 25.390 0.388 WEL 25.4 LNG 25.40 31 Ga gallium use 25.86 0.371 CRC 25.86 0.371 WEL 25.9 LNG 26.06 32 Ge germanium use 23.222 0.320 CRC 23.222 0.320 WEL 23.35 LNG 23.3 33 As arsenic (alpha, gray) use 24.64 0.329 CRC 24.64 0.329 WEL 24.6 LNG 24.64 34 Se selenium (hexagonal) use 25.363 0.321 CRC 25.363 0.321 WEL 25.36 LNG 24.98 35 Br bromine use (Br2) 75.69 0.474 CRC 36.057 0.226 WEL (liquid) 75.69 WEL (Br2, gas, nonstd state) 36.0 LNG (Br2, liquid) 75.67 36 Kr krypton (gas) use 20.786 0.248 CRC 20.786 0.248 WEL 20.786 LNG 20.786 37 Rb rubidium use 31.060 0.363 CRC 31.060 0.363 WEL 31.1 LNG 31.06 38 Sr strontium use 26.4 0.301 CRC 26.4 0.301 WEL 26 LNG 26.79 39 Y yttrium use 26.53 0.298 CRC 26.53 0.298 WEL 26.5 LNG 26.51 40 Zr zirconium use 25.36 0.278 CRC 25.36 0.278 WEL 25.4 LNG 25.40 41 Nb niobium use 24.60 0.265 CRC 24.60 0.265 WEL 24.6 LNG 24.67 42 Mo molybdenum use 24.06 0.251 CRC 24.06 0.251 WEL 24.1 LNG 24.13 43 Tc technetium use 24.27 LNG 24.27 44 Ru ruthenium use 24.06 0.238 CRC 24.06 0.238 WEL 24.1 LNG 24.1 45 Rh rhodium use 24.98 0.243 CRC 24.98 0.243 WEL 25.0 LNG 24.98 46 Pd palladium use 25.98 0.244 CRC 25.98 0.246 [sic] WEL 26.0 LNG 25.94 47 Ag silver use 25.350 0.235 CRC 25.350 0.235 WEL 25.4 LNG 25.4 48 Cd cadmium use 26.020 0.232 CRC 26.020 0.232 WEL 26.0 LNG 25.9 49 In indium use 26.74 0.233 CRC 26.74 0.233 WEL 26.7 LNG 26.7 50 Sn tin (white) use 27.112 0.228 CRC 27.112 0.228 WEL 27.0 LNG 26.99 50 Sn tin (gray, nonstd state) use 25.77 0.217 WEL 25.8 LNG 25.77 51 Sb antimony use 25.23 0.207 CRC 25.23 0.207 WEL 25.2 LNG 25.2 52 Te tellurium use 25.73 0.202 CRC 25.73 0.202 WEL 25.7 LNG 25.70 53 I iodine use (I2) 54.44 0.214 CRC 36.888 0.145 WEL (solid) 54.44 WEL (I2, gas, nonstd state) 36.9 LNG (I2, solid) 54.44 LNG (I2, gas, nonstd state) 36.86 54 Xe xenon (gas) use 20.786 0.158 CRC 20.786 0.158 WEL 20.786 LNG 20.786 55 Cs caesium use 32.210 0.242 CRC 32.210 0.242 WEL 32.2 LNG 32.20 56 Ba barium use 28.07 0.204 CRC 28.07 0.204 WEL 28.1 LNG 28.10 57 La lanthanum use 27.11 0.195 CRC 27.11 0.195 WEL 27.1 LNG 27.11 58 Ce cerium (gamma, fcc) use 26.94 0.192 CRC 26.94 0.192 WEL 26.9 LNG 26.9 59 Pr praseodymium use 27.20 0.193 CRC 27.20 0.193 WEL 27.2 LNG 27.20 60 Nd neodymium use 27.45 0.190 CRC 27.45 0.190 WEL 27.4 LNG 27.5 62 Sm samarium use 29.54 0.197 CRC 29.54 0.197 WEL 29.5 LNG 29.54 63 Eu europium use 27.66 0.182 CRC 27.66 0.182 WEL 27.7 LNG 27.66 64 Gd gadolinium use 37.03 0.236 CRC 37.03 0.236 WEL 37.0 LNG 37.03 65 Tb terbium use 28.91 0.182 CRC 28.91 0.182 WEL 28.9 LNG 28.91 66 Dy dysprosium use 27.7 0.170 CRC 27.7 0.170 WEL 27.2 LNG 27.7 67 Ho holmium use 27.15 0.165 CRC 27.15 0.165 WEL 27.2 LNG 27.15 68 Er erbium use 28.12 0.168 CRC 28.12 0.168 WEL 28.1 LNG 28.12 69 Tm thulium use 27.03 0.160 CRC 27.03 0.160 WEL 27.0 LNG 27.03 70 Yb ytterbium use 26.74 0.155 CRC 26.74 0.155 WEL 26.7 LNG 26.74 71 Lu lutetium use 26.86 0.154 CRC 26.86 0.154 WEL 26.9 LNG 26.86 72 Hf hafnium (hexagonal) use 25.73 0.144 CRC 25.73 0.144 WEL 25.7 LNG 25.69 73 Ta tantalum use 25.36 0.140 CRC 25.36 0.140 WEL 25.4 LNG 25.40 74 W tungsten use 24.27 0.132 CRC 24.27 0.132 WEL 24.3 LNG 24.3 75 Re rhenium use 25.48 0.137 CRC 25.48 0.137 WEL 25.5 LNG 25.5 76 Os osmium use 24.7 0.130 CRC 24.7 0.130 WEL 25 LNG 24.7 77 Ir iridium use 25.10 0.131 CRC 25.10 0.131 WEL 25.1 LNG 25.06 78 Pt platinum use 25.86 0.133 CRC 25.86 0.133 WEL 25.9 79 Au gold use 25.418 0.129 CRC 25.418 0.129 WEL 25.42 LNG 25.36 80 Hg mercury (liquid) use 27.983 0.140 CRC 27.983 0.140 WEL 27.98 LNG 28.00 81 Tl thallium use 26.32 0.129 CRC 26.32 0.129 WEL 26.3 LNG 26.32 82 Pb lead use 26.650 0.129 CRC 26.650 0.129 WEL 26.4 LNG 26.84 83 Bi bismuth use 25.52 0.122 CRC 25.52 0.122 WEL 25.5 LNG 25.5 84 Po polonium use 26.4 LNG 26.4 86 Rn radon (gas) use 20.786 0.094 CRC 20.786 0.094 WEL 20.79 LNG 20.79 87 Fr francium use 31.80 LNG 31.80 89 Ac actinium use 27.2 0.120 CRC 27.2 0.120 WEL 27.2 LNG 27.2 90 Th thorium use 26.230 0.113 CRC 26.230 0.113 WEL 27.3 LNG 27.32 92 U uranium use 27.665 0.116 CRC 27.665 0.116 WEL 27.7 LNG 27.66 93 Np neptunium use 29.46 LNG 29.46 94 Pu plutonium use 35.5 LNG 35.5 95 Am americium use 62.7 LNG 62.7 == Notes == * All values refer to 25 °C and to the thermodynamically stable standard state at that temperature unless noted. {{OrganicBox complete \|wiki_name=Lysine \|image=110px\|Skeletal structure of L-lysine 130px\|3D structure of L-lysine \|name=-2,6-Diaminohexanoic acid \|C=6 \|H=14 \|N=2 \|O=2 \|mass=146.19 \|abbreviation=K, Lys \|synonyms= \|SMILES=NCCCCC(N)C(=O)O \|InChI=1/C6H14N2O2/c7-4-2-1-3-5(8)6(9)10/h5H,1-4,7-8H2,(H,9,10)/f/h9H \|CAS=56-87-1 \|DrugBank= \|EINECS=200-294-2 \|PubChem=866 (DL) , 5962 (L) \|index_of_refraction= \|abbe_number= \|dielectric_constant= \|magnetic_susceptibility= \|lambda_max= \|extinction_coefficient= \|absorption_bands= \|proton_NMR= \|carbon_NMR= \|other_NMR= \|mass_spectrometry= \|triple_point_K= \|triple_point_C= \|triple_point_Pa= \|criticle_point_K= \|criticle_point_C= \|criticle_point_Pa= \|delta_fus_H_o= \|delta_fus_S_o= \|delta_vap_H_o= \|delta_vap_S_o= \|delta_f_H_o= \|S_o_solid= \|heat_capacity_solid= \|density_solid= \|melting_point_C=224 \|melting_point_F= \|melting_point_K= \|delta_f_H_o_liquid= \|S_o_liquid= \|heat_capacity_liquid= \|density_liquid= \|viscosity_liquid= \|boiling_point_C= \|boiling_point_F= \|boiling_point_K= \|delta_f_H_o_gas= \|S_o_gas= \|heat_capacity_gas= \|viscosity_gas= \|MSDS= \|main_hazards= \|nfpa_health= \|nfpa_flammability= \|nfpa_reactivity= \|nfpa_special= \|flash_point= \|r_phrases= \|s_phrases= \|RTECS_number= \|XLogP=-2.926 \|isoelectric_point=9.74 \|disociation_constant=2.15, 9.16, 10.67 \|tautomers= \|H_bond_donor=3 \|H_bond_acceptor=4 }} ==References== # (Lysine) # (DL-Lysine) # (L-Lysine) Category:Chemical data pages Category:Chemical data pages cleanup == Heat of fusion == kJ/mol 1 H hydrogen (H2) use (H2) 0.1 CRC (H2) 0.12 LNG (H2) 0.117 WEL (per mol H atoms) 0.0585 2 He helium use 0.0138 LNG 0.0138 WEL 0.02 3 Li lithium use 3.00 CRC 3.00 LNG 3.00 WEL 3.0 4 Be beryllium use 7.895 CRC 7.895 LNG 7.895 WEL 7.95 5 B boron use 50.2 CRC 50.2 LNG 50.2 WEL 50 6 C carbon (graphite) use (graphite) 117 CRC (graphite) 117 LNG (graphite) 117 7 N nitrogen (N2) use (N2) 0.720 CRC (N2) 0.71 LNG (N2) 0.720 WEL (per mol N atoms) 0.36 8 O oxygen (O2) use (O2) 0.444 CRC (O2) 0.44 LNG (O2) 0.444 WEL (per mol O atoms) 0.222 9 F fluorine (F2) use (F2) 0.510 CRC (F2) 0.51 LNG (F2) 0.510 WEL (per mol F atoms) 0.26 10 Ne neon use 0.335 CRC 0.328 LNG 0.335 WEL 0.34 11 Na sodium use 2.60 CRC 2.60 LNG 2.60 WEL 2.60 12 Mg magnesium use 8.48 CRC 8.48 LNG 8.48 WEL 8.7 13 Al aluminium use 10.71 CRC 10.789 LNG 10.71 WEL 10.7 14 Si silicon use 50.21 CRC 50.21 LNG 50.21 WEL 50.2 15 P phosphorus use 0.66 CRC (white) 0.66 LNG 0.66 WEL 0.64 16 S sulfur use (mono) 1.727 CRC (mono) 1.72 LNG (mono) 1.727 WEL 1.73 17 Cl chlorine (Cl2) use (Cl2) 6.406 CRC (Cl2) 6.40 LNG (Cl2) 6.406 WEL (per mol Cl atoms) 3.2 18 Ar argon use 1.18 CRC 1.18 LNG 1.12 WEL 1.18 19 K potassium use 2.321 CRC 2.33 LNG 2.321 WEL 2.33 20 Ca calcium use 8.54 CRC 8.54 LNG 8.54 WEL 8.54 21 Sc scandium use 14.1 CRC 14.1 LNG 14.1 WEL 16 22 Ti titanium use 14.15 CRC 14.15 LNG 14.15 WEL 18.7 23 V vanadium use 21.5 CRC 21.5 LNG 21.5 WEL 22.8 24 Cr chromium use 21.0 CRC 21.0 LNG 21.0 WEL 20.5 25 Mn manganese use 12.91 CRC 12.91 LNG 12.9 WEL 13.2 26 Fe iron use 13.81 CRC 13.81 LNG 13.81 WEL 13.8 27 Co cobalt use 16.06 CRC 16.06 LNG 16.2 WEL 16.2 28 Ni nickel use 17.48 CRC 17.04 LNG 17.48 WEL 17.2 29 Cu copper use 13.26 CRC 12.93 LNG 13.26 WEL 13.1 30 Zn zinc use 7.32 CRC 7.068 LNG 7.32 WEL 7.35 31 Ga gallium use 5.59 CRC 5.576 LNG 5.59 WEL 5.59 32 Ge germanium use 36.94 CRC 36.94 LNG 36.94 WEL 31.8 33 As arsenic use (gray) 24.44 CRC (gray) 24.44 LNG 24.44 WEL 27.7 34 Se selenium use (gray) 6.69 CRC (gray) 6.69 LNG 6.69 WEL 5.4 35 Br bromine (Br2) use (Br2) 10.57 CRC (Br2) 10.57 LNG (Br2) 10.57 WEL (per mol Br atoms) 5.8 36 Kr krypton use 1.64 CRC 1.64 LNG 1.37 WEL 1.64 37 Rb rubidium use 2.19 CRC 2.19 LNG 2.19 WEL 2.19 38 Sr strontium use 7.43 CRC 7.43 LNG 7.43 WEL 8 39 Y yttrium use 11.42 CRC 11.4 LNG 11.42 WEL 11.4 40 Zr zirconium use 14 13.96 ± 0.36 CRC 21.00 LNG 21.00 WEL 21 41 Nb niobium use 30 CRC 30 LNG 30 WEL 26.8 42 Mo molybdenum use 37.48 CRC 37.48 LNG 37.48 WEL 36 43 Tc technetium use 33.29 CRC 33.29 LNG 33.29 WEL 23 44 Ru ruthenium use 38.59 CRC 38.59 LNG 38.59 WEL 25.7 45 Rh rhodium use 26.59 CRC 26.59 LNG 26.59 WEL 21.7 46 Pd palladium use 16.74 CRC 16.74 LNG 16.74 WEL 16.7 47 Ag silver use 11.28 CRC 11.28 LNG 11.95 WEL 11.3 48 Cd cadmium use 6.21 CRC 6.21 LNG 6.19 WEL 6.3 49 In indium use 3.281 CRC 3.281 LNG 3.28 WEL 3.26 50 Sn tin use (white) 7.03 CRC (white) 7.173 LNG (white) 7.03 WEL 7.0 51 Sb antimony use 19.79 CRC 19.79 LNG 19.87 WEL 19.7 52 Te tellurium use 17.49 CRC 17.49 LNG 17.49 WEL 17.5 53 I iodine (I2) use (I2) 15.52 CRC (I2) 15.52 LNG (I2) 150.66 [sic] WEL (per mol I atoms) 7.76 54 Xe xenon use 2.27 CRC 2.27 LNG 1.81 WEL 2.30 55 Cs caesium use 2.09 CRC 2.09 LNG 2.09 WEL 2.09 56 Ba barium use 7.12 CRC 7.12 LNG 7.12 WEL 8.0 57 La lanthanum use 6.20 CRC 6.20 LNG 6.20 WEL 6.2 58 Ce cerium use 5.46 CRC 5.46 LNG 5.46 WEL 5.5 59 Pr praseodymium use 6.89 CRC 6.89 LNG 6.89 WEL 6.9 60 Nd neodymium use 7.14 CRC 7.14 LNG 7.14 WEL 7.1 61 Pm promethium use 7.13 LNG 7.13 WEL about 7.7 62 Sm samarium use 8.62 CRC 8.62 LNG 8.62 WEL 8.6 63 Eu europium use 9.21 CRC 9.21 LNG 9.21 WEL 9.2 64 Gd gadolinium use 10.05 CRC 10.0 LNG 10.05 WEL 10.0 65 Tb terbium use 10.15 CRC 10.15 LNG 10.15 WEL 10.8 66 Dy dysprosium use 11.06 CRC 11.06 LNG 11.06 WEL 11.1 67 Ho holmium use 17.0 CRC 17.0 LNG 16.8 WEL 17.0 68 Er erbium use 19.90 CRC 19.9 LNG 19.90 WEL 19.9 69 Tm thulium use 16.84 CRC 16.84 LNG 16.84 WEL 16.8 70 Yb ytterbium use 7.66 CRC 7.66 LNG 7.66 WEL 7.7 71 Lu lutetium use ca. 22 CRC 22 LNG (22) WEL about 22 72 Hf hafnium use 27.2 CRC 27.2 LNG 27.2 WEL 25.5 73 Ta tantalum use 36.57 CRC 36.57 LNG 36.57 WEL 36 74 W tungsten use 52.31 CRC 52.31 LNG 52.31 WEL 35 75 Re rhenium use 60.43 CRC 60.43 LNG 60.43 WEL 33 76 Os osmium use 57.85 CRC 57.85 LNG 57.85 WEL 31 77 Ir iridium use 41.12 CRC 41.12 LNG 41.12 WEL 26 78 Pt platinum use 22.17 CRC 22.17 LNG 22.17 WEL 20 79 Au gold use 12.55 CRC 12.72 LNG 12.55 WEL 12.5 80 Hg mercury use 2.29 CRC 2.29 LNG 2.29 WEL 2.29 81 Tl thallium use 4.14 CRC 4.14 LNG 4.14 WEL 4.2 82 Pb lead use 4.77 CRC 4.782 LNG 4.77 WEL 4.77 83 Bi bismuth use 11.30 CRC 11.145 LNG 11.30 WEL 10.9 84 Po polonium use ca. 13 WEL about 13 85 At astatine use WEL (per mol At atoms) about 6 86 Rn radon use 3.247 LNG 3.247 WEL 3 87 Fr francium use ca. 2 WEL about 2 88 Ra radium use 8.5 LNG 8.5 WEL about 8 89 Ac actinium use 14 WEL 14 90 Th thorium use 13.81 CRC 13.81 LNG 13.81 WEL 16 91 Pa protactinium use 12.34 CRC 12.34 LNG 12.34 WEL 15 92 U uranium use 9.14 CRC 9.14 LNG 9.14 WEL 14 93 Np neptunium use 3.20 CRC 3.20 LNG 3.20 WEL 10 94 Pu plutonium use 2.82 CRC 2.82 LNG 2.82 95 Am americium use 14.39 CRC 14.39 LNG 14.39 == Notes == * Values refer to the enthalpy change between the liquid phase and the most stable solid phase at the melting point (normal, 101.325 kPa). == References == === CRC === As quoted from various sources in an online version of: * David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? ==Thermal conductivity== 1 H hydrogen use 180.5 mW/(m·K) CR2 (P=0) 186.9 mW/(m·K) LNG 0.1805 W/(m·K) WEL 0.1805 W/(m·K) 2 He helium use 151.3 mW/(m·K) CR2 (P=0) 156.7 mW/(m·K) LNG 0.1513 W/(m·K) WEL 0.1513 W/(m·K) 3 Li lithium use 84.8 W/(m·K) CRC 0.847 W/(cm·K) LNG 84.8 W/(m·K) WEL 85 W/(m·K) 4 Be beryllium use 200 W/(m·K) CRC 2.00 W/(cm·K) LNG 200 W/(m·K) WEL 190 W/(m·K) 5 B boron use 27.4 W/(m·K) LNG 27.4 W/(m·K) WEL 27 W/(m·K) 6 C carbon (graphite) use (graphite) (119-165) W/(m·K) LNG (119-165) W/(m·K) LNG (amorphous) 1.59 W/(m·K) WEL 140 W/(m·K) CRC pyrolytic graphite (parallel to the layer planes) 19.5 W/(cm·K) (perpendicular) 0.0570 W/(cm·K) 6 C carbon (diamond) use (diamond) (900-2320) W/(m·K) LNG (900-2320) W/(m·K) CRC (type I) 8.95 W/(cm·K) (type IIa) 23.0 W/(cm·K) (type IIb) 13.5 W/(cm·K) 7 N nitrogen use 25.83 mW/(m·K) CR2 26.0 mW/(m·K) LNG 0.02583 W/(m·K) WEL 0.02583 W/(m·K) 8 O oxygen use 26.58 mW/(m·K) CR2 26.3 mW/(m·K) LNG (gas) 0.02658 W/(m·K) LNG (liquid) 0.149 W/(m·K) WEL 0.02658 W/(m·K) 9 F fluorine use 27.7 mW/(m·K) LNG 0.0277 W/(m·K) WEL 0.0277 W/(m·K) 10 Ne neon use 49.1 mW/(m·K) CR2 (P=0) 49.8 mW/(m·K) LNG 0.0491 W/(m·K) WEL 0.0491 W/(m·K) 11 Na sodium use 142 W/(m·K) CRC 1.41 W/(cm·K) LNG 142 W/(m·K) WEL 140 W/(m·K) 12 Mg magnesium use 156 W/(m·K) CRC 1.56 W/(cm·K) LNG 156 W/(m·K) WEL 160 W/(m·K) 13 Al aluminium use 237 W/(m·K) CRC 2.37 W/(cm·K) LNG 237 W/(m·K) WEL 235 W/(m·K) 14 Si silicon use 149 W/(m·K) LNG 149 W/(m·K) WEL 150 W/(m·K) 15 P phosphorus use (white) 0.236 W/(m·K) LNG (white) 0.23617 W/(m·K) [sic] WEL 0.236 W/(m·K) 16 S sulfur use (amorphous) 0.205 W/(m·K) LNG (amorphous) 0.205 W/(m·K) WEL 0.205 W/(m·K) 17 Cl chlorine use 8.9 mW/(m·K) LNG 0.0089 W/(m·K) WEL 0.0089 W/(m·K) 18 Ar argon use 17.72 mW/(m·K) CR2 17.9 mW/(m·K) LNG 0.01772 W/(m·K) WEL 0.01772 W/(m·K) 19 K potassium use 102.5 W/(m·K) CRC 1.024 W/(cm·K) LNG 102.5 W/(m·K) WEL 100 W/(m·K) 20 Ca calcium use 201 W/(m·K) CRC 2.00 W/(cm·K) LNG 201 W/(m·K) WEL 200 W/(m·K) 21 Sc scandium use 15.8 W/(m·K) CRC 0.158 W/(cm·K) LNG 15.8 W/(m·K) WEL 16 W/(m·K) 22 Ti titanium use 21.9 W/(m·K) CRC 0.219 W/(cm·K) LNG 21.9 W/(m·K) WEL 22 W/(m·K) 23 V vanadium use 30.7 W/(m·K) CRC 0.307 W/(cm·K) LNG 30.7 W/(m·K) WEL 31 W/(m·K) 24 Cr chromium use 93.9 W/(m·K) CRC 0.937 W/(cm·K) LNG 93.9 W/(m·K) WEL 94 W/(m·K) 25 Mn manganese use 7.81 W/(m·K) CRC 0.0782 W/(cm·K) LNG 7.81 W/(m·K) WEL 7.8 W/(m·K) 26 Fe iron use 80.4 W/(m·K) CRC 0.802 W/(cm·K) LNG 80.4 W/(m·K) WEL 80 W/(m·K) 27 Co cobalt use 100 W/(m·K) CRC 1.00 W/(cm·K) LNG 100 W/(m·K) WEL 100 W/(m·K) 28 Ni nickel use 90.9 W/(m·K) CRC 0.907 W/(cm·K) LNG 90.9 W/(m·K) WEL 91 W/(m·K) 29 Cu copper use 401 W/(m·K) CRC 4.01 W/(cm·K) LNG 401 W/(m·K) WEL 400 W/(m·K) 30 Zn zinc use 116 W/(m·K) CRC 1.16 W/(cm·K) LNG 116 W/(m·K) WEL 120 W/(m·K) 31 Ga gallium use 40.6 W/(m·K) CRC 0.406 W/(cm·K) LNG (liquid) 29.4 W/(m·K) LNG (solid) 40.6 W/(m·K) WEL 29 W/(m·K) 32 Ge germanium use 60.2 W/(m·K) LNG 60.2 W/(m·K) WEL 60 W/(m·K) 33 As arsenic use 50.2 W/(m·K) LNG 50.2 W/(m·K) WEL 50 W/(m·K) 34 Se selenium use (amorphous) 0.519 W/(m·K) LNG (amorphous) 0.519 W/(m·K) WEL 0.52 W/(m·K) 35 Br bromine use 0.122 W/(m·K) LNG 0.122 W/(m·K) WEL 0.12 W/(m·K) 36 Kr krypton use 9.43 mW/(m·K) CR2 (P=0) 9.5 mW/(m·K) LNG 9.43 W/(m·K) [sic] WEL 0.00943 W/(m·K) 37 Rb rubidium use 58.2 W/(m·K) CRC 0.582 W/(cm·K) LNG 58.2 W/(m·K) WEL 58 W/(m·K) 38 Sr strontium use 35.4 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.4 W/(m·K) WEL 35 W/(m·K) 39 Y yttrium use 17.2 W/(m·K) CRC 0.172 W/(cm·K) LNG 17.2 W/(m·K) WEL 17 W/(m·K) 40 Zr zirconium use 22.6 W/(m·K) CRC 0.227 W/(cm·K) LNG 22.6 W/(m·K) WEL 23 W/(m·K) 41 Nb niobium use 53.7 W/(m·K) CRC 0.537 W/(cm·K) LNG 53.7 W/(m·K) WEL 54 W/(m·K) 42 Mo molybdenum use 138 W/(m·K) CRC 1.38 W/(cm·K) LNG 138 W/(m·K) WEL 139 W/(m·K) 43 Tc technetium use 50.6 W/(m·K) CRC 0.506 W/(cm·K) LNG 50.6 W/(m·K) WEL 51 W/(m·K) 44 Ru ruthenium use 117 W/(m·K) CRC 1.17 W/(cm·K) LNG 117 W/(m·K) WEL 120 W/(m·K) 45 Rh rhodium use 150 W/(m·K) CRC 1.50 W/(cm·K) LNG 150 W/(m·K) WEL 150 W/(m·K) 46 Pd palladium use 71.8 W/(m·K) CRC 0.718 W/(cm·K) LNG 71.8 W/(m·K) WEL 72 W/(m·K) 47 Ag silver use 429 W/(m·K) CRC 4.29 W/(cm·K) LNG 429 W/(m·K) WEL 430 W/(m·K) 48 Cd cadmium use 96.6 W/(m·K) CRC 0.968 W/(cm·K) LNG 96.6 W/(m·K) WEL 97 W/(m·K) 49 In indium use 81.8 W/(m·K) CRC 0.816 W/(cm·K) LNG 81.8 W/(m·K) WEL 82 W/(m·K) 50 Sn tin use 66.8 W/(m·K) CRC 0.666 W/(cm·K) LNG 66.8 W/(m·K) WEL 67 W/(m·K) 51 Sb antimony use 24.4 W/(m·K) CRC 0.243 W/(cm·K) LNG 24.4 W/(m·K) WEL 24 W/(m·K) 52 Te tellurium use (1.97-3.38) W/(m·K) LNG (1.97-3.38) W/(m·K) WEL 3 W/(m·K) 53 I iodine use 0.449 W/(m·K) CRC (300 K) 0.45 W/(m·K) LNG 449 W/(m·K) [sic] WEL 0.449 W/(m·K) 54 Xe xenon use 5.65 mW/(m·K) CR2 (P=0) 5.5 mW/(m·K) LNG 0.00565 W/(m·K) WEL 0.00565 W/(m·K) 55 Cs caesium use 35.9 W/(m·K) CRC 0.359 W/(cm·K) LNG 35.9 W/(m·K) WEL 36 W/(m·K) 56 Ba barium use 18.4 W/(m·K) CRC 0.184 W/(cm·K) LNG 18.4 W/(m·K) WEL 18 W/(m·K) 57 La lanthanum use 13.4 W/(m·K) CRC 0.134 W/(cm·K) LNG 13.4 W/(m·K) WEL 13 W/(m·K) 58 Ce cerium use 11.3 W/(m·K) CRC 0.113 W/(cm·K) LNG 11.3 W/(m·K) WEL 11 W/(m·K) 59 Pr praseodymium use 12.5 W/(m·K) CRC 0.125 W/(cm·K) LNG 12.5 W/(m·K) WEL 13 W/(m·K) 60 Nd neodymium use 16.5 W/(m·K) CRC 0.165 W/(cm·K) LNG 16.5 W/(m·K) WEL 17 W/(m·K) 61 Pm promethium use 17.9 W/(m·K) CRC (est.) 0.15 W/(cm·K) LNG 17.9 W/(m·K) WEL 15 W/(m·K) 62 Sm samarium use 13.3 W/(m·K) CRC 0.133 W/(cm·K) LNG 13.3 W/(m·K) WEL 13 W/(m·K) 63 Eu europium use (est.) 13.9 W/(m·K) CRC (est.) 0.139 W/(cm·K) LNG 13.9 W/(m·K) WEL 14 W/(m·K) 64 Gd gadolinium use 10.6 W/(m·K) (300 K) 10.6 W/(m·K) CRC (100 °C) 0.105 W/(cm·K) LNG 10.5 W/(m·K) WEL 11 W/(m·K) 65 Tb terbium use 11.1 W/(m·K) CRC 0.111 W/(cm·K) LNG 11.1 W/(m·K) WEL 11 W/(m·K) 66 Dy dysprosium use 10.7 W/(m·K) CRC 0.107 W/(cm·K) LNG 10.7 W/(m·K) WEL 11 W/(m·K) 67 Ho holmium use 16.2 W/(m·K) CRC 0.162 W/(cm·K) LNG 16.2 W/(m·K) WEL 16 W/(m·K) 68 Er erbium use 14.5 W/(m·K) CRC 0.145 W/(cm·K) LNG 14.5 W/(m·K) WEL 15 W/(m·K) 69 Tm thulium use 16.9 W/(m·K) CRC 0.169 W/(cm·K) LNG 16.9 W/(m·K) WEL 17 W/(m·K) 70 Yb ytterbium use 38.5 W/(m·K) CRC 0.385 W/(cm·K) LNG 38.5 W/(m·K) WEL 39 W/(m·K) 71 Lu lutetium use 16.4 W/(m·K) CRC 0.164 W/(cm·K) LNG 16.4 W/(m·K) WEL 16 W/(m·K) 72 Hf hafnium use 23.0 W/(m·K) CRC 0.230 W/(cm·K) LNG 23.0 W/(m·K) WEL 23 W/(m·K) 73 Ta tantalum use 57.5 W/(m·K) CRC 0.575 W/(cm·K) LNG 57.5 W/(m·K) WEL 57 W/(m·K) 74 W tungsten use 173 W/(m·K) CRC 1.74 W/(cm·K) LNG 173 W/(m·K) WEL 170 W/(m·K) 75 Re rhenium use 48.0 W/(m·K) CRC 0.479 W/(cm·K) LNG 48.0 W/(m·K) WEL 48 W/(m·K) 76 Os osmium use 87.6 W/(m·K) CRC 0.876 W/(cm·K) LNG 87.6 W/(m·K) WEL 88 W/(m·K) 77 Ir iridium use 147 W/(m·K) CRC 1.47 W/(cm·K) LNG 147 W/(m·K) WEL 150 W/(m·K) 78 Pt platinum use 71.6 W/(m·K) CRC 0.716 W/(cm·K) LNG 71.6 W/(m·K) WEL 72 W/(m·K) 79 Au gold use 318 W/(m·K) CRC 3.17 W/(cm·K) LNG 318 W/(m·K) WEL 320 W/(m·K) 80 Hg mercury use 8.30 W/(m·K) CRC 0.0834 W/(cm·K) LNG 8.30 W/(m·K) WEL 8.3 W/(m·K) 81 Tl thallium use 46.1 W/(m·K) CRC 0.461 W/(cm·K) LNG 46.1 W/(m·K) WEL 46 W/(m·K) 82 Pb lead use 35.3 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.3 W/(m·K) WEL 35 W/(m·K) 83 Bi bismuth use 7.97 W/(m·K) CRC 0.0787 W/(cm·K) LNG 7.97 W/(m·K) WEL 8 W/(m·K) 84 Po polonium use CRC 0.20 W/(cm·K) LNG 0.2 W/(m·K) 85 At astatine use 1.7 W/(m·K) LNG 1.7 W/(m·K) WEL 2 W/(m·K) 86 Rn radon use 3.61 mW/(m·K) LNG 0.00361 W/(m·K) WEL 0.00361 W/(m·K) 88 Ra radium use 18.6 W/(m·K) LNG 18.6 W/(m·K) WEL 19 W/(m·K) 89 Ac actinium use 12 W/(m·K) LNG 12 W/(m·K) WEL 12 W/(m·K) 90 Th thorium use 54.0 W/(m·K) CRC 0.540 W/(cm·K) LNG 54.0 W/(m·K) WEL 54 W/(m·K) 91 Pa protactinium use 47 W/(m·K) LNG 47 W/(m·K) WEL 47 W/(m·K) 92 U uranium use 27.5 W/(m·K) CRC 0.276 W/(cm·K) LNG 27.5 W/(m·K) WEL 27 W/(m·K) 93 Np neptunium use 6.3 W/(m·K) CRC 0.063 W/(cm·K) LNG 6.3 W/(m·K) WEL 6 W/(m·K) 94 Pu plutonium use 6.74 W/(m·K) CRC 0.0674 W/(cm·K) LNG 6.74 W/(m·K) WEL 6 W/(m·K) 95 Am americium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) 97 Bk berkelium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) ==Notes== * Ref. CRC: Values refer to 27 °C unless noted. :(d) N.B. Vargaftik, Int. J. Thermophys. 11, 467, (1990). ===LNG=== J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6; Table 6.5 Critical Properties ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; D. Ambrose, M.B. Ewing, M.L. McGlashan, Critical constants and second virial coefficients of gases (retrieved Dec 2005) ===SMI=== W.E. Forsythe (ed.), Smithsonian Physical Tables 9th ed., online version (1954; Knovel 2003). Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? :(c) O. Sifner, J. Klomfar, J. Phys. Chem. Ref. Data 23, 63, (1994). :(b) I.G. Dillon, P.A. Nelson, B.S. Swanson, J. Chem. Phys. 44, 4229, (1966). K (? °C), ? K (? °C), ? J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? Boca Raton, Florida, 2003; Section 6, Fluid Properties; Thermal Conductivity of Gases ===LNG=== As quoted from this source in an online version of: J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 4; Table 4.1, Electronic Configuration and Properties of the Elements Ho, C. Y., Powell, R. W., and Liley, P. E., J. Phys. Chem. Ref. Data 3:Suppl. 1 (1974) ===WEL=== As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. Ellis (Ed.) in Nuffield Advanced Science Book of Data, Longman, London, UK, 1972. == See also == Category:Thermodynamic properties Category:Chemical element data pages Boca Raton, Florida, 2003; Section 6, Fluid Properties; Enthalpy of Fusion === LNG === As quoted from various sources in: * J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6, Thermodynamic Properties; Table 6.4, Heats of Fusion, Vaporization, and Sublimation and Specific Heat at Various Temperatures of the Elements and Inorganic Compounds === WEL === As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. Table 259, Critical Temperatures, Pressures, and Densities of Gases == See also == Category:Phase transitions Category:Units of pressure Category:Temperature Category:Properties of chemical elements Category:Chemical element data pages J/(mol K) Heat capacity cp ? J/(mol K) Heat capacity cp ? J/(mol K) Heat capacity cp ?	2.57	0.0761	0.8185	-114.40	4.4	D
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. An average human produces about $10 \mathrm{MJ}$ of heat each day through metabolic activity. If a human body were an isolated system of mass $65 \mathrm{~kg}$ with the heat capacity of water, what temperature rise would the body experience?	The normal human body temperature is often stated as . Human body temperature varies. Normal human body temperature varies slightly from person to person and by the time of day. In humans, the average internal temperature is widely accepted to be 37 °C (98.6 °F), a "normal" temperature established in the 1800s. The normal human body temperature range is typically stated as . An individual's body temperature typically changes by about between its highest and lowest points each day. Normal human body-temperature (normothermia, euthermia) is the typical temperature range found in humans. In adults a review of the literature has found a wider range of for normal temperatures, depending on the gender and location measured. While some people think of these averages as representing normal or ideal measurements, a wide range of temperatures has been found in healthy people. The range for normal human body temperatures, taken orally, is . The typical daytime temperatures among healthy adults are as follows: * Temperature in the anus (rectum/rectal), vagina, or in the ear (tympanic) is about * Temperature in the mouth (oral) is about * Temperature under the arm (axillary) is about Generally, oral, rectal, gut, and core body temperatures, although slightly different, are well-correlated. It has been found that physically active individuals have larger changes in body temperature throughout the day. * J.V. Iribarne and W.L. Godson, Atmospheric Thermodynamics, published by D. Reidel Publishing Company, Dordrecht, Holland, 1973, 222 pages Category:Atmospheric thermodynamics Category:Atmospheric temperature This will depend on the latent heat release as: T_e \approx T + \frac{L_v}{c_{pd}} r where: * L_v : latent heat of evaporation (2400 kJ/kg at 25°C to 2600 kJ/kg at −40°C) * c_{pd} : specific heat at constant pressure for air (≈ 1004 J/(kg·K)) Tables exist for exact values of the last two coefficients. == See also == * Wet-bulb temperature * Potential temperature * Atmospheric thermodynamics * Equivalent potential temperature ==Bibliography== * M Robitzsch, Aequivalenttemperatur und Aequivalentthemometer, Meteorologische Zeitschrift, 1928, pp. 313-315. The commonly given value 98.6 °F is simply the exact conversion of the nineteenth-century German standard of 37 °C. In atmospheric science, equivalent temperature is the temperature of air in a parcel from which all the water vapor has been extracted by an adiabatic process. Rectal temperature is expected to be approximately 1 Fahrenheit (or 0.55 Celsius) degree higher than an oral temperature taken on the same person at the same time. The body temperature of a healthy person varies during the day by about with lower temperatures in the morning and higher temperatures in the late afternoon and evening, as the body's needs and activities change. The molecular-scale temperature is the defining property of the U.S. Standard Atmosphere, 1962. The heat uptake results from a persistent warming imbalance in Earth's energy budget that is most fundamentally caused by the anthropogenic increase in atmospheric greenhouse gases. Springer, Cham, 2017. 441-493. == Historical understanding == In the 19th century, most books quoted "blood heat" as 98 °F, until a study published the mean (but not the variance) of a large sample as .Inwit Publishing, Inc. and Inwit, LLC – Writings, Links and Software Demonstrations – A Fahrenheit–Celsius Activity, inwit.com Subsequently, that mean was widely quoted as "37 °C or 98.4 °F"Oxford Dictionary of English, 2010 edition, entry on "blood heat"Collins English Dictionary, 1979 edition, entry on "blood heat" until editors realized 37 °C is equal to 98.6 °F, not 98.4 °F. thumb \|upright=1.35 \|Upper ocean heat content (OHC) has been increasing because oceans have absorbed a large portion of the excess heat trapped in the atmosphere by human-caused global warming.	0.11	0.068	37.0	269	0.332	C
1.19(a) The critical constants of methane are $p_{\mathrm{c}}=45.6 \mathrm{~atm}, V_{\mathrm{c}}=98.7 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$, and $T_{\mathrm{c}}=190.6 \mathrm{~K}$. Estimate the radius of the molecules.	Methane has a boiling point of −161.5 °C at a pressure of one atmosphere. Methane's heat of combustion is 55.5 MJ/kg.Energy Content of some Combustibles (in MJ/kg) . Cooling methane at normal pressure results in the formation of methane I. However the authors stress "our findings are preliminary with regard to the methane emission strength". Note that these are all negative temperature values. thumb\|432px\|left\|Methane vapor pressure vs. temperature. Uses formula \log_{10} P_\text{mm Hg} = 6.61184 - \frac{389.93}{266.00 + T_{^\circ\text{C}}} given in Lange's Handbook of Chemistry, 10th ed. Note that formula loses accuracy near Tcrit = −82.6 °C == Spectral data == thumb\|right\|450px\|Methane infrared spectrum UV-Vis λmax ? nm Extinction coefficient, ε ? {{Chembox \| ImageFile1 = File:Tris(dimethylamino)methan Struktur.svg \| ImageSize1 = 150px \| ImageFile2 = Tris(dimethylamino)methane-3D-balls-by- AHRLS-2012.png \| ImageSize2 = 150px \| ImageFile3 = Tris(dimethylamino)methane-3D-sticks-by-AHRLS-2012.png \| ImageSize3 = 150px \| ImageAlt = \| PIN = N,N,N,N,N,N-Hexamethylmethanetriamine \| OtherNames = N,N,N,N,N,N-hexamethylmethanetriamine [bis(dimethylamino)methyl]dimethylamine \| Section1 = \| Section2 = \| Section3 = }} Tris(dimethylamino)methane (TDAM) is the simplest representative of the tris(dialkylamino)methanes of the general formula (R2N)3CH in which three of the four of methane's hydrogen atoms are replaced by dimethylamino groups (−N(CH3)2). Methane has also been detected on other planets, including Mars, which has implications for astrobiology research. ==Properties and bonding== Methane is a tetrahedral molecule with four equivalent C–H bonds. Gas d (Å) b (cmmol) V (Å) r (Å) Hydrogen 0.74611 26.61 44.19 2.02 Nitrogen 1.0975 39.13 64.98 2.25 Oxygen 1.208 31.83 52.86 2.06 Chlorine 1.988 56.22 93.36 2.39 van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Solid methane exists in several modifications. Temperatures in excess of 1200 °C are required to break the bonds of methane to produce Hydrogen gas and solid carbon. Indeed, there is no reason to assume that the van der Waals radius is a fixed property of the atom in all circumstances: rather, it tends to vary with the particular chemical environment of the atom in any given case. === Van der Waals equation of state === The van der Waals equation of state is the simplest and best-known modification of the ideal gas law to account for the behaviour of real gases: \left (p + a\left (\frac{n}{\tilde{V}}\right )^2\right ) (\tilde{V} - nb) = nRT, where is pressure, is the number of moles of the gas in question and and depend on the particular gas, \tilde{V} is the volume, is the specific gas constant on a unit mole basis and the absolute temperature; is a correction for intermolecular forces and corrects for finite atomic or molecular sizes; the value of equals the van der Waals volume per mole of the gas. The reaction is moderately endothermic as shown in the reaction equation below. : :( 74.8 kJ/mol) ==Generation== === Geological routes === left\|thumb\|upright=1.35\|Abiotic sources of methane have been found in more than 20 countries and in several deep ocean regions so far.The two main routes for geological methane generation are (i) organic (thermally generated, or thermogenic) and (ii) inorganic (abiotic). Scott Rowland and Robin Taylor re-examined these 1964 figures in the light of more recent crystallographic data: on the whole, the agreement was very good, although they recommend a value of 1.09 Å for the van der Waals radius of hydrogen as opposed to Bondi's 1.20 Å. Methane at scales of the atmosphere is commonly measured in teragrams (Tg ) or millions of metric tons (MMT ), which mean the same thing. D-166. b = 23.7 cm/mol. Helium is a monatomic gas, and each mole of helium contains atoms (the Avogadro constant, N): V_{\rm w} = {b\over{N_{\rm A}}} Therefore, the van der Waals volume of a single atom V = 39.36 Å, which corresponds to r = 2.11 Å (≈ 200 picometers). Methane is an important greenhouse gas with a global warming potential of 40 compared to (potential of 1) over a 100-year period, and above 80 over a 20-year period. At about 891 kJ/mol, methane's heat of combustion is lower than that of any other hydrocarbon, but the ratio of the heat of combustion (891 kJ/mol) to the molecular mass (16.0 g/mol, of which 12.0 g/mol is carbon) shows that methane, being the simplest hydrocarbon, produces more heat per mass unit (55.7 kJ/g) than other complex hydrocarbons. The largest reservoir of methane is under the seafloor in the form of methane clathrates. Methane is a strong GHG with a global warming potential 84 times greater than CO2 in a 20-year time frame. The positions of the hydrogen atoms are not fixed in methane I, i.e. methane molecules may rotate freely. At high pressures, such as are found on the bottom of the ocean, methane forms a solid clathrate with water, known as methane hydrate.	0.0408	0.05882352941	0.118	1260	22	C
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The enthalpy of vaporization of chloroform $\left(\mathrm{CHCl}_3\right)$ is $29.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at its normal boiling point of $334.88 \mathrm{~K}$. Calculate the entropy change of the surroundings.	The entropy of vaporization of at its boiling point has the extraordinarily high value of 136.9 J/(K·mol). It is valid for many liquids; for instance, the entropy of vaporization of toluene is 87.30 J/(K·mol), that of benzene is 89.45 J/(K·mol), and that of chloroform is 87.92 J/(K·mol). The entropy of vaporization is then equal to the heat of vaporization divided by the boiling point: : \Delta S_\text{vap} = \frac{\Delta H_\text{vap}}{T_\text{vap}}. thumb\|The Mollier enthalpy–entropy diagram for water and steam. J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? In thermodynamics, Trouton's rule states that the entropy of vaporization is almost the same value, about 85–88 J/(K·mol), for various kinds of liquids at their boiling points.Compare 85 J/(K·mol) in and 88 J/(K·mol) in The entropy of vaporization is defined as the ratio between the enthalpy of vaporization and the boiling temperature. J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? According to Trouton's rule, the entropy of vaporization (at standard pressure) of most liquids has similar values. Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? In thermodynamics, the entropy of vaporization is the increase in entropy upon vaporization of a liquid. For example, the entropies of vaporization of water, ethanol, formic acid and hydrogen fluoride are far from the predicted values. J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? The Mollier diagram coordinates are enthalpy h and humidity ratio x. J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? J/(mol·K) Solid properties Std enthalpy change of formation ΔfH ~~o~~ solid −118 kJ/mol Standard molar entropy S ~~o~~ solid ? K (? °C), ? K (? °C), ? K (? °C), ?	-87.8	0.139	1.7	1.775	6.0	A
Recent communication with the inhabitants of Neptune has revealed that they have a Celsius-type temperature scale, but based on the melting point $(0^{\circ} \mathrm{N})$ and boiling point $(100^{\circ} \mathrm{N})$ of their most common substance, hydrogen. Further communications have revealed that the Neptunians know about perfect gas behaviour and they find that, in the limit of zero pressure, the value of $p V$ is $28 \mathrm{dm}^3$ atm at $0^{\circ} \mathrm{N}$ and $40 \mathrm{dm}^3$ atm at $100^{\circ} \mathrm{N}$. What is the value of the absolute zero of temperature on their temperature scale?	Below 0.9 kelvin at their saturated vapor pressure, a mixture of the two isotopes undergoes a phase separation into a normal fluid (mostly helium-3) that floats on a denser superfluid consisting mostly of helium-4. At these low temperatures, the melting pressure of helium-3 varies from about 2.9 MPa to nearly 4.0 MPa. thumb\|0 °C = 32 °F A degree of frost is a non-standard unit of measure for air temperature meaning degrees below melting point (also known as "freezing point") of water (0 degrees Celsius or 32 degrees Fahrenheit). Its boiling point and critical point depend on which isotope of helium is present: the common isotope helium-4 or the rare isotope helium-3. Although this gives a disadvantage of non-monotonicity, in that two different temperatures can give the same pressure, the scale is otherwise robust since the melting pressure of helium-3 is insensitive to many experimental factors. == See also == * International Temperature Scale of 1990 (ITS-90) — the calibration standard used for all temperatures above 0.6 K * Leiden scale == References == Category:Temperature Category:Scales of temperature At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temperature of . The zero point energy of liquid helium is less if its atoms are less confined by their neighbors. It is based on the melting pressure of solidified helium-3. When based on Celsius, 0 degrees of frost is the same as 0 °C, and any other value is simply the negative of the Celsius temperature. At the temperature of approximately 315 mK, a minimum of pressure (2.9 MPa) occurs. Because of the very weak interatomic forces in helium, the element remains a liquid at atmospheric pressure all the way from its liquefaction point down to absolute zero. Smaller gas planets and planets closer to their star will lose atmospheric mass more quickly via hydrodynamic escape than larger planets and planets farther out.Mass-radius relationships for exoplanets, Damian C. Swift, Jon Eggert, Damien G. Hicks, Sebastien Hamel, Kyle Caspersen, Eric Schwegler, and Gilbert W. Collins A low-mass gas planet can still have a radius resembling that of a gas giant if it has the right temperature.Mass-Radius Relationships for Very Low Mass Gaseous Planets, Konstantin Batygin, David J. Stevenson, 18 Apr 2013 Neptune-like planets are considerably rarer than sub-Neptunes, despite being only slightly bigger.Superabundance of Exoplanet Sub-Neptunes Explained by Fugacity Crisis, Edwin S. Kite, Bruce Fegley Jr., Laura Schaefer, Eric B. Ford, 5 Dec 2019 This "radius cliff" separates sub-Neptunes (radius < 3 Earth radii) from Neptunes (radius > 3 Earth radii). Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. When based on Fahrenheit, 0 degrees of frost is equal to 32 °F. The business was named after the Kelvin temperature scale. The density of liquid helium-4 at its boiling point and a pressure of one atmosphere (101.3 kilopascals) is about , or about one-eighth the density of liquid water. ==Liquefaction== Helium was first liquefied on July 10, 1908, by the Dutch physicist Heike Kamerlingh Onnes at the University of Leiden in the Netherlands. The molecular-scale temperature is the defining property of the U.S. Standard Atmosphere, 1962. thumb\|upright=1.1\|Artist's conception of a mini-Neptune or "gas dwarf" A Mini- Neptune (sometimes known as a gas dwarf or transitional planet) is a planet less massive than Neptune but resembling Neptune in that it has a thick hydrogen–helium atmosphere, probably with deep layers of ice, rock or liquid oceans (made of water, ammonia, a mixture of both, or heavier volatiles). Important early work on the characteristics of liquid helium was done by the Soviet physicist Lev Landau, later extended by the American physicist Richard Feynman. ==Data== Properties of liquid helium Helium-4 Helium-3 Critical temperature Boiling point at one atmosphere Minimum melting pressure at Superfluid transition temperature at saturated vapor pressure 1 mK in the absence of a magnetic field ==Gallery== File:Liquid Helium.jpg\|Liquid helium (in a vacuum bottle) at and boiling slowly. See the table below for the values of these physical quantities. The Provisional Low Temperature Scale of 2000 (PLTS-2000) is an equipment calibration standard for making measurements of very low temperatures, in the range of 0.9 mK (millikelvin) to 1 K, adopted by the International Committee for Weights and Measures in October 2000. Liquid helium can be solidified only under very low temperatures and high pressures.	135.36	4943	2283.63	-233	47	D
A gas at $250 \mathrm{~K}$ and $15 \mathrm{~atm}$ has a molar volume 12 per cent smaller than that calculated from the perfect gas law. Calculate the compression factor under these conditions.	For an ideal gas the compressibility factor is Z=1 per definition. In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. The compressibility factor is defined in thermodynamics and engineering frequently as: :Z = \frac{p}{\rho R_\text{specific} T}, where p is the pressure, \rho is the density of the gas and R_\text{specific} = \frac{R}{M} is the specific gas constant, page 327 M being the molar mass, and the T is the absolute temperature (kelvin or Rankine scale). Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts that plot Z as a function of pressure at constant temperature. The compression ratio is the ratio between the volume of the cylinder and combustion chamber in an internal combustion engine at their maximum and minimum values. Experimental values for the compressibility factor confirm this. For example, methyl chloride, a highly polar molecule and therefore with significant intermolecular forces, the experimental value for the compressibility factor is Z=0.9152 at a pressure of 10 atm and temperature of 100 °C. page 3-268 For air (small non-polar molecules) at approximately the same conditions, the compressibility factor is only Z=1.0025 (see table below for 10 bars, 400 K). ===Compressibility of air=== Normal air comprises in crude numbers 80 percent nitrogen and 20 percent oxygen . Compression ratio is a ratio of volumes. Figure 2 is an example of a generalized compressibility factor graph derived from hundreds of experimental PVT data points of 10 pure gases, namely methane, ethane, ethylene, propane, n-butane, i-pentane, n-hexane, nitrogen, carbon dioxide and steam. The compressibility factor should not be confused with the compressibility (also known as coefficient of compressibility or isothermal compressibility) of a material, which is the measure of the relative volume change of a fluid or solid in response to a pressure change. ==Definition and physical significance== thumb\|A graphical representation of the behavior of gases and how that behavior relates to compressibility factor. As for the compressibility of gases, the principle of corresponding states indicates that any pure gas at the same reduced temperature, T_r, and reduced pressure, P_r, should have the same compressibility factor. The closer the gas is to its critical point or its boiling point, the more Z deviates from the ideal case. === Fugacity === The compressibility factor is linked to the fugacity by the relation: : f = P \exp\left(\int \frac{Z-1}{P} dP\right) ==Generalized compressibility factor graphs for pure gases== thumb\|400px\|Generalized compressibility factor diagram. There are more detailed generalized compressibility factor graphs based on as many as 25 or more different pure gases, such as the Nelson-Obert graphs. * Real Gases includes a discussion of compressibility factors. For a gas that is a mixture of two or more pure gases (air or natural gas, for example), the gas composition must be known before compressibility can be calculated. Above the Boyle temperature, the compressibility factor is always greater than unity and increases slowly but steadily as pressure increases. ==Experimental values== It is extremely difficult to generalize at what pressures or temperatures the deviation from the ideal gas becomes important. The reduced specific volume is defined by, : u_R = \frac{ u_\text{actual}}{RT_\text{cr}/P_\text{cr}} where u_\text{actual} is the specific volume. page 140 Once two of the three reduced properties are found, the compressibility chart can be used. The dynamic compression ratio accounts for these factors. In order to obtain a generalized graph that can be used for many different gases, the reduced pressure and temperature, P_r and T_r, are used to normalize the compressibility factor data. The quantum gases hydrogen, helium, and neon do not conform to the corresponding-states behavior and the reduced pressure and temperature for those three gases should be redefined in the following manner to improve the accuracy of predicting their compressibility factors when using the generalized graphs: : T_r = \frac{T}{T_c + 8} and P_r = \frac{P}{P_c + 8} where the temperatures are in kelvins and the pressures are in atmospheres. ==Reading a generalized compressibility chart== In order to read a compressibility chart, the reduced pressure and temperature must be known. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document) In general, deviation from ideal behaviour becomes more significant the closer a gas is to a phase change, the lower the temperature or the larger the pressure. Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound- specific empirical constants as input.	0.5117	10	0.88	-6.04697	7.25	C
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Suppose that $3.0 \mathrm{mmol} \mathrm{N}_2$ (g) occupies $36 \mathrm{~cm}^3$ at $300 \mathrm{~K}$ and expands to $60 \mathrm{~cm}^3$. Calculate $\Delta G$ for the process.	The value of ΔL must however be taken from the relevant cartridge data information in the C.I.P. Tables. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . We have : \Delta U = \sum U_{products} - \sum U_{reactants} This also signifies that the amount of heat absorbed at constant volume could be identified with the change in the thermodynamic quantity internal energy. In geochemistry, hydrology, paleoclimatology and paleoceanography, δ15N (pronounced "delta fifteen n") or delta-N-15 is a measure of the ratio of the two stable isotopes of nitrogen, 15N:14N. ==Formulas== Two very similar expressions for are in wide use in hydrology. The delta L problem (ΔL problem) refers to certain firearm chambers and the incompatibility of some ammunition made for that chamber. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other exactly defined physical constants. ==Specific gas constant== Rspecific for dry air Unit 287.052874 J⋅kg−1⋅K−1 53.3523 ft⋅lbf⋅lb−1⋅°R−1 1,716.46 ft⋅lbf⋅slug−1⋅°R−1 The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture. Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. ==References== ==External links== * Ideal gas calculator – Ideal gas calculator provides the correct information for the moles of gas involved. Instead of a mole the constant can be expressed by considering the normal cubic meter. Firearms users that have to rely on their weapon under adverse conditions, such as big five and other dangerous game hunters, obviously have to check the correct functioning of the firearm and ammunition they intend to use before exposing themselves to potentially dangerous situations. ==Delta L (ΔL) problem== The length specification "S" is a basic dimension (or a datum reference) for the computation of the dimensions of firearms cartridges and chambers. The enthalpy of formation of one mole of ethane gas refers to the reaction 2 C (graphite) + 3 H2 (g) → C2H6 (g). In general the first law requires that : Q = \Delta U + W (work) If W is only pressure–volume work, then at constant pressure : Q_P = \Delta U + P \Delta V Assuming that the change in state variables is due solely to a chemical reaction, we have : Q_P = \sum U_{products} - \sum U_{reactants} + P \left(\sum V_{products} - \sum V_{reactants}\right) : Q_P = \sum \left(U_{products} + P V_{products} \right) - \sum \left(U_{reactants} + P V_{reactants} \right) As enthalpy or heat content is defined by H = U + PV , we have : Q_P = \sum H_{products} - \sum H_{reactants} = \Delta H By convention, the enthalpy of each element in its standard state is assigned a value of zero. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . When only expansion work is possible for a process we have \Delta U = Q_V; this implies that the heat of reaction at constant volume is equal to the change in the internal energy \Delta U of the reacting system. Value of R Unit SI units J⋅K−1⋅mol−1 m3⋅Pa⋅K−1⋅mol−1 kg⋅m2⋅s−2⋅K−1⋅mol−1 Other common units L⋅Pa⋅K−1⋅mol−1 L⋅kPa⋅K−1⋅mol−1 L⋅bar⋅K−1⋅mol−1 erg⋅K−1⋅mol−1 atm⋅ft3⋅lbmol−1⋅°R−1 psi⋅ft3⋅lbmol−1⋅°R−1 BTU⋅lbmol−1⋅°R−1 inH2O⋅ft3⋅lbmol−1⋅°R−1 torr⋅ft3⋅lbmol−1⋅°R−1 L⋅atm⋅K−1⋅mol−1 L⋅Torr⋅K−1⋅mol−1 cal⋅K−1⋅mol−1 m3⋅atm⋅K−1⋅mol−1 The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . Since the atmosphere is 99.6337% 14N and 0.3663% 15N, a is 0.003663 in the former case and 0.003663/0.996337 = 0.003676 in the latter. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in). == Heat of vaporization == kJ/mol 1 H hydrogen (H2) use (H2) 0.904 CRC (H2) 0.90 LNG 0.904 2 He helium use 0.0829 CRC 0.08 LNG 0.0829 WEL 0.083 3 Li lithium use 136 LNG 147.1 WEL 147 Zhang et al. 136 4 Be beryllium use 292 LNG 297 WEL 297 Zhang et al. 292 5 B boron use 508 CRC 480 LNG 480 WEL 507 Zhang et al. 508 6 C carbon use WEL (sublimation) 715 7 N nitrogen (N2) use (N2) 5.57 CRC (N2) 5.57 LNG (N2) 5.577 WEL (per mole N atoms) 2.79 Zhang et al. 5.58 8 O oxygen (O2) use (O2) 6.82 CRC (O2) 6.82 LNG (O2) 6.820 WEL (per mole O atoms) 3.41 Zhang et al. 6.82 9 F fluorine (F2) use (F2) 6.62 CRC (F2) 6.62 LNG (F2) 6.62 WEL (per mole F atoms) 3.27 Zhang et al. 6.32 10 Ne neon use 1.71 CRC 1.71 LNG 1.71 WEL 1.75 Zhang et al. 1.9 11 Na sodium use 97.42 LNG 97.42 WEL 97.7 Zhang et al. 97.4 12 Mg magnesium use 128 LNG 128 WEL 128 Zhang et al. 132 13 Al aluminium use 284 CRC 294 LNG 294.0 WEL 293 Zhang et al. 284 14 Si silicon use 359 LNG 359 WEL 359 Zhang et al. 383 15 P phosphorus use 12.4 CRC 12.4 LNG 12.4 WEL 12.4 Zhang et al. 51.9 (white) 16 S sulfur use (mono) 45 CRC 45 LNG (mono) 45 WEL 9.8 Zhang et al. 45 17 Cl chlorine (Cl2) use (Cl2) 20.41 CRC (Cl2) 20.41 LNG (Cl2) 20.41 WEL (per mole Cl atoms) 10.2 Zhang et al. 20.4 18 Ar argon use 6.53 CRC 6.43 LNG 6.43 WEL 6.5 Zhang et al. 6.53 19 K potassium use 76.90 LNG 76.90 WEL 76.9 Zhang et al. 79.1 20 Ca calcium use 154.7 LNG 154.7 WEL 155 Zhang et al. 153 21 Sc scandium use 332.7 LNG 332.7 WEL 318 Zhang et al. 310 22 Ti titanium use 425 LNG 425 WEL 425 Zhang et al. 427 23 V vanadium use 444 LNG 459 WEL 453 Zhang et al. 451 24 Cr chromium use 339.5 LNG 339.5 WEL 339 Zhang et al. 347 25 Mn manganese use 221 LNG 221 WEL 220 Zhang et al. 225 26 Fe iron use 340 LNG 340 WEL 347 Zhang et al. 354 27 Co cobalt use 377 LNG 377 WEL 375 Zhang et al. 390 28 Ni nickel use 379 LNG 377.5 WEL 378 Zhang et al. 379 29 Cu copper use 300.4 LNG 300.4 WEL 300 Zhang et al. 305 30 Zn zinc use 115 LNG 123.6 WEL 119 Zhang et al. 115 31 Ga gallium use 256 CRC 254 LNG 254 WEL 256 Zhang et al. 256 32 Ge germanium use 334 CRC 334 LNG 334 WEL 334 Zhang et al. 330 33 As arsenic use 32.4 WEL 32.4 (sublimation) Zhang et al. 32.4 34 Se selenium use 95.48 CRC 95.48 LNG 95.48 WEL 26 Zhang et al. 95.5 35 Br bromine (Br2) use (Br2) 29.96 CRC (Br2) 29.96 LNG (Br2) 29.96 WEL (per mole Br atoms) 14.8 Zhang et al. 30 36 Kr krypton use 9.08 CRC 9.08 LNG 9.08 WEL 9.02 Zhang et al. 9.03 37 Rb rubidium use 75.77 LNG 75.77 WEL 72 Zhang et al. 69 38 Sr strontium use 141 LNG 136.9 WEL 137 Zhang et al. 141 39 Y yttrium use 390 LNG 365 WEL 380 Zhang et al. 363 40 Zr zirconium use 573 LNG 573 WEL 580 Zhang et al. 591 41 Nb niobium use 689.9 LNG 689.9 WEL 690 Zhang et al. 682 42 Mo molybdenum use 617 LNG 617 WEL 600 Zhang et al. 617 43 Tc technetium use 585.2 LNG 585.2 WEL 550 44 Ru ruthenium use 619 LNG 591.6 WEL 580 Zhang et al. 619 45 Rh rhodium use 494 LNG 494 WEL 495 Zhang et al. 493 46 Pd palladium use 358 LNG 362 WEL 380 Zhang et al. 358 47 Ag silver use 254 LNG 258 WEL 255 Zhang et al. 254 48 Cd cadmium use 99.87 CRC 99.87 LNG 99.9 WEL 100 Zhang et al. 100 49 In indium use 231.8 LNG 231.8 WEL 230 Zhang et al. 225 50 Sn tin use (white) 296.1 LNG (white) 296.1 WEL 290 Zhang et al. 296 51 Sb antimony use 193.43 LNG 193.43 WEL 68 Zhang et al. 193 52 Te tellurium use 114.1 CRC 114.1 LNG 114.1 WEL 48 Zhang et al. 114 53 I iodine (I2) use (I2) 41.57 CRC (I2) 41.57 LNG (I2) 41.6 WEL (per mole I atoms) 20.9 Zhang et al. 41.6 54 Xe xenon use 12.64 CRC 12.57 LNG 12.64 WEL 12.64 Zhang et al. 12.6 55 Cs caesium use 63.9 LNG 63.9 WEL 65 Zhang et al. 66.1 56 Ba barium use 140.3 CRC 140 LNG 140.3 WEL 140 Zhang et al. 142 57 La lanthanum use 400 LNG 402.1 WEL 400 Zhang et al. 400 58 Ce cerium use 398 LNG 398 WEL 350 Zhang et al. 398 59 Pr praseodymium use 331 LNG 331 WEL 330 Zhang et al. 331 60 Nd neodymium use 289 LNG 289 WEL 285 Zhang et al. 289 61 Pm promethium use 289 LNG 289 WEL 290 62 Sm samarium use 192 LNG 165 WEL 175 Zhang et al. 192 63 Eu europium use 176 LNG 176 WEL 175 Zhang et al. 176 64 Gd gadolinium use 301.3 LNG 301.3 WEL 305 Zhang et al. 301 65 Tb terbium use 391 LNG 293 WEL 295 Zhang et al. 391 66 Dy dysprosium use 280 LNG 280 WEL 280 Zhang et al. 280 67 Ho holmium use 251 LNG 71 WEL 265 Zhang et al. 251 68 Er erbium use 280 LNG 280 WEL 285 Zhang et al. 280 69 Tm thulium use 191 LNG 247 WEL 250 Zhang et al. 191 70 Yb ytterbium use 129 LNG 159 WEL 160 Zhang et al. 129 71 Lu lutetium use 414 LNG 414 WEL 415 Zhang et al. 414 72 Hf hafnium use 648 LNG 571 WEL 630 Zhang et al. 648 73 Ta tantalum use 732.8 LNG 732.8 WEL 735 Zhang et al. 753 74 W tungsten use 806.7 LNG 806.7 WEL 800 Zhang et al. 774 75 Re rhenium use 704 LNG 704 WEL 705 Zhang et al. 707 76 Os osmium use 678 LNG 738 WEL 630 Zhang et al. 678 77 Ir iridium use 564 LNG 231.8 WEL 560 Zhang et al. 564 78 Pt platinum use 510 LNG 469 WEL 490 Zhang et al. 510 79 Au gold use 342 CRC 324 LNG 324 WEL 330 Zhang et al. 342 80 Hg mercury use 59.11 CRC 59.11 LNG 59.1 WEL 59.2 Zhang et al. 58.2 81 Tl thallium use 165 LNG 165 WEL 165 Zhang et al. 162 82 Pb lead use 179.5 CRC 179.5 LNG 179.5 WEL 178 Zhang et al. 177 83 Bi bismuth use 179 CRC 151 LNG 151 WEL 160 Zhang et al. 179 84 Po polonium use 102.91 LNG 102.91 WEL about 100 85 At astatine use 54.39 (At2) GME 54.39 (At2) WEL about 40 86 Rn radon use 18.10 LNG 18.10 WEL 17 87 Fr francium use ca. 65 WEL about 65 88 Ra radium use 113 LNG 113 WEL about 125 89 Ac actinium use 400 WEL 400 90 Th thorium use 514 LNG 514 WEL 530 91 Pa protactinium use 481 LNG 481 WEL 470 92 U uranium use 417.1 LNG 417.1 WEL 420 93 Np neptunium use 336 LNG 336 WEL 335 94 Pu plutonium use 333.5 LNG 333.5 WEL 325 == Notes == * Values refer to the enthalpy change in the conversion of liquid to gas at the boiling point (normal, 101.325 kPa). == References == ===Zhang et al.=== ===CRC=== As quoted from various sources in an online version of: * David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 84th Edition. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB): R = N_{\rm A} k. For this reason it is important to note which standard concentration value is being used when consulting tables of enthalpies of formation. ==Introduction== Two initial thermodynamic systems, each isolated in their separate states of internal thermodynamic equilibrium, can, by a thermodynamic operation, be coalesced into a single new final isolated thermodynamic system. The standard enthalpy of reaction (denoted \Delta_{\text {rxn}} H^\ominus or \Delta H_{\text {reaction}}^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states.	257	0.0761	0.082	13	-3.8	E
1.18(a) A vessel of volume $22.4 \mathrm{dm}^3$ contains $2.0 \mathrm{~mol} \mathrm{H}_2$ and $1.0 \mathrm{~mol} \mathrm{~N}_2$ at $273.15 \mathrm{~K}$. Calculate their total pressure.	With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with :\text{pressure} = \text{weight density} \times \text{depth}. The exact formula varies with the tank shape but depends on the density, ρ, and maximum allowable stress σ of the material in addition to the pressure P and volume V of the vessel. * IS 2825–1969 (RE1977)_code_unfired_Pressure_vessels. New York:McGraw-Hill, , pg 108 thumb\|300px\|Stress in the cylinder body of a pressure vessel. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. Flows with a higher Mach number M cannot approximate the total pressure using the incompressible formula given above. * P_0 is the pressure at the surface. * \rho(z) is the density of the material above the depth z. * g is the gravity acceleration in m/s^2 . upright=1.4\|thumb\|A welded steel pressure vessel constructed as a horizontal cylinder with domed ends. Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. Then we have :\text{pressure} = \frac{\text{force}}{\text{area}} = \frac{\text{weight}}{\text{area}} = \frac{\text{weight density} \times \text{volume}}{\text{area}}, :\text{pressure} = \frac{\text{weight density} \times \text{(area} \times \text{depth)}}{\text{area}}. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation , where g is the gravitational acceleration. Pressure is related to energy density and may be expressed in units such as joules per cubic metre (J/m3, which is equal to Pa). Derivation of this equation This is derived from the definitions of pressure and weight density. PV Publishing, Inc. Oklahoma City, OK ==Further reading== * Megyesy, Eugene F. (2008, 14th ed.) Pressure Vessel Handbook. For a cylinder with hemispherical ends, :M = 2 \pi R^2 (R + W) P {\rho \over \sigma}, where R is the Radius (m) W is the middle cylinder width only, and the overall width is W + 2R (m) ====Cylindrical vessel with semi-elliptical ends==== In a vessel with an aspect ratio of middle cylinder width to radius of 2:1, :M = 6 \pi R^3 P {\rho \over \sigma}. ====Gas storage==== In looking at the first equation, the factor PV, in SI units, is in units of (pressurization) energy. Hydraulic (filled with water) testing pressure is usually 50% higher than the working pressure. ==== Vessel thread ==== Until 1990, high pressure cylinders were produced with conical (tapered) threads. The pressure coefficient is used in aerodynamics and hydrodynamics. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. * EN 286 (Parts 1 to 4): European standard for simple pressure vessels (air tanks), harmonized with Council Directive 87/404/EEC. Further the volume of the gas is (4πr3)/3. Almost all pressure vessel design standards contain variations of these two formulas with additional empirical terms to account for variation of stresses across thickness, quality control of welds and in-service corrosion allowances. Pressure is a scalar quantity.	3930	0.21	524.0	3.0	-131.1	D
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the total change in entropy, when a sample of nitrogen gas of mass $14 \mathrm{~g}$ at $298 \mathrm{~K}$ and $1.00 \mathrm{bar}$ doubles its volume in an adiabatic reversible expansion.	After the removal of the partition, the n_i = nx_i moles of component i may explore the combined volume V\,, which causes an entropy increase equal to nx_i R \ln(V/V_i) = - nR x_i \ln x_i for each component gas. However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. In this case, the increase in entropy is entirely due to the irreversible processes of expansion of the two gases, and involves no heat or work flow between the system and its surroundings. ===Gibbs free energy of mixing=== The Gibbs free energy change \Delta G_\text{mix} = \Delta H_\text{mix} - T\Delta S_\text{mix} determines whether mixing at constant (absolute) temperature T and pressure p is a spontaneous process. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absorbed in any changes between different crystal structures). It states that the entropy of such "mixing" of perfect gases is zero. ====Mixing at constant total volume and changing partial volumes, with mechanically controlled varying pressure, and constant temperature==== An experimental demonstration may be considered. Upon removal of the dividing partition, they expand into a final common volume (the sum of the two initial volumes), and the entropy of mixing \Delta S_{mix} is given by :\Delta S_{mix} = -nR(x_1\ln x_1 + x_2\ln x_2)\,. where R is the gas constant, n the total number of moles and x_i the mole fraction of component i\,, which initially occupies volume V_i = x_iV\,. The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . We can use Boltzmann's equation for the entropy change as applied to the mixing process :\Delta S_\text{mix}= k_\text{B} \ln\Omega where k_\text{B} is the Boltzmann constant. According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings: :(\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings})>0 Molar entropy is not the same for all gases. The lowest value is when the mole fraction is 0.5 for a mixture of two components, or 1/n for a mixture of n components. thumb\|The entropy of mixing for an ideal solution of two species is maximized when the mole fraction of each species is 0.5. ==Solutions and temperature dependence of miscibility== ===Ideal and regular solutions=== The above equation for the entropy of mixing of ideal gases is valid also for certain liquid (or solid) solutions—those formed by completely random mixing so that the components move independently in the total volume. This quantity combines two physical effects—the enthalpy of mixing, which is a measure of the energy change, and the entropy of mixing considered here. For ideal gases, the entropy of mixing at prescribed common temperature and pressure has nothing to do with mixing in the sense of intermingling and interactions of molecular species, but is only to do with expansion into the common volume.Bailyn, M. (1994). A version of Statistical Mechanics for Students of Physics and Chemistry, Cambridge University Press, Cambridge UK, pages 163-164 the conflating of the just-mentioned two mechanisms for the entropy of mixing is well established in customary terminology, but can be confusing unless it is borne in mind that the independent variables are the common initial and final temperature and total pressure; if the respective partial pressures or the total volume are chosen as independent variables instead of the total pressure, the description is different. ====Mixing with each gas kept at constant partial volume, with changing total volume==== In contrast to the established customary usage, "mixing" might be conducted reversibly at constant volume for each of two fixed masses of gases of equal volume, being mixed by gradually merging their initially separate volumes by use of two ideal semipermeable membranes, each permeable only to one of the respective gases, so that the respective volumes available to each gas remain constant during the merge. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. The entropy of vaporization is then equal to the heat of vaporization divided by the boiling point: : \Delta S_\text{vap} = \frac{\Delta H_\text{vap}}{T_\text{vap}}. We again obtain the entropy of mixing on multiplying by the Boltzmann constant k_\text{B}.	+4.1	9.73	0.0	7.136	-1.46	C
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. Concerns over the harmful effects of chlorofluorocarbons on stratospheric ozone have motivated a search for new refrigerants. One such alternative is 2,2-dichloro-1,1,1-trifluoroethane (refrigerant 123). Younglove and McLinden published a compendium of thermophysical properties of this substance (J. Phys. Chem. Ref. Data 23, 7 (1994)), from which properties such as the Joule-Thomson coefficient $\mu$ can be computed. Compute the temperature change that would accompany adiabatic expansion of $2.0 \mathrm{~mol}$ of this refrigerant from $1.5 \mathrm{bar}$ to 0.5 bar at $50^{\circ} \mathrm{C}$.	Note the trend of the CClF2-X series in the table below. ==Ozone depleting potential of common compounds== Compound R No. ODP Trichlorofluoromethane (CCl3F) R-11 1.00 1,1,1,2-Tetrafluoroethane (CF3-CH2F) R-134a 0.000015 Chlorodifluoromethane (CClF2-H) R-22 0.05 Chlorotrifluoromethane (CClF2-F) R-13 1.00 Dichlorodifluoromethane (CClF2-Cl) R-12 1.00 Bromochlorodifluoromethane (CClF2-Br) R-12B1 7.9 Carbon tetrachloride (CCl4) R-10 0.82 Nitrous oxide (N2O) R-744A 0.017 Alkanes (Propane, Isobutane, etc.) 0 Ammonia (NH3) R-717 0 Carbon dioxide (CO2) R-744 0 Nitrogen (N2) R-728 0 ==References== ==External links== * List of ozone depleting substances with their ODPs * Scientific Assessment of Ozone Depletion: 1991 Category:Ozone depletion Property Value Ozone depletion potential (ODP) 0.44 (CCl3F = 1) Global warming potential (GWP: 100-year) 5,860 \- 7,670 (CO2 = 1) Atmospheric lifetime 1,020 \- 1,700 years == See also == * IPCC list of greenhouse gases * List of refrigerants == References == Category:Ozone depletion Category:Greenhouse gases Category:Refrigerants Category:Chlorofluorocarbons 1,1,1,2-Tetrafluoroethane (also known as norflurane (INN), R-134a, Klea®134a, Freon 134a, Forane 134a, Genetron 134a, Green Gas, Florasol 134a, Suva 134a, or HFC-134a) is a hydrofluorocarbon (HFC) and haloalkane refrigerant with thermodynamic properties similar to R-12 (dichlorodifluoromethane) but with insignificant ozone depletion potential and a lower 100-year global warming potential (1,430, compared to R-12's GWP of 10,900). Even though 1,1,1,2-Tetrafluoroethane has insignificant ozone depletion potential (ozone layer) and negligible acidification potential (acid rain), it has a 100-year global warming potential (GWP) of 1430 and an approximate atmospheric lifetime of 14 years. ==The Physical Properties of Greenhouse Gases== Gas Alternate Name Formula 1998 Level Increase since 1750 Radiative forcing (Wm−2) Specific heat at STP (J kg−1) Carbon dioxide (CO2) 365ppm 87 ppm 1.46 819 Methane (CH4) 1,745ppb 1,045ppb 0.48 2191 Nitrous oxide (N2O) 314ppb 44ppb 0.15 880 Tetrafluoromethane Carbon tetrafluoride (CF4) 80ppt 40ppt 0.003 1330 Hexafluoroethane (C2F6) 3 ppt 3ppt 0.001 Sulfur hexafluoride (SF6) 4.2ppt 4.2ppt 0.002 HFC-23* Trifluoromethane (CHF3) 14ppt 14ppt 0.002 HFC-134a* 1,1,1,2-tetrafluoroethane (C2H2F4) 7.5ppt 7.5ppt 0.001 HFC-152a* 1,1-Difluoroethane (C2H4F2) 0.5ppt 0.5ppt 0.000 Water vapour (H2O(G)) 2000 Category:Greenhouse gases Retrieved 21 August 2011. == History and environmental impacts == 1,1,1,2-Tetrafluoroethane was introduced in the early 1990s as a replacement for dichlorodifluoromethane (R-12), which has massive ozone depleting properties. Hydrochlorofluorocarbons have ODPs mostly in range 0.005 - 0.2 due to the presence of the hydrogen which causes them to react readily in the troposphere, therefore reducing their chance to reach the stratosphere where the ozone layer is present. This colorless gas is of interest as a more environmentally friendly (lower GWP; global warming potential) refrigerant in air conditioners. Some of the properties of cyclic ozone have been predicted theoretically. A phaseout and transition to HFO-1234yf and other refrigerants, with GWPs similar to CO2, began in 2012 within the automotive market. == Uses == 1,1,1,2-Tetrafluoroethane is a non-flammable gas used primarily as a "high-temperature" refrigerant for domestic refrigeration and automobile air conditioners. It should have more energy than ordinary ozone. Chloropentafluoroethane is a chlorofluorocarbon (CFC) once used as a refrigerant and also known as R-115 and CFC-115. It has been speculated that, if cyclic ozone could be made in bulk, and if it proved to have good stability properties, it could be added to liquid oxygen to improve the specific impulse of rocket fuel. Chlorofluorocarbons have ODPs roughly equal to 1. The Society of Automotive Engineers (SAE) has proposed that it be best replaced by a new fluorochemical refrigerant HFO-1234yf (CFCF=CH) in automobile air-conditioning systems.HFO-1234yf A Low GWP Refrigerant For MAC . It was defined as a measure of destructive effects of a substance compared to a reference substance.Ozone-Depletion and Chlorine- Loading Potential of Chlorofluorocarbon Alternatives Precisely, ODP of a given substance is defined as the ratio of global loss of ozone due to the given substance to the global loss of ozone due to CFC-11 of the same mass. It has the formula CFCHF and a boiling point of −26.3 °C (−15.34 °F) at atmospheric pressure. Currently, the possibility of cyclic ozone is confirmed within diverse theoretical approaches. ==References== ==External links== * Category:Allotropes of oxygen Category:Hypothetical chemical compounds Category:Three-membered rings Category:Homonuclear triatomic molecules The ozone depletion potential (ODP) of a chemical compound is the relative amount of degradation to the ozone layer it can cause, with trichlorofluoromethane (R-11 or CFC-11) being fixed at an ODP of 1.0. It would differ from ordinary ozone in how those three oxygen atoms are arranged. It has also been studied as a potential inhalational anesthetic, but it is nonanaesthetic at doses used in inhalers. == See also == * List of refrigerants * Tetrabromoethane * Tetrachloroethane == References == == External links == * * European Fluorocarbons Technical Committee (EFCTC) * MSDS at Oxford University * Concise International Chemical Assessment Document 11, at inchem.org * Pressure temperature calculator * * R134a 2 phase computer cooling Category:Fluoroalkanes Category:Refrigerants Category:Automotive chemicals Category:Propellants Category:Airsoft Category:Excipients Category:Greenhouse gases Category:GABAA receptor positive allosteric modulators Category:General anesthetics The ozone depletion potential increases with the heavier halogens since the C-X bond strength is lower.	0.23	-2.99	10.7598	1.1	0.2115	B
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the Carnot efficiency of a modern steam turbine that operates with steam at $300^{\circ} \mathrm{C}$ and discharges at $80^{\circ} \mathrm{C}$.	Latest generation gas turbine engines have achieved an efficiency of 46% in simple cycle and 61% when used in combined cycle. ==External combustion engines== ===Steam engine=== ::See also: Steam engine#Efficiency ::See also: Timeline of steam power ====Piston engine==== Steam engines and turbines operate on the Rankine cycle which has a maximum Carnot efficiency of 63% for practical engines, with steam turbine power plants able to achieve efficiency in the mid 40% range. The thermal efficiency of modern steam turbine plants with reheat cycles can reach 47%, and in combined cycle plants, in which a steam turbine is powered by exhaust heat from a gas turbine, it can approach 60%. Thermal engineering by Rathore and Mahesh; Tata McGraw Hill publications. ==Further reading== Basic concepts in Turbo machinery by Ingarm. * http://www.turbinesinfo.com/steam-turbine-efficiency. * http://www.physicsforums.com › Physics › General Physics/ * https://web.archive.org/web/20150219211612/http://www.techloud.net/2012/04/losses- in-steam-turbines.html * http://www.learnthermo.com/examples/ch05/p-5c-2.php Category:Steam turbines Its theoretical efficiency depends on the compression ratio r of the engine and the specific heat ratio γ of the gas in the combustion chamber. \eta_{\rm th} = 1 - \frac{1}{r^{\gamma-1}} Thus, the efficiency increases with the compression ratio. The efficiency of steam engines is primarily related to the steam temperature and pressure and the number of stages or expansions. So, for a boiler that produces 210 kW (or 700,000 BTU/h) output for each 300 kW (or 1,000,000 BTU/h) heat-equivalent input, its thermal efficiency is 210/300 = 0.70, or 70%. See graph:Steam Engine Efficiency In earliest steam engines the boiler was considered part of the engine. As is the case with the gas turbine, the steam turbine works most efficiently at full power, and poorly at slower speeds. The efficiency depends largely on the ratio of the pressure inside the combustion chamber p2 to the pressure outside p1 \eta_{\rm th} = 1 - \left(\frac{p_2}{p_1}\right)^\frac{1-\gamma}{\gamma} ===Other inefficiencies=== One should not confuse thermal efficiency with other efficiencies that are used when discussing engines. In a combined cycle plant, thermal efficiencies approach 60%.GE Power’s H Series Turbine Such a real-world value may be used as a figure of merit for the device. One other factor negatively affecting the gas turbine efficiency is the ambient air temperature. Steam engine efficiency improved as the operating principles were discovered, which led to the development of the science of thermodynamics. For example, if an automobile engine burns gasoline at a temperature of T_{\rm H} = 816^\circ \text{C} = 1500^\circ \text{F} = 1089 \text{K} and the ambient temperature is T_{\rm C} = 21^\circ \text{C} = 70^\circ \text{F} = 294 \text{K}, then its maximum possible efficiency is: :\eta_{\rm th} \le \left (1 - \frac{294 K}{1089 K} \right ) 100\% = 73.0\% It can be seen that since T_{\rm C} is fixed by the environment, the only way for a designer to increase the Carnot efficiency of an engine is to increase T_{\rm H}, the temperature at which the heat is added to the engine. A very well-designed and built steam locomotive used to get around 7-8% efficiency in its heyday. Today they are considered separate, so it is necessary to know whether stated efficiency is overall, which includes the boiler, or just of the engine. Engines in large diesel trucks, buses, and newer diesel cars can achieve peak efficiencies around 45%. ===Gas turbine=== The gas turbine is most efficient at maximum power output in the same way reciprocating engines are most efficient at maximum load. There is an overall theoretical limit to the efficiency of any heat engine due to temperature, called the Carnot efficiency. The Carnot cycle achieves maximum efficiency because all the heat is added to the working fluid at the maximum temperature T_{\rm H}, and removed at the minimum temperature T_{\rm C}. Comparisons of efficiency and power of the early steam engines is difficult for several reasons: 1) there was no standard weight for a bushel of coal, which could be anywhere from 82 to 96 pounds (37 to 44 kg). Despite of being at very low pressure the exhaust coming out of the turbine and entering the condenser carries some of kinetic energy and useful enthalpy, which is direct energy loss. ==Radiation and convection losses== The steam turbine operates at a relatively high temperature; therefore some of the heat energy of steam is radiated and convected from the body of the turbine to its surrounding. In thermodynamics, the thermal efficiency (\eta_{\rm th}) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc. The most efficient reciprocating steam engine design (per stage) was the uniflow engine, but by the time it appeared steam was being displaced by diesel engines, which were even more efficient and had the advantages of requiring less labor (for coal handling and oiling), being a more dense fuel, and displaced less cargo. ====Steam turbine==== The steam turbine is the most efficient steam engine and for this reason is universally used for electrical generation.	0.9731	22	0.38	35.64	6.6	C
The discovery of the element argon by Lord Rayleigh and Sir William Ramsay had its origins in Rayleigh's measurements of the density of nitrogen with an eye toward accurate determination of its molar mass. Rayleigh prepared some samples of nitrogen by chemical reaction of nitrogencontaining compounds; under his standard conditions, a glass globe filled with this 'chemical nitrogen' had a mass of $2.2990 \mathrm{~g}$. He prepared other samples by removing oxygen, carbon dioxide, and water vapour from atmospheric air; under the same conditions, this 'atmospheric nitrogen' had a mass of $2.3102 \mathrm{~g}$ (Lord Rayleigh, Royal Institution Proceedings 14, 524 (1895)). With the hindsight of knowing accurate values for the molar masses of nitrogen and argon, compute the mole fraction of argon in the latter sample on the assumption that the former was pure nitrogen and the latter a mixture of nitrogen and argon.	Argon was first isolated from air in 1894 by Lord Rayleigh and Sir William Ramsay at University College London by removing oxygen, carbon dioxide, water, and nitrogen from a sample of clean air. After the two men identified argon, Ramsay investigated other atmospheric gases. Until 1957, the symbol for argon was "A", but now it is "Ar". ==Occurrence== Argon constitutes 0.934% by volume and 1.288% by mass of Earth's atmosphere. Most of the argon in Earth's atmosphere was produced by electron capture of long-lived ( + e− → + ν) present in natural potassium within Earth. Before isolating the gas, they had determined that nitrogen produced from chemical compounds was 0.5% lighter than nitrogen from the atmosphere. It forms at pressures between 4.3 and 220 GPa, though Raman measurements suggest that the H2 molecules in Ar(H2)2 dissociate above 175 GPa. ==Production== Argon is extracted industrially by the fractional distillation of liquid air in a cryogenic air separation unit; a process that separates liquid nitrogen, which boils at 77.3 K, from argon, which boils at 87.3 K, and liquid oxygen, which boils at 90.2 K. The content of 39Ar in natural argon is measured to be of (8.0±0.6)×10−16 g/g, or (1.01±0.08) Bq/kg of 36, 38, 40Ar. Almost all of the argon in the Earth's atmosphere is the product of 40K decay, since 99.6% of Earth atmospheric argon is 40Ar, whereas in the Sun and presumably in primordial star-forming clouds, argon consists of < 15% 38Ar and mostly (85%) 36Ar. Argon is the most abundant noble gas in Earth's crust, comprising 0.00015% of the crust. Sir William Ramsay (; 2 October 1852 – 23 July 1916) was a Scottish chemist who discovered the noble gases and received the Nobel Prize in Chemistry in 1904 "in recognition of his services in the discovery of the inert gaseous elements in air" along with his collaborator, John William Strutt, 3rd Baron Rayleigh, who received the Nobel Prize in Physics that same year for their discovery of argon. The predominance of radiogenic is the reason the standard atomic weight of terrestrial argon is greater than that of the next element, potassium, a fact that was puzzling when argon was discovered. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). Earth's crust and seawater contain 1.2 ppm and 0.45 ppm of argon, respectively. ==Isotopes== The main isotopes of argon found on Earth are (99.6%), (0.34%), and (0.06%). Argon is a chemical element with the symbol Ar and atomic number 18. This discovery caused the recognition that argon could form weakly bound compounds, even though it was not the first. Argon (18Ar) has 26 known isotopes, from 29Ar to 54Ar and 1 isomer (32mAr), of which three are stable (36Ar, 38Ar, and 40Ar). Before 1962, argon and the other noble gases were considered to be chemically inert and unable to form compounds; however, compounds of the heavier noble gases have since been synthesized. Nearly all of the argon in Earth's atmosphere is radiogenic argon-40, derived from the decay of potassium-40 in Earth's crust. Correspondingly, solar argon contains 84.6% (according to solar wind measurements), and the ratio of the three isotopes 36Ar : 38Ar : 40Ar in the atmospheres of the outer planets is 8400 : 1600 : 1. * On triple point pressure at 83.8058 K. ==External links== * Argon at The Periodic Table of Videos (University of Nottingham) * USGS Periodic Table – Argon * Diving applications: Why Argon? Rayleigh had noticed a discrepancy between the density of nitrogen made by chemical synthesis and nitrogen isolated from the air by removal of the other known components. That proposed element was named gnomium.	5.1	200	0.011	8	4.5	C
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \mathrm{~mol} \mathrm{CO}_2(\mathrm{~g})$, initially at $25^{\circ} \mathrm{C}$ and $10 \mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \mathrm{~m}}=28.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and calculate $w$.	If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. A carbon dioxide generator or CO2 generator is a machine used to enhance carbon dioxide levels in order to promote plant growth in greenhouses or other enclosed areas. Pressure gain combustion is a combustion process whereby gas expansion by heat release is constrained, causing a rise in stagnation pressure and allowing work extraction by expansion to the initial pressure. In a fire, the pressure in a gas cylinder rises in direct proportion to its temperature. For gases that are liquid under storage, e.g., propane, the outlet pressure is dependent on the vapor pressure of the gas, and does not fall until the cylinder is nearly exhausted, although it will vary according to the temperature of the cylinder contents. Accumulation of carbon dioxide is predominantly a result of hypoperfusion and not hypoxia. Gastric tonometry describes the measurement of the carbon dioxide level inside the stomach in order to assess the degree of blood flow to the stomach and bowel. Normocapnia or normocarbia is a state of normal arterial carbon dioxide pressure, usually about 40 mmHg. == See also == * * * == References == The Free Dictionary - Normocapnia Category:Diving medicine Category:Pulmonology A gas cylinder is a pressure vessel for storage and containment of gases at above atmospheric pressure. For gases that remain gaseous under ambient storage conditions, the upstream pressure gauge can be used to estimate how much gas is left in the cylinder according to pressure. The manifold may be arranged to allow simultaneous flow from all the cylinders, or, for a cascade filling system, where gas is tapped off cylinders according to the lowest positive pressure difference between storage and destination cylinder, being a more efficient use of pressurised gas. === Gas storage quads === thumb\|Helium quad for surface-supplied diving gas A gas quad is a group of high pressure cylinders mounted on a transport and storage frame. Each cylinder shall be painted externally in the colours corresponding to its gaseous contents. == Common sizes == The below are example cylinder sizes and do not constitute an industry standard. size Diameter × height, including 5.5 inches for valve and cap (inches) Nominal tare weight, including 4.5 lb for valve and cap (lb) Water capacity (lb) Internal volume, 70 °F (21 °C), 1atm Internal volume, 70 °F (21 °C), 1atm U.S. DOT specs size Diameter × height, including 5.5 inches for valve and cap (inches) Nominal tare weight, including 4.5 lb for valve and cap (lb) Water capacity (lb) (liters) (cu.ft) U.S. DOT specs 2HP 43.3 1.53 3AA3500 K 110 49.9 1.76 3AA2400 A 96 43.8 1.55 3AA2015 B 37.9 17.2 0.61 3AA2015 C 15.2 6.88 0.24 3AA2015 D 4.9 2.24 0.08 3AA2015 AL 64.8 29.5 1.04 3AL2015 BL 34.6 15.7 0.55 3AL2216 CL 13 5.9 0.21 3AL2216 XL 238 108 3.83 4BA240 SSB 41.6 18.9 0.67 3A1800 10S 8.3 3.8 0.13 3A1800 LB 1 0.44 0.016 3E1800 XF 60.9 2.15 8AL XG 278 126.3 4.46 4AA480 XM 120 54.3 1.92 3A480 XP 124 55.7 1.98 4BA300 QT (includes 4.5 inches for valve) (includes 1.5 lb for valve) 2.0 0.900 0.0318 4B-240ET LP5 47.7 21.68 0.76 4BW240 Medical E (excludes valve and cap) (excludes valve and cap) 9.9 4.5 0.16 3AA2015 (US DOT specs define material, making, and maximum pressure in psi. Carbon tetroxide or Oxygen carbonate (in its C2v isomer) is a highly unstable oxide of carbon with formula . Because the introduction of a nasogastric tube is almost routine in critically ill patients, the measurement of gastric carbon dioxide can be an easy method to monitor tissue perfusion. It was proposed as an intermediate in the O-atom exchange between carbon dioxide () and oxygen () at high temperatures. Tonometry is based on the principle that at equilibrium the partial pressure of a diffusible gas such as CO2 is the same in both the wall and lumen of a viscus. Using compressed CO2 is an alternative to generators. == See also == ==References== Category:Horticulture Category:Industrial gases A typical gas cylinder design is elongated, standing upright on a flattened bottom end, with the valve and fitting at the top for connecting to the receiving apparatus. ISO 11439: Gas cylinders — High-pressure cylinders for the on-board storage of natural gas as a fuel for automotive vehicles * ISO 15500-5: Road vehicles — Compressed natural gas (CNG) fuel system components — Part 5: Manual cylinder valve * US DOT CFR Title 49, part 178, Subpart C — Specification for CylindersUS DOT e-CFR (Electronic Code of Federal Regulations) Title 49, part 178, Subpart C — Specification for Cylinders — eg DOT 3AL = seamless aluminum * US DOT Aluminum Tank Alloy 6351-T6 amendment for SCUBA, SCBA, Oxygen Service — Visual Eddy inspectionFederal Register / Vol. 71, No. 167 / Tuesday, August 29, 2006 / Rules and Regulations Title 49 CFR Parts 173 and 180 Visual Edddy * AS 2896-2011:Medical gas systems—Installation and testing of non-flammable medical gas pipeline systems pipeline systems (Australian Standards). === Color coding === Gas cylinders are often color- coded, but the codes are not standard across different jurisdictions, and sometimes are not regulated. High-pressure gas cylinders are also called bottles. The regulator is adjusted to control the downstream pressure, which will limit the maximum flow of gas out of the cylinder at the pressure shown by the downstream gauge. Pressure vessels for gas storage may also be classified by volume.	4.16	-20	0.264	-2.5	15.425	B
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When a certain freon used in refrigeration was expanded adiabatically from an initial pressure of $32 \mathrm{~atm}$ and $0^{\circ} \mathrm{C}$ to a final pressure of $1.00 \mathrm{~atm}$, the temperature fell by $22 \mathrm{~K}$. Calculate the Joule-Thomson coefficient, $\mu$, at $0^{\circ} \mathrm{C}$, assuming it remains constant over this temperature range.	The temperature change produced during a Joule–Thomson expansion is quantified by the Joule–Thomson coefficient, \mu_{\mathrm{JT}}. This equation can be used to obtain Joule–Thomson coefficients from the more easily measured isothermal Joule–Thomson coefficient. The temperature of this point, the Joule–Thomson inversion temperature, depends on the pressure of the gas before expansion. Since this is true at all temperatures for ideal gases (see expansion in gases), the Joule–Thomson coefficient of an ideal gas is zero at all temperatures. ==Joule's second law== It is easy to verify that for an ideal gas defined by suitable microscopic postulates that αT = 1, so the temperature change of such an ideal gas at a Joule–Thomson expansion is zero. Thus, for N2 gas below 621 K, a Joule–Thomson expansion can be used to cool the gas until liquid N2 forms. ==Physical mechanism== There are two factors that can change the temperature of a fluid during an adiabatic expansion: a change in internal energy or the conversion between potential and kinetic internal energy. This expression can now replace \mu_{\mathrm{T}} in the earlier equation for \mu_{\mathrm{JT}} to obtain: :\mu_{\mathrm{JT}} \equiv \left( \frac{\partial T}{\partial P} \right)_H = \frac V {C_{\mathrm{p}}} (\alpha T - 1).\, This provides an expression for the Joule–Thomson coefficient in terms of the commonly available properties heat capacity, molar volume, and thermal expansion coefficient. The first step in obtaining these results is to note that the Joule–Thomson coefficient involves the three variables T, P, and H. In a Joule–Thomson expansion the enthalpy remains constant. The physical mechanism associated with the Joule–Thomson effect is closely related to that of a shock wave, although a shock wave differs in that the change in bulk kinetic energy of the gas flow is not negligible. ==The Joule–Thomson (Kelvin) coefficient== thumb\|400px\|Fig. 1 – Joule–Thomson coefficients for various gases at atmospheric pressure The rate of change of temperature T with respect to pressure P in a Joule–Thomson process (that is, at constant enthalpy H) is the Joule–Thomson (Kelvin) coefficient \mu_{\mathrm{JT}}. At room temperature, all gases except hydrogen, helium, and neon cool upon expansion by the Joule–Thomson process when being throttled through an orifice; these three gases experience the same effect but only at lower temperatures. This produces a decrease in temperature and results in a positive Joule–Thomson coefficient. The cooling produced in the Joule–Thomson expansion makes it a valuable tool in refrigeration.Keenan, J.H. (1970). This means that the mass fraction of the liquid in the liquid–gas mixture leaving the throttling valve is 40%. ==Derivation of the Joule–Thomson coefficient== It is difficult to think physically about what the Joule–Thomson coefficient, \mu_{\mathrm{JT}}, represents. For an ideal gas, \mu_\text{JT} is always equal to zero: ideal gases neither warm nor cool upon being expanded at constant enthalpy. ==Applications== In practice, the Joule–Thomson effect is achieved by allowing the gas to expand through a throttling device (usually a valve) which must be very well insulated to prevent any heat transfer to or from the gas. At high temperature, Z and PV decrease as the gas expands; if the decrease is large enough, the Joule–Thomson coefficient will be negative. Thus at low temperature, Z and PV will increase as the gas expands, resulting in a positive Joule–Thomson coefficient. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). This coefficient can be expressed in terms of the gas's volume V, its heat capacity at constant pressure C_{\mathrm{p}}, and its coefficient of thermal expansion \alpha as: :\mu_{\mathrm{JT}} = \left( {\partial T \over \partial P} \right)_H = \frac V {C_{\mathrm{p}}}(\alpha T - 1)\, See the below for the proof of this relation. With that in mind, the following table explains when the Joule–Thomson effect cools or warms a real gas: If the gas temperature is then \mu_\text{JT} is since \partial P is thus \partial T must be so the gas below the inversion temperature positive always negative negative cools above the inversion temperature negative always negative positive warms Helium and hydrogen are two gases whose Joule–Thomson inversion temperatures at a pressure of one atmosphere are very low (e.g., about 45 K, −228 °C for helium). Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). In a Joule–Thomson process the specific enthalpy h remains constant.See e.g. M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th Edition (2006) John Wiley & Sons, Inc. page 147 To prove this, the first step is to compute the net work done when a mass m of the gas moves through the plug. The temperature may depend on pressure, because at lower pressure there will be more dissociation of the combustion products, implying a lower adiabatic temperature. ≈6332 Aluminium Oxygen 3732 6750 Lithium Oxygen 2438 4420 Phosphorus (white) Oxygen 2969 5376 Zirconium Oxygen 4005 7241 ==Thermodynamics== thumb\|right\|300px\|First law of thermodynamics for a closed reacting system From the first law of thermodynamics for a closed reacting system we have :{}_RQ_P - {}_RW_P = U_P - U_R where, {}_RQ_P and {}_RW_P are the heat and work transferred from the system to the surroundings during the process, respectively, and U_R and U_P are the internal energy of the reactants and products, respectively.	0.444444444444444	0.9992093669	3.2	-1.32	0.71	E
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The volume of a certain liquid varies with temperature as $$ V=V^{\prime}\left\{0.75+3.9 \times 10^{-4}(T / \mathrm{K})+1.48 \times 10^{-6}(T / \mathrm{K})^2\right\} $$ where $V^{\prime}$ is its volume at $300 \mathrm{~K}$. Calculate its expansion coefficient, $\alpha$, at $320 \mathrm{~K}$.	== Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. Coefficients from this source: : ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975 allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known. == Equations == : \ln P_{\rm r} = f^{(0)} + \omega \cdot f^{(1)} : f^{(0)}=5.92714 - \frac{6.09648}{T_{\rm r}} - 1.28862 \cdot \ln T_{\rm r} + 0.169347 \cdot T_{\rm r}^6 : f^{(1)}=15.2518 - \frac{15.6875}{T_{\rm r}}-13.4721 \cdot \ln T_{\rm r} + 0.43577 \cdot T_{\rm r}^6 with :P_{\rm r}=\frac{P}{P_{\rm c}} (reduced pressure) and T_{\rm r}=\frac{T}{T_{\rm c}} (reduced temperature). == Typical errors == The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). The unit system used (K or R for T) is irrelevant because of the usage of the reduced values Tr and Pr. ==See also== Vapour pressure of water Antoine equation Tetens equation Arden Buck equation Goff–Gratch equation == References == Category:Thermodynamic models Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. Auflage, McGraw-Hill, 1988 == Example calculation == For benzene with Tc = 562.12 KBrunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006 * Pc = 4898 kPa * Tb = 353.15 KSilva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006 * ω = 0.2120Dortmund Data Bank the following calculation for T=Tb results: * Tr = 353.15 / 562.12 = 0.628247 * f(0) = -3.167428 * f(1) = -3.429560 * Pr = exp( f(0) \+ ω f(1) ) = 0.020354 * P = Pr * Pc = 99.69 kPa The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). The expansion ratio of a liquefied and cryogenic substance is the volume of a given amount of that substance in liquid form compared to the volume of the same amount of substance in gaseous form, at room temperature and normal atmospheric pressure. We assume the expansion occurs without exchange of heat (adiabatic expansion). Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures. Therefore, the heat capacity ratio in this example is 1.4. An experimental value should be used rather than one based on this approximation, where possible. Calculations of the (saturation) vapour pressure of water are commonly used in meteorology. The analysis here shows the simple unattributed formula and the Antoine equation are reasonably accurate at 100 °C, but quite poor for lower temperatures above freezing. The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. Hence the use of pressure relief valves and vent valves are important.Safetygram-27 Cryogenic Liquid Containers The expansion ratio of liquefied and cryogenic from the boiling point to ambient is: nitrogen – 1 to 696 liquid helium – 1 to 745 argon – 1 to 842 liquid hydrogen – 1 to 850 liquid oxygen – 1 to 860 neon – Neon has the highest expansion ratio with 1 to 1445. ==See also== Liquid-to-gas ratio Boiling liquid expanding vapor explosion Thermal expansion ==References== ==External links== cryogenic-gas- hazards Category:Cryogenics Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature.	0.00131	5840	12.0	29.36	0.03	A
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The standard enthalpy of formation of the metallocene bis(benzene)chromium was measured in a calorimeter. It was found for the reaction $\mathrm{Cr}\left(\mathrm{C}_6 \mathrm{H}_6\right)_2(\mathrm{~s}) \rightarrow \mathrm{Cr}(\mathrm{s})+2 \mathrm{C}_6 \mathrm{H}_6(\mathrm{~g})$ that $\Delta_{\mathrm{r}} U^{\bullet}(583 \mathrm{~K})=+8.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Estimate the standard enthalpy of formation of the compound at $583 \mathrm{~K}$. The constant-pressure molar heat capacity of benzene is $136.1 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ in its liquid range and $81.67 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ as a gas.	Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). ==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.18 1.293 65 KAL 33.2 1.297 65.0 SMI −239.9 13.2 kgf/cm² 0.0310 1 H hydrogen (equilibrium) LNG −240.17 1.294 12.77 atm 65.4 0.0308 1 H hydrogen (normal) LNG −239.91 1.297 12.8 atm 65.0 0.0310 1 D deuterium KAL 38.2 1.65 60 1 D deuterium (equilibrium) LNG −234.8 1.650 16.28 atm 60.4 0.0668 1 D deuterium (normal) LNG −234.7 1.665 16.43 atm 60.3 0.0669 2 He helium use 5.19 −267.96 0.227 CRC.a 5.19 −267.96 0.227 57 KAL 5.19 0.227 57.2 SMI −267.9 2.34 kgf/cm² 0.0693 2 He helium (equilibrium) LNG −267.96 0.2289 2.261 atm 0.06930 2 He helium-3 LNG −269.85 0.1182 1.13 atm 72.5 0.0414 2 He helium-4 LNG −267.96 0.227 2.24 atm 57.3 0.0698 3 Li lithium use (3223) (2950) (67) CRC.b (3223) 2950 (67) (66) 7 N nitrogen use 126.21 −146.94 3.39 CRC.a 126.21 −146.94 3.39 90 KAL 126.2 3.39 89.5 SMI −147.1 34.7 kgf/cm² 0.3110 7 N nitrogen-14 LNG −146.94 3.39 33.5 atm 89.5 0.313 7 N nitrogen-15 LNG −146.8 3.39 33.5 atm 90.4 0.332 8 O oxygen use 154.59 −118.56 5.043 CRC.a 154.59 −118.56 5.043 73 LNG −118.56 5.043 49.77 atm 73.4 0.436 KAL 154.6 5.04 73.4 SMI −118.8 51.4 kgf/cm² 0.430 9 F fluorine use 144.13 −129.02 5.172 CRC.a 144.13 −129.02 5.172 66 LNG −129.0 5.215 51.47 atm 66.2 0.574 KAL 144.3 5.22 66 10 Ne neon use 44.4 −228.7 2.76 CRC.a 44.4 −228.7 2.76 42 LNG −228.71 2.77 27.2 atm 41.7 0.4835 KAL 44.4 2.76 41.7 SMI −228.7 26.8 kgf/cm² 0.484 11 Na sodium use (2573) (2300) (35) CRC.b (2573) 2300 (35) (116) 15 P phosphorus use 994 721 CRC.a 994 721 LNG 721 16 S sulfur use 1314 1041 20.7 CRC.a 1314 1041 20.7 LNG 1041 11.7 116 atm KAL 1314 20.7 SMI 1040 17 Cl chlorine use 416.9 143.8 7.991 CRC.a 416.9 143.8 7.991 123 LNG 143.8 7.71 76.1 atm 124 0.573 KAL 416.9 7.98 124 SMI 144.0 78.7 kgf/cm² 0.573 18 Ar argon use 150.87 −122.28 4.898 CRC.a 150.87 −122.28 4.898 75 LNG −122.3 4.87 48.1 atm 74.6 0.536 KAL 150.9 4.90 74.6 SMI −122 49.7 kgf/cm² 0.531 19 K potassium use (2223) (1950) (16) CRC.b (2223) 1950 (16) (209) 33 As arsenic use 1673 1400 CRC.a 1673 1400 35 LNG 1400 34 Se selenium use 1766 1493 27.2 CRC.a 1766 1493 27.2 LNG 1493 35 Br bromine use 588 315 10.34 CRC.a 588 315 10.34 127 LNG 315 10.3 102 atm 135 1.184 KAL 588 10.3 127 SMI 302 1.18 36 Kr krypton use 209.41 −63.74 5.50 CRC.a 209.41 −63.74 5.50 91 LNG −63.75 5.50 54.3 atm 91.2 0.9085 KAL 209.4 5.50 91.2 37 Rb rubidium use (2093) (1820) (16) CRC.b (2093) 1820 (16) (247) LNG 1832 250 0.34 53 I iodine use 819 546 11.7 CRC.a 819 546 155 LNG 546 11.7 115 atm 155 0.164 KAL 819 155 SMI 553 54 Xe xenon use 289.77 16.62 5.841 CRC.c 289.77 16.62 5.841 118 LNG 16.583 5.84 57.64 atm 118 1.105 KAL 289.7 5.84 118 SMI 16.6 60.2 kgf/cm² 1.155 55 Cs caesium use 1938 1665 9.4 CRC.d 1938 1665 9.4 341 LNG 1806 300 0.44 80 Hg mercury use 1750 1477 172.00 CRC.a 1750 1477 172.00 43 LNG 1477 160.8 1587 atm KAL 1750 172 42.7 SMI 1460±20 1640±50 kgf/cm² 0.5 86 Rn radon use 377 104 6.28 CRC.a 377 104 6.28 LNG 104 6.28 62 atm 139 1.6 KAL 377 6.3 SMI 104 64.1 kgf/cm² ==References== ===CRC.a-d=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 85th Edition, online version. As quoted from these sources: :a - Lide, D.R., and Kehiaian, H.V., CRC Handbook of Thermophysical and Thermochemical Data, CRC Press, Boca Raton, Florida, 1994. :b - Stull, D., in American Institute of Physics Handbook, Third Edition, Gray, D.E., Ed., McGraw Hill, New York, 1972. :c - Hultgren, R., Desai, P.D., Hawkins, D.T., Gleiser, M., Kelley, K.K., and Wagman, D.D., Selected Values of Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, OH, 1973. :d - TRCVP, Vapor Pressure Database, Version 2.2P, Thermodynamic Research Center, Texas A&M; University, College Station, TX. :e - Barin, I., Thermochemical Data of Pure Substances, VCH Publishers, New York, 1993. :f - Ohse, R.W. Handbook of Thermodynamic and Transport Properties of Alkali Metals, Blackwell Scientific Publications, Oxford, 1994. :g - Gschneidner, K.A., in CRC Handbook of Chemistry and Physics, 77th Edition, p. 4-112, CRC Press, Boca Raton, Florida, 1996. :h - . :i - Wagner, W., and de Reuck, K.M., International Thermodynamic Tables of the Fluid State, No. 9. == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. The standard enthalpy of formation is then determined using Hess's law. For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol . == Hess's law == For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). ==Thermal conductivity== 1 H hydrogen use 180.5 mW/(m·K) CR2 (P=0) 186.9 mW/(m·K) LNG 0.1805 W/(m·K) WEL 0.1805 W/(m·K) 2 He helium use 151.3 mW/(m·K) CR2 (P=0) 156.7 mW/(m·K) LNG 0.1513 W/(m·K) WEL 0.1513 W/(m·K) 3 Li lithium use 84.8 W/(m·K) CRC 0.847 W/(cm·K) LNG 84.8 W/(m·K) WEL 85 W/(m·K) 4 Be beryllium use 200 W/(m·K) CRC 2.00 W/(cm·K) LNG 200 W/(m·K) WEL 190 W/(m·K) 5 B boron use 27.4 W/(m·K) LNG 27.4 W/(m·K) WEL 27 W/(m·K) 6 C carbon (graphite) use (graphite) (119-165) W/(m·K) LNG (119-165) W/(m·K) LNG (amorphous) 1.59 W/(m·K) WEL 140 W/(m·K) CRC pyrolytic graphite (parallel to the layer planes) 19.5 W/(cm·K) (perpendicular) 0.0570 W/(cm·K) 6 C carbon (diamond) use (diamond) (900-2320) W/(m·K) LNG (900-2320) W/(m·K) CRC (type I) 8.95 W/(cm·K) (type IIa) 23.0 W/(cm·K) (type IIb) 13.5 W/(cm·K) 7 N nitrogen use 25.83 mW/(m·K) CR2 26.0 mW/(m·K) LNG 0.02583 W/(m·K) WEL 0.02583 W/(m·K) 8 O oxygen use 26.58 mW/(m·K) CR2 26.3 mW/(m·K) LNG (gas) 0.02658 W/(m·K) LNG (liquid) 0.149 W/(m·K) WEL 0.02658 W/(m·K) 9 F fluorine use 27.7 mW/(m·K) LNG 0.0277 W/(m·K) WEL 0.0277 W/(m·K) 10 Ne neon use 49.1 mW/(m·K) CR2 (P=0) 49.8 mW/(m·K) LNG 0.0491 W/(m·K) WEL 0.0491 W/(m·K) 11 Na sodium use 142 W/(m·K) CRC 1.41 W/(cm·K) LNG 142 W/(m·K) WEL 140 W/(m·K) 12 Mg magnesium use 156 W/(m·K) CRC 1.56 W/(cm·K) LNG 156 W/(m·K) WEL 160 W/(m·K) 13 Al aluminium use 237 W/(m·K) CRC 2.37 W/(cm·K) LNG 237 W/(m·K) WEL 235 W/(m·K) 14 Si silicon use 149 W/(m·K) LNG 149 W/(m·K) WEL 150 W/(m·K) 15 P phosphorus use (white) 0.236 W/(m·K) LNG (white) 0.23617 W/(m·K) [sic] WEL 0.236 W/(m·K) 16 S sulfur use (amorphous) 0.205 W/(m·K) LNG (amorphous) 0.205 W/(m·K) WEL 0.205 W/(m·K) 17 Cl chlorine use 8.9 mW/(m·K) LNG 0.0089 W/(m·K) WEL 0.0089 W/(m·K) 18 Ar argon use 17.72 mW/(m·K) CR2 17.9 mW/(m·K) LNG 0.01772 W/(m·K) WEL 0.01772 W/(m·K) 19 K potassium use 102.5 W/(m·K) CRC 1.024 W/(cm·K) LNG 102.5 W/(m·K) WEL 100 W/(m·K) 20 Ca calcium use 201 W/(m·K) CRC 2.00 W/(cm·K) LNG 201 W/(m·K) WEL 200 W/(m·K) 21 Sc scandium use 15.8 W/(m·K) CRC 0.158 W/(cm·K) LNG 15.8 W/(m·K) WEL 16 W/(m·K) 22 Ti titanium use 21.9 W/(m·K) CRC 0.219 W/(cm·K) LNG 21.9 W/(m·K) WEL 22 W/(m·K) 23 V vanadium use 30.7 W/(m·K) CRC 0.307 W/(cm·K) LNG 30.7 W/(m·K) WEL 31 W/(m·K) 24 Cr chromium use 93.9 W/(m·K) CRC 0.937 W/(cm·K) LNG 93.9 W/(m·K) WEL 94 W/(m·K) 25 Mn manganese use 7.81 W/(m·K) CRC 0.0782 W/(cm·K) LNG 7.81 W/(m·K) WEL 7.8 W/(m·K) 26 Fe iron use 80.4 W/(m·K) CRC 0.802 W/(cm·K) LNG 80.4 W/(m·K) WEL 80 W/(m·K) 27 Co cobalt use 100 W/(m·K) CRC 1.00 W/(cm·K) LNG 100 W/(m·K) WEL 100 W/(m·K) 28 Ni nickel use 90.9 W/(m·K) CRC 0.907 W/(cm·K) LNG 90.9 W/(m·K) WEL 91 W/(m·K) 29 Cu copper use 401 W/(m·K) CRC 4.01 W/(cm·K) LNG 401 W/(m·K) WEL 400 W/(m·K) 30 Zn zinc use 116 W/(m·K) CRC 1.16 W/(cm·K) LNG 116 W/(m·K) WEL 120 W/(m·K) 31 Ga gallium use 40.6 W/(m·K) CRC 0.406 W/(cm·K) LNG (liquid) 29.4 W/(m·K) LNG (solid) 40.6 W/(m·K) WEL 29 W/(m·K) 32 Ge germanium use 60.2 W/(m·K) LNG 60.2 W/(m·K) WEL 60 W/(m·K) 33 As arsenic use 50.2 W/(m·K) LNG 50.2 W/(m·K) WEL 50 W/(m·K) 34 Se selenium use (amorphous) 0.519 W/(m·K) LNG (amorphous) 0.519 W/(m·K) WEL 0.52 W/(m·K) 35 Br bromine use 0.122 W/(m·K) LNG 0.122 W/(m·K) WEL 0.12 W/(m·K) 36 Kr krypton use 9.43 mW/(m·K) CR2 (P=0) 9.5 mW/(m·K) LNG 9.43 W/(m·K) [sic] WEL 0.00943 W/(m·K) 37 Rb rubidium use 58.2 W/(m·K) CRC 0.582 W/(cm·K) LNG 58.2 W/(m·K) WEL 58 W/(m·K) 38 Sr strontium use 35.4 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.4 W/(m·K) WEL 35 W/(m·K) 39 Y yttrium use 17.2 W/(m·K) CRC 0.172 W/(cm·K) LNG 17.2 W/(m·K) WEL 17 W/(m·K) 40 Zr zirconium use 22.6 W/(m·K) CRC 0.227 W/(cm·K) LNG 22.6 W/(m·K) WEL 23 W/(m·K) 41 Nb niobium use 53.7 W/(m·K) CRC 0.537 W/(cm·K) LNG 53.7 W/(m·K) WEL 54 W/(m·K) 42 Mo molybdenum use 138 W/(m·K) CRC 1.38 W/(cm·K) LNG 138 W/(m·K) WEL 139 W/(m·K) 43 Tc technetium use 50.6 W/(m·K) CRC 0.506 W/(cm·K) LNG 50.6 W/(m·K) WEL 51 W/(m·K) 44 Ru ruthenium use 117 W/(m·K) CRC 1.17 W/(cm·K) LNG 117 W/(m·K) WEL 120 W/(m·K) 45 Rh rhodium use 150 W/(m·K) CRC 1.50 W/(cm·K) LNG 150 W/(m·K) WEL 150 W/(m·K) 46 Pd palladium use 71.8 W/(m·K) CRC 0.718 W/(cm·K) LNG 71.8 W/(m·K) WEL 72 W/(m·K) 47 Ag silver use 429 W/(m·K) CRC 4.29 W/(cm·K) LNG 429 W/(m·K) WEL 430 W/(m·K) 48 Cd cadmium use 96.6 W/(m·K) CRC 0.968 W/(cm·K) LNG 96.6 W/(m·K) WEL 97 W/(m·K) 49 In indium use 81.8 W/(m·K) CRC 0.816 W/(cm·K) LNG 81.8 W/(m·K) WEL 82 W/(m·K) 50 Sn tin use 66.8 W/(m·K) CRC 0.666 W/(cm·K) LNG 66.8 W/(m·K) WEL 67 W/(m·K) 51 Sb antimony use 24.4 W/(m·K) CRC 0.243 W/(cm·K) LNG 24.4 W/(m·K) WEL 24 W/(m·K) 52 Te tellurium use (1.97-3.38) W/(m·K) LNG (1.97-3.38) W/(m·K) WEL 3 W/(m·K) 53 I iodine use 0.449 W/(m·K) CRC (300 K) 0.45 W/(m·K) LNG 449 W/(m·K) [sic] WEL 0.449 W/(m·K) 54 Xe xenon use 5.65 mW/(m·K) CR2 (P=0) 5.5 mW/(m·K) LNG 0.00565 W/(m·K) WEL 0.00565 W/(m·K) 55 Cs caesium use 35.9 W/(m·K) CRC 0.359 W/(cm·K) LNG 35.9 W/(m·K) WEL 36 W/(m·K) 56 Ba barium use 18.4 W/(m·K) CRC 0.184 W/(cm·K) LNG 18.4 W/(m·K) WEL 18 W/(m·K) 57 La lanthanum use 13.4 W/(m·K) CRC 0.134 W/(cm·K) LNG 13.4 W/(m·K) WEL 13 W/(m·K) 58 Ce cerium use 11.3 W/(m·K) CRC 0.113 W/(cm·K) LNG 11.3 W/(m·K) WEL 11 W/(m·K) 59 Pr praseodymium use 12.5 W/(m·K) CRC 0.125 W/(cm·K) LNG 12.5 W/(m·K) WEL 13 W/(m·K) 60 Nd neodymium use 16.5 W/(m·K) CRC 0.165 W/(cm·K) LNG 16.5 W/(m·K) WEL 17 W/(m·K) 61 Pm promethium use 17.9 W/(m·K) CRC (est.) 0.15 W/(cm·K) LNG 17.9 W/(m·K) WEL 15 W/(m·K) 62 Sm samarium use 13.3 W/(m·K) CRC 0.133 W/(cm·K) LNG 13.3 W/(m·K) WEL 13 W/(m·K) 63 Eu europium use (est.) 13.9 W/(m·K) CRC (est.) 0.139 W/(cm·K) LNG 13.9 W/(m·K) WEL 14 W/(m·K) 64 Gd gadolinium use 10.6 W/(m·K) (300 K) 10.6 W/(m·K) CRC (100 °C) 0.105 W/(cm·K) LNG 10.5 W/(m·K) WEL 11 W/(m·K) 65 Tb terbium use 11.1 W/(m·K) CRC 0.111 W/(cm·K) LNG 11.1 W/(m·K) WEL 11 W/(m·K) 66 Dy dysprosium use 10.7 W/(m·K) CRC 0.107 W/(cm·K) LNG 10.7 W/(m·K) WEL 11 W/(m·K) 67 Ho holmium use 16.2 W/(m·K) CRC 0.162 W/(cm·K) LNG 16.2 W/(m·K) WEL 16 W/(m·K) 68 Er erbium use 14.5 W/(m·K) CRC 0.145 W/(cm·K) LNG 14.5 W/(m·K) WEL 15 W/(m·K) 69 Tm thulium use 16.9 W/(m·K) CRC 0.169 W/(cm·K) LNG 16.9 W/(m·K) WEL 17 W/(m·K) 70 Yb ytterbium use 38.5 W/(m·K) CRC 0.385 W/(cm·K) LNG 38.5 W/(m·K) WEL 39 W/(m·K) 71 Lu lutetium use 16.4 W/(m·K) CRC 0.164 W/(cm·K) LNG 16.4 W/(m·K) WEL 16 W/(m·K) 72 Hf hafnium use 23.0 W/(m·K) CRC 0.230 W/(cm·K) LNG 23.0 W/(m·K) WEL 23 W/(m·K) 73 Ta tantalum use 57.5 W/(m·K) CRC 0.575 W/(cm·K) LNG 57.5 W/(m·K) WEL 57 W/(m·K) 74 W tungsten use 173 W/(m·K) CRC 1.74 W/(cm·K) LNG 173 W/(m·K) WEL 170 W/(m·K) 75 Re rhenium use 48.0 W/(m·K) CRC 0.479 W/(cm·K) LNG 48.0 W/(m·K) WEL 48 W/(m·K) 76 Os osmium use 87.6 W/(m·K) CRC 0.876 W/(cm·K) LNG 87.6 W/(m·K) WEL 88 W/(m·K) 77 Ir iridium use 147 W/(m·K) CRC 1.47 W/(cm·K) LNG 147 W/(m·K) WEL 150 W/(m·K) 78 Pt platinum use 71.6 W/(m·K) CRC 0.716 W/(cm·K) LNG 71.6 W/(m·K) WEL 72 W/(m·K) 79 Au gold use 318 W/(m·K) CRC 3.17 W/(cm·K) LNG 318 W/(m·K) WEL 320 W/(m·K) 80 Hg mercury use 8.30 W/(m·K) CRC 0.0834 W/(cm·K) LNG 8.30 W/(m·K) WEL 8.3 W/(m·K) 81 Tl thallium use 46.1 W/(m·K) CRC 0.461 W/(cm·K) LNG 46.1 W/(m·K) WEL 46 W/(m·K) 82 Pb lead use 35.3 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.3 W/(m·K) WEL 35 W/(m·K) 83 Bi bismuth use 7.97 W/(m·K) CRC 0.0787 W/(cm·K) LNG 7.97 W/(m·K) WEL 8 W/(m·K) 84 Po polonium use CRC 0.20 W/(cm·K) LNG 0.2 W/(m·K) 85 At astatine use 1.7 W/(m·K) LNG 1.7 W/(m·K) WEL 2 W/(m·K) 86 Rn radon use 3.61 mW/(m·K) LNG 0.00361 W/(m·K) WEL 0.00361 W/(m·K) 88 Ra radium use 18.6 W/(m·K) LNG 18.6 W/(m·K) WEL 19 W/(m·K) 89 Ac actinium use 12 W/(m·K) LNG 12 W/(m·K) WEL 12 W/(m·K) 90 Th thorium use 54.0 W/(m·K) CRC 0.540 W/(cm·K) LNG 54.0 W/(m·K) WEL 54 W/(m·K) 91 Pa protactinium use 47 W/(m·K) LNG 47 W/(m·K) WEL 47 W/(m·K) 92 U uranium use 27.5 W/(m·K) CRC 0.276 W/(cm·K) LNG 27.5 W/(m·K) WEL 27 W/(m·K) 93 Np neptunium use 6.3 W/(m·K) CRC 0.063 W/(cm·K) LNG 6.3 W/(m·K) WEL 6 W/(m·K) 94 Pu plutonium use 6.74 W/(m·K) CRC 0.0674 W/(cm·K) LNG 6.74 W/(m·K) WEL 6 W/(m·K) 95 Am americium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) 97 Bk berkelium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) ==Notes== * Ref. CRC: Values refer to 27 °C unless noted. In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. However the standard enthalpy of combustion is readily measurable using bomb calorimetry. Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. This calculation has a tacit assumption of ideal solution between reactants and products where the enthalpy of mixing is zero. J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method. == Use in calculation for other reactions == The standard enthalpy change of any reaction can be calculated from the standard enthalpies of formation of reactants and products using Hess's law. The heat of reaction is then minus the sum of the standard enthalpies of formation of the reactants (each being multiplied by its respective stoichiometric coefficient, ) plus the sum of the standard enthalpies of formation of the products (each also multiplied by its respective stoichiometric coefficient), as shown in the equation below: :\Delta_{\text{r}} H^{\ominus } = \sum u \Delta_{\text{f}} H^{\ominus }(\text{products}) - \sum u \Delta_{\text{f}} H^{\ominus}(\text{reactants}). J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products Elements in their standard states make no contribution to the enthalpy calculations for the reaction, since the enthalpy of an element in its standard state is zero. From these sources: :a - K.K. Kelley, Bur. Mines Bull. 383, (1935). :b - :c - Brewer, The thermodynamic and physical properties of the elements, Report for the Manhattan Project, (1946). :d - :e - :f - :g - ; :h - :i - . :j - :k - Int. National Critical Tables, vol. 3, p. 306, (1928). :l - :m - :n - :o - :p - :q - :r - :s - H.A. Jones, I. Langmuir, Gen. Electric Rev., vol. 30, p. 354, (1927). == See also == Category:Properties of chemical elements Category:Chemical element data pages This is true for all enthalpies of formation. :(d) N.B. Vargaftik, Int. J. Thermophys. 11, 467, (1990). ===LNG=== J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6; Table 6.5 Critical Properties ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; D. Ambrose, M.B. Ewing, M.L. McGlashan, Critical constants and second virial coefficients of gases (retrieved Dec 2005) ===SMI=== W.E. Forsythe (ed.), Smithsonian Physical Tables 9th ed., online version (1954; Knovel 2003). For example, the standard enthalpy of formation of carbon dioxide is the enthalpy of the following reaction under the above conditions: :C(s, graphite) + O2(g) -> CO2(g) All elements are written in their standard states, and one mole of product is formed.	0.33333333	7200	116.0	1068	4	C
A car tyre (i.e. an automobile tire) was inflated to a pressure of $24 \mathrm{lb} \mathrm{in}^{-2}$ $(1.00 \mathrm{atm}=14.7 \mathrm{lb} \mathrm{in}^{-2})$ on a winter's day when the temperature was $-5^{\circ} \mathrm{C}$. What pressure will be found, assuming no leaks have occurred and that the volume is constant, on a subsequent summer's day when the temperature is $35^{\circ} \mathrm{C}$?	So if the tire was filled at 80 °F to 32 psi (or 47 psi absolute when we add atmospheric pressure), the change would be 4.7 psi for this 30 Celsius degree change, or 0.16 psi per Celsius degree or 0.1 psi per Fahrenheit degree or 1 psi for every 10 Fahrenheit degrees. Hence, for a tire filled to 32 psi, the approximation usually made is that within the range of normal atmospheric temperatures and pressures: Tire pressure increases 1 psi for each 10 Fahrenheit degree increase in temperature, or conversely decreases 1 psi for each 10 Fahrenheit degree decrease in temperature and in SI units, tire pressure increases 1.1 kPa for each 1 Celsius degree increase in temperature, or conversely decreases 1.1 kPa for each 1 Celsius degree decrease in temperature. Ambient temperature affects the cold tire pressure. To understand this, assume the tire was filled when it was 300 kelvin (approximately 27 degrees Celsius or 80 degrees Fahrenheit). From the table below, one can see that these are only approximations: == Variation of tire pressure with temperature in Fahrenheit and Celsius == (Assuming atmospheric pressure is 14.696 psi, or 101.3 kPA.) Most passenger cars are recommended to have a tire pressure of 30 to 35 pounds per square inch when not warmed by driving. 40% of passenger cars have at least one tire under-inflated by 6 psi or more. Cold tire absolute pressure (gauge pressure plus atmospheric pressure) varies directly with the absolute temperature, measured in kelvin. For tires that need inflation greater than 32 psi it might be easier to use a Rule of Thumb of 2% pressure change for a change of 10 degrees Fahrenheit. Cold inflation pressure is the inflation pressure of tires before a car is driven and the tires (tyres) warmed up. From physics, the ideal gas law states that PV = nRT, where P is absolute pressure, T is absolute temperature, V is the volume (assumed to be relatively constant in the case of a tire), and nR is constant for a given number of molecules of gas. The European Union concludes that tire under-inflation today is responsible for over 20 million liters of unnecessarily-burned fuel, dumping over 2 million tonnes of CO2 into the atmosphere, and for 200 million tires being prematurely wasted worldwide. If the temperature varies 10% (i.e., by 30 kelvins [also 30 degrees Celsius or 54 degrees Fahrenheit]), the pressure varies 10%. Tires do not only leak air if punctured, they also leak air naturally, and over a year, even a typical new, properly mounted tire can lose from 20 to 60 kPa (3 to 9 psi), roughly 10% or even more of its initial pressure. * Environmental efficiency: Under-inflated tires, as estimated by the US Department of Transportation, release over 26 billion kilograms (57.5 billion pounds) of unnecessary carbon-monoxide pollutants into the atmosphere each year in the United States alone. Cold inflation may refer to: * Cold inflation pressure, the pressure in tires before they are warmed up by the car's motion; * One of the two dynamical realizations of cosmological inflation the other being warm inflation. Some units also measure and alert temperatures of the tire as well. These systems can identify under-inflation for each individual tire. Extreme under-inflation can even lead to thermal and mechanical overload caused by overheating and subsequent, sudden destruction of the tire itself. Further, a difference of in pressure on a set of duals literally drags the lower pressured tire 2.5 metres per kilometre (13 feet per mile). The European Union reports that an average under-inflation of 40 kPa produces an increase of fuel consumption of 2% and a decrease of tire life of 25%. The frost point for a given parcel of air is always higher than the dew point, as breaking the stronger bonding between water molecules on the surface of ice compared to the surface of (supercooled) liquid water requires a higher temperature. == See also == * Bubble point * Carburetor heat * Hydrocarbon dew point * Psychrometrics * Thermodynamic diagrams ==References== ==External links== * Often Needed Answers about Temp, Humidity & Dew Point from the sci.geo.meteorology Category:Atmospheric thermodynamics Category:Temperature Category:Psychrometrics Category:Threshold temperatures Category:Gases Category:Meteorological data and networks Category:Humidity and hygrometry sv:Luftfuktighet#Daggpunkt The Boyle temperature is formally defined as the temperature for which the second virial coefficient, B_{2}(T), becomes zero.	30	4.49	0.00131	2	0.5768	A
Suppose that $10.0 \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})$ is confined to $4.860 \mathrm{dm}^3$ at $27^{\circ} \mathrm{C}$. Predict the pressure exerted by the ethane from the van der Waals equations of state.	The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. In the derivation of ideal gas laws on the basis of kinetic theory of gases some assumption have been made. ===Compressibility factor=== The compressibility factor for the Van der Waals equation is: : Z = \frac{P V_m}{RT} = \frac{V_m}{V_m-b} - \frac{a}{V_m RT} Or in reduced form by substitution of P_r=P/P_c, T_r=T/T_c, V_r=V_m/V_c: : Z = \frac{V_r}{V_r-\frac{1}{3}} - \frac{9}{8 V_r T_r} At the critical point: : Z_c = \frac{P_c V_c}{RT_c} = \frac{3}{8} = 0.375 ==Validity== The Van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.. Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and b (volume occupied by molecules) values, then a and b for the mixture can be calculated as :m = total number of moles of gas present, :for each i, m_i = number of moles of gas i present, and x_i = \frac{m_i}{m} :a = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{a_i a_j}) :b = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{b_i b_j}) and the rule of adding partial pressures becomes invalid if the numerical result of the equation \left(p + ({n^2 a}/{V^2})\right)\left(V-nb\right) = nRT is significantly different from the ideal gas equation pV = nRT . ===Reduced form=== The Van der Waals equation can also be expressed in terms of reduced properties: :\left(P_r + \frac{3}{V_r^2}\right)\left(V_r-\frac{1}{3}\right) = \frac{8}{3}T_r The equation in reduced form is exactly the same for every gas, this is consistent with the Theorem of corresponding states. However, near the phase transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the Van der Waals equation fails to accurately model observed experimental behavior. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. Van der Waals forces are responsible for certain cases of pressure broadening (van der Waals broadening) of spectral lines and the formation of van der Waals molecules. These van der Waals interactions are up to 40 times stronger than in H2, which has only one valence electron, and they are still not strong enough to achieve an aggregate state other than gas for Xe under standard conditions. The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. An isotherm of the Van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal. == Other parameters, forms and applications == ===Other thermodynamic parameters=== We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. The ideal gas law states that the volume V occupied by n moles of any gas has a pressure P at temperature T given by the following relationship, where R is the gas constant: :PV=nRT To account for the volume occupied by real gas molecules, the Van der Waals equation replaces V/n in the ideal gas law with (V_m-b), where Vm is the molar volume of the gas and b is the volume occupied by the molecules of one mole: :P(V_m - b)=R T thumb\|Van der Waals equation on a wall in Leiden The second modification made to the ideal gas law accounts for interaction between molecules of the gas. Above the critical temperature, TC, the Van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region. Blaney and G. E. Ewing, Annual Review of Physical Chemistry, Vol. 27, pp. 553-586 (1976): Van der Waals Molecules. Even with its acknowledged shortcomings, the pervasive use of the Van der Waals equation in standard university physical chemistry textbooks makes clear its importance as a pedagogic tool to aid understanding fundamental physical chemistry ideas involved in developing theories of vapour–liquid behavior and equations of state. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for the finite size of the molecules. * Van der Waals forces are independent of temperature except for dipole-dipole interactions. In this case specific volume changes are small and it can be written in a simplified form: :(p+A)(V-B)=CT, \, where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters. == See also == * Gas laws * Ideal gas * Inversion temperature * Iteration * Maxwell construction * Real gas * Theorem of corresponding states * Van der Waals constants (data page) * Redlich–Kwong equation of state ==References== ==Further reading== * * . J/(mol K) Liquid properties Std enthalpy change of formation, ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy, S ~~o~~ liquid 126.7 J/(mol K) Heat capacity, cp 68.5 J/(mol K) at −179 °C Gas properties Std enthalpy change of formation, ΔfH ~~o~~ gas −83.8 kJ/mol Standard molar entropy, S ~~o~~ gas 229.6 J/(mol K) Enthalpy of combustion, ΔcH ~~o~~ −1560.7 kJ/mol Heat capacity, cp 52.49 J/(mol K) at 25 °C van der Waals' constantsLange's Handbook of Chemistry 10th ed, pp 1522-1524 a = 556.2 L2 kPa/mol2 b = 0.06380 L/mol ==Vapor pressure of liquid== P in mm Hg 1 10 40 100 400 760 1520 3800 7600 15200 30400 45600 T in °C −159.5 −142.9 −129.8 −119.3 −99.6 −88.6 −75.0 −52.8 −32.0 −6.4 23.6 — Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. == Melting point data == Mean value for acceptable data: −183.01 °C (90.14 K). The VRT spectroscopic study of Van der Waals molecules is one of the most direct routes to the understanding of intermolecular forces. == See also == * Van der Waals radius * Van der Waals strain * Van der Waals surface * –articles about specific chemicals * Researchers active in this field: Donald Levy Richard J. Saykally Richard Smalley William Klemperer == References == == Further reading == * So far three special issues of Chemical Reviews have been devoted to vdW molecules: I. Vol. 88(6) (1988). * Early reviews of vdW molecules: G. E. Ewing, Accounts of Chemical Research, Vol. 8, pp. 185-192, (1975): Structure and Properties of Van der Waals molecules. A Van der Waals molecule is a weakly bound complex of atoms or molecules held together by intermolecular attractions such as Van der Waals forces or by hydrogen bonds.	-11.2	1410	1.4	35.2	4.5	D
Use the van der Waals parameters for chlorine to calculate approximate values of the radius of a $\mathrm{Cl}_2$ molecule regarded as a sphere.	Values from other sources may differ significantly (see text) The van der Waals radius, r, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It may be calculated for atoms if the Van der Waals radius is known, and for molecules if its atoms radii and the inter- atomic distances and angles are known. These various methods give values for the van der Waals radius which are similar (1–2 Å, 100–200 pm) but not identical. The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances, and angles) are known. Petitjean, On the Analytical Calculation of Van der Waals Surfaces and Volumes: Some Numerical Aspects, Journal of Computational Chemistry, Volume 15, Number 5, 1994, pp. 507–523. == External links == * VSAs for various molecules by Anton Antonov, The Wolfram Demonstrations Project, 2007. Gas d (Å) b (cmmol) V (Å) r (Å) Hydrogen 0.74611 26.61 44.19 2.02 Nitrogen 1.0975 39.13 64.98 2.25 Oxygen 1.208 31.83 52.86 2.06 Chlorine 1.988 56.22 93.36 2.39 van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. * Analytical calculation of Van der Waals surfaces and volumes. Van der Waals radii Element radius (Å) Hydrogen 1.2 (1.09) Carbon 1.7 Nitrogen 1.55 Oxygen 1.52 Fluorine 1.47 Phosphorus 1.8 Sulfur 1.8 Chlorine 1.75 Copper 1.4 Van der Waals radii taken from Bondi's compilation (1964). van der Waals radii Element radius (Å) Hydrogen 1.2 (1.09) Carbon 1.7 Nitrogen 1.55 Oxygen 1.52 Fluorine 1.47 Phosphorus 1.8 Sulfur 1.8 Chlorine 1.75 Copper 1.4 van der Waals radii taken from Bondi's compilation (1964). Useful tabulated values of Van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will be seen to present different values for the Van der Waals radius of the same atom. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the Avogadro constant N. Indeed, there is no reason to assume that the van der Waals radius is a fixed property of the atom in all circumstances: rather, it tends to vary with the particular chemical environment of the atom in any given case. === Van der Waals equation of state === The van der Waals equation of state is the simplest and best-known modification of the ideal gas law to account for the behaviour of real gases: \left (p + a\left (\frac{n}{\tilde{V}}\right )^2\right ) (\tilde{V} - nb) = nRT, where is pressure, is the number of moles of the gas in question and and depend on the particular gas, \tilde{V} is the volume, is the specific gas constant on a unit mole basis and the absolute temperature; is a correction for intermolecular forces and corrects for finite atomic or molecular sizes; the value of equals the van der Waals volume per mole of the gas. Hence the molar van der Waals volume, which only counts the volume occupied by the atoms or molecules, is usually about times smaller than the molar volume for a gas at standard temperature and pressure. ==Table of van der Waals radii== == Methods of determination == Van der Waals radii may be determined from the mechanical properties of gases (the original method), from the critical point, from measurements of atomic spacing between pairs of unbonded atoms in crystals or from measurements of electrical or optical properties (the polarizability and the molar refractivity). Blaney and G. E. Ewing, Annual Review of Physical Chemistry, Vol. 27, pp. 553-586 (1976): Van der Waals Molecules. The van der Waals constant b volume can be used to calculate the van der Waals volume of an atom or molecule with experimental data derived from measurements on gases. As well, it has been argued that the Van der Waals radius is not a fixed property of an atom in all circumstances, rather, that it will vary with the chemical environment of the atom. == Gallery == File:3D ammoniac.PNG\|alt=Ammonia, van-der-Waals-based model\|Ammonia, NH3, space- filling, Van der Waal's-based representation, nitrogen (N) in blue, hydrogen (H) in white. The van der Waals volume of an atom or molecule may also be determined by experimental measurements on gases, notably from the van der Waals constant b, the polarizability α, or the molar refractivity A. For a molecule, it is the volume enclosed by the van der Waals surface. Tabulated values of van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will often have different values for the van der Waals radius of the same atom. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases.	2	210	22.0	0.8561	0.139	E
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \mathrm{~mol}$ of diatomic perfect gas molecules at $200 \mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \mathrm{~K}$. Given that $C_{V, \mathrm{~m}}=27.5 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, calculate $\Delta U$.	Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. A calorically perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, and enthalpy H that are functions of temperature only, i.e., U = U(T), H = H(T) * has heat capacities C_V, C_P that are constant, i.e., dU = C_V dT, dH = C_P dT and \Delta U = C_V \Delta T, \Delta H = C_P \Delta T, where \Delta is any finite (non-differential) change in each quantity. Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. From both statistical mechanics and the simpler kinetic theory of gases, we expect the heat capacity of a monatomic ideal gas to be constant, since for such a gas only kinetic energy contributes to the internal energy and to within an arbitrary additive constant U = (3/2) n R T , and therefore C_V = (3/2) n R , a constant. The temperature dependence at constant pressure is \left(\frac{\partial \ln f}{\partial T}\right)_P = \frac{\Delta H_\mathrm{m}}{R T^2}, where is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum. This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure. For a diatomic gas, often 5 degrees of freedom are assumed to contribute at room temperature since each molecule has 3 translational and 2 rotational degrees of freedom, and the single vibrational degree of freedom is often not included since vibrations are often not thermally active except at high temperatures, as predicted by quantum statistical mechanics. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). * Values from CRC refer to "100 kPa (1 bar or 0.987 standard atmospheres)". Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of nitrogen as an ideal gas at . In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. This error is corrected in the above equation. ==Measurement== The fugacity can be deduced from measurements of volume as a function of pressure at constant temperature. Lange indirectly defines the values to be at a standard state pressure of "1 atm (101325 Pa)", although citing the same NBS and JANAF sources among others. A conversion factor is included into the original first coefficients of the equations to provide the pressure in pascals (CR2: 5.006, SMI: -0.875). Thus we observe that for a monatomic gas, with 3 translational degrees of freedom per atom: : \gamma = \frac{5}{3} = 1.6666\ldots, As an example of this behavior, at 273 K (0 °C) the noble gases He, Ne, and Ar all have nearly the same value of , equal to 1.664. When calculating the fugacity of the compressed phase, one can generally assume the volume is constant. == Specific heat capacity == J/(mol·K) J/(g·K) 1 H hydrogen (H2, gas) use 28.836 14.304 CRC 28.836 14.304 WEL 28.82 LNG 28.84 2 He helium (gas) use 20.786 5.193 CRC 20.786 5.193 WEL 20.786 LNG 20.786 3 Li lithium use 24.860 3.582 CRC 24.860 3.582 WEL 24.8 LNG 24.8 4 Be beryllium use 16.443 1.825 CRC 16.443 1.825 WEL 16.4 LNG 16.38 5 B boron (rhombic) use 11.087 1.026 CRC 11.087 1.026 WEL 11.1 LNG 11.1 6 C carbon (graphite) use 8.517 0.709 CRC 8.517 0.709 WEL 8.53 LNG 8.517 6 C carbon (diamond, nonstd state) use 6.115 0.509 WEL 6.115 LNG 6.116 7 N nitrogen (N2, gas) use 29.124 1.040 CRC 29.124 1.040 WEL 29.12 LNG 29.124 8 O oxygen (O2, gas) use 29.378 0.918 CRC 29.378 0.918 WEL 29.4 LNG 29.4 9 F fluorine (F2, gas) use 31.304 0.824 CRC 31.304 0.824 WEL 31.3 LNG 31.30 10 Ne neon (gas) use 20.786 1.030 CRC 20.786 1.030 WEL 20.786 LNG 20.786 11 Na sodium use 28.230 1.228 CRC 28.230 1.228 WEL 28.2 LNG 28.15 12 Mg magnesium use 24.869 1.023 CRC 24.869 1.023 WEL 24.9 LNG 24.87 13 Al aluminium use 24.200 0.897 CRC 24.200 0.897 WEL 24.4 LNG 24.4 14 Si silicon use 19.789 0.705 CRC 19.789 0.705 WEL 20.0 LNG 20.00 15 P phosphorus (white) use 23.824 0.769 CRC 23.824 0.769 WEL 23.84 LNG 23.83 15 P phosphorus (red, nonstd state) use 21.19 0.684 WEL 21.2 LNG 21.19 16 S sulfur (rhombic) use 22.75 0.710 CRC 22.75 0.710 WEL 22.6 LNG 22.60 16 S sulfur (monoclinic, nonstd state) use 23.23 0.724 LNG 23.23 17 Cl chlorine (Cl2 gas) use 33.949 0.479 CRC 33.949 0.479 WEL 33.91 LNG 33.95 18 Ar argon (gas) use 20.786 0.520 CRC 20.786 0.520 WEL 20.786 LNG 20.79 19 K potassium use 29.600 0.757 CRC 29.600 0.757 WEL 29.6 LNG 29.60 20 Ca calcium use 25.929 0.647 CRC 25.929 0.647 WEL 25.3 LNG 25.9 21 Sc scandium use 25.52 0.568 CRC 25.52 0.568 WEL 25.5 LNG 25.52 22 Ti titanium use 25.060 0.523 CRC 25.060 0.523 WEL 25.0 LNG 25.0 23 V vanadium use 24.89 0.489 CRC 24.89 0.489 WEL 24.9 LNG 24.90 24 Cr chromium use 23.35 0.449 CRC 23.35 0.449 WEL 23.3 LNG 23.43 25 Mn manganese use 26.32 0.479 CRC 26.32 0.479 WEL 26.3 LNG 26.30 26 Fe iron (alpha) use 25.10 0.449 CRC 25.10 0.449 WEL 25.1 LNG 25.09 27 Co cobalt use 24.81 0.421 CRC 24.81 0.421 WEL 24.8 LNG 24.8 28 Ni nickel use 26.07 0.444 CRC 26.07 0.444 WEL 26.1 LNG 26.1 29 Cu copper use 24.440 0.385 CRC 24.440 0.385 WEL 24.43 LNG 24.44 30 Zn zinc use 25.390 0.388 CRC 25.390 0.388 WEL 25.4 LNG 25.40 31 Ga gallium use 25.86 0.371 CRC 25.86 0.371 WEL 25.9 LNG 26.06 32 Ge germanium use 23.222 0.320 CRC 23.222 0.320 WEL 23.35 LNG 23.3 33 As arsenic (alpha, gray) use 24.64 0.329 CRC 24.64 0.329 WEL 24.6 LNG 24.64 34 Se selenium (hexagonal) use 25.363 0.321 CRC 25.363 0.321 WEL 25.36 LNG 24.98 35 Br bromine use (Br2) 75.69 0.474 CRC 36.057 0.226 WEL (liquid) 75.69 WEL (Br2, gas, nonstd state) 36.0 LNG (Br2, liquid) 75.67 36 Kr krypton (gas) use 20.786 0.248 CRC 20.786 0.248 WEL 20.786 LNG 20.786 37 Rb rubidium use 31.060 0.363 CRC 31.060 0.363 WEL 31.1 LNG 31.06 38 Sr strontium use 26.4 0.301 CRC 26.4 0.301 WEL 26 LNG 26.79 39 Y yttrium use 26.53 0.298 CRC 26.53 0.298 WEL 26.5 LNG 26.51 40 Zr zirconium use 25.36 0.278 CRC 25.36 0.278 WEL 25.4 LNG 25.40 41 Nb niobium use 24.60 0.265 CRC 24.60 0.265 WEL 24.6 LNG 24.67 42 Mo molybdenum use 24.06 0.251 CRC 24.06 0.251 WEL 24.1 LNG 24.13 43 Tc technetium use 24.27 LNG 24.27 44 Ru ruthenium use 24.06 0.238 CRC 24.06 0.238 WEL 24.1 LNG 24.1 45 Rh rhodium use 24.98 0.243 CRC 24.98 0.243 WEL 25.0 LNG 24.98 46 Pd palladium use 25.98 0.244 CRC 25.98 0.246 [sic] WEL 26.0 LNG 25.94 47 Ag silver use 25.350 0.235 CRC 25.350 0.235 WEL 25.4 LNG 25.4 48 Cd cadmium use 26.020 0.232 CRC 26.020 0.232 WEL 26.0 LNG 25.9 49 In indium use 26.74 0.233 CRC 26.74 0.233 WEL 26.7 LNG 26.7 50 Sn tin (white) use 27.112 0.228 CRC 27.112 0.228 WEL 27.0 LNG 26.99 50 Sn tin (gray, nonstd state) use 25.77 0.217 WEL 25.8 LNG 25.77 51 Sb antimony use 25.23 0.207 CRC 25.23 0.207 WEL 25.2 LNG 25.2 52 Te tellurium use 25.73 0.202 CRC 25.73 0.202 WEL 25.7 LNG 25.70 53 I iodine use (I2) 54.44 0.214 CRC 36.888 0.145 WEL (solid) 54.44 WEL (I2, gas, nonstd state) 36.9 LNG (I2, solid) 54.44 LNG (I2, gas, nonstd state) 36.86 54 Xe xenon (gas) use 20.786 0.158 CRC 20.786 0.158 WEL 20.786 LNG 20.786 55 Cs caesium use 32.210 0.242 CRC 32.210 0.242 WEL 32.2 LNG 32.20 56 Ba barium use 28.07 0.204 CRC 28.07 0.204 WEL 28.1 LNG 28.10 57 La lanthanum use 27.11 0.195 CRC 27.11 0.195 WEL 27.1 LNG 27.11 58 Ce cerium (gamma, fcc) use 26.94 0.192 CRC 26.94 0.192 WEL 26.9 LNG 26.9 59 Pr praseodymium use 27.20 0.193 CRC 27.20 0.193 WEL 27.2 LNG 27.20 60 Nd neodymium use 27.45 0.190 CRC 27.45 0.190 WEL 27.4 LNG 27.5 62 Sm samarium use 29.54 0.197 CRC 29.54 0.197 WEL 29.5 LNG 29.54 63 Eu europium use 27.66 0.182 CRC 27.66 0.182 WEL 27.7 LNG 27.66 64 Gd gadolinium use 37.03 0.236 CRC 37.03 0.236 WEL 37.0 LNG 37.03 65 Tb terbium use 28.91 0.182 CRC 28.91 0.182 WEL 28.9 LNG 28.91 66 Dy dysprosium use 27.7 0.170 CRC 27.7 0.170 WEL 27.2 LNG 27.7 67 Ho holmium use 27.15 0.165 CRC 27.15 0.165 WEL 27.2 LNG 27.15 68 Er erbium use 28.12 0.168 CRC 28.12 0.168 WEL 28.1 LNG 28.12 69 Tm thulium use 27.03 0.160 CRC 27.03 0.160 WEL 27.0 LNG 27.03 70 Yb ytterbium use 26.74 0.155 CRC 26.74 0.155 WEL 26.7 LNG 26.74 71 Lu lutetium use 26.86 0.154 CRC 26.86 0.154 WEL 26.9 LNG 26.86 72 Hf hafnium (hexagonal) use 25.73 0.144 CRC 25.73 0.144 WEL 25.7 LNG 25.69 73 Ta tantalum use 25.36 0.140 CRC 25.36 0.140 WEL 25.4 LNG 25.40 74 W tungsten use 24.27 0.132 CRC 24.27 0.132 WEL 24.3 LNG 24.3 75 Re rhenium use 25.48 0.137 CRC 25.48 0.137 WEL 25.5 LNG 25.5 76 Os osmium use 24.7 0.130 CRC 24.7 0.130 WEL 25 LNG 24.7 77 Ir iridium use 25.10 0.131 CRC 25.10 0.131 WEL 25.1 LNG 25.06 78 Pt platinum use 25.86 0.133 CRC 25.86 0.133 WEL 25.9 79 Au gold use 25.418 0.129 CRC 25.418 0.129 WEL 25.42 LNG 25.36 80 Hg mercury (liquid) use 27.983 0.140 CRC 27.983 0.140 WEL 27.98 LNG 28.00 81 Tl thallium use 26.32 0.129 CRC 26.32 0.129 WEL 26.3 LNG 26.32 82 Pb lead use 26.650 0.129 CRC 26.650 0.129 WEL 26.4 LNG 26.84 83 Bi bismuth use 25.52 0.122 CRC 25.52 0.122 WEL 25.5 LNG 25.5 84 Po polonium use 26.4 LNG 26.4 86 Rn radon (gas) use 20.786 0.094 CRC 20.786 0.094 WEL 20.79 LNG 20.79 87 Fr francium use 31.80 LNG 31.80 89 Ac actinium use 27.2 0.120 CRC 27.2 0.120 WEL 27.2 LNG 27.2 90 Th thorium use 26.230 0.113 CRC 26.230 0.113 WEL 27.3 LNG 27.32 92 U uranium use 27.665 0.116 CRC 27.665 0.116 WEL 27.7 LNG 27.66 93 Np neptunium use 29.46 LNG 29.46 94 Pu plutonium use 35.5 LNG 35.5 95 Am americium use 62.7 LNG 62.7 == Notes == All values refer to 25 °C and to the thermodynamically stable standard state at that temperature unless noted.	524	+65.49	0.33333333	635.7	+4.1	E
1.7(a) In an attempt to determine an accurate value of the gas constant, $R$, a student heated a container of volume $20.000 \mathrm{dm}^3$ filled with $0.25132 \mathrm{g}$ of helium gas to $500^{\circ} \mathrm{C}$ and measured the pressure as $206.402 \mathrm{cm}$ of water in a manometer at $25^{\circ} \mathrm{C}$. Calculate the value of $R$ from these data. (The density of water at $25^{\circ} \mathrm{C}$ is $0.99707 \mathrm{g} \mathrm{cm}^{-3}$; a manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid.)	Note that data could have been collected with three different amounts of the same gas, which would have rendered this experiment easy to do in the eighteenth century. ==History== == See also == * Thermodynamic instruments * Boyle's law * Combined gas law * Gay-Lussac's law * Avogadro's law * Ideal gas law ==References== Category:Thermometers Category:Gases fr:Thermomètre#Thermomètre à gaz thumb\|400px\|Diagram showing pressure difference induced by a temperature difference. thumb\|upright=1.75\|An illustration of Dalton's law using the gases of air at sea level. :V \propto T\, or :\frac{V}{T}=k V is the volume, T is the thermodynamic temperature, k is the constant for the system. k is not a fixed constant across all systems and therefore needs to be found experimentally for a given system through testing with known temperature values. ==Pressure Thermometer and Absolute Zero== thumb\|left\|180px\|Plots of pressure vs temperature for three different gas samples extrapolate to absolute zero. thumb\|500px\|Two variants of a gas thermometer A gas thermometer is a thermometer that measures temperature by the variation in volume or pressure of a gas. ==Volume Thermometer== This thermometer functions by Charles's Law. Gas volume corrector - device for calculating, summing and determining increments of gas volume, measured by gas meter if it were operating base conditions. The psychrometric constant \gamma relates the partial pressure of water in air to the air temperature. Using Charles's Law, the temperature can be measured by knowing the volume of gas at a certain temperature by using the formula, written below. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings. :: \gamma =\frac{ \left( c_p \right)_{air} * P }{ \lambda_v * MW_{ratio} } : \gamma = psychrometric constant [kPa °C−1], : P = atmospheric pressure [kPa], : \lambda_v = latent heat of water vaporization, 2.45 [MJ kg−1], : c_p = specific heat of air at constant pressure, [MJ kg−1 °C−1], : MW_{ratio} = ratio molecular weight of water vapor/dry air = 0.622. The constant volume gas thermometer plays a crucial role in understanding how absolute zero could be discovered long before the advent of cryogenics. Consider a graph of pressure versus temperature made not far from standard conditions (well above absolute zero) for three different samples of any ideal gas (a, b, c). For this purpose, uses as input the gas volume, measured by the gas meter and other parameters such as: gas pressure and temperature. To the extent that the gas is ideal, the pressure depends linearly on temperature, and the extrapolation to zero pressure occurs at absolute zero. Charles's Law states that when the temperature of a gas increases, so does the volume. . The prover determines the meter factor, which is the volume of air passed divided by the volume of air measured.Fundamentals of Meter Provers and Proving Methods https://asgmt.com/wp-content/uploads/2018/05/070.pdf ==Types== ===Manual bell prover=== Since the early 1900s, bell provers have been the most common reference standard used in gas meter proving, and has provided standards for the gas industry that is unfortunately susceptible to a myriad of immeasurable uncertainties. Since atmospheric pressure, P, depends upon altitude, so does \gamma. There are two types of gas volume correctors: Type 1- gas volume corrector with specific types of transducers for pressure and temperature or temperature only. Although \left( c_p \right)_{H_2 O} is constant, varied air composition results in varied \left( c_p \right)_{air} . A gas meter prover is a device to verify the accuracy of a gas meter. Translating it to the correct levels of the device that is holding the gas. In particular, the short average distances between molecules increases intermolecular forces between gas molecules enough to substantially change the pressure exerted by them, an effect not included in the ideal gas model. ==See also== * * * * * * * * * ==References== Category:Gas laws Category:Physical chemistry Category:Engineering thermodynamics de:Partialdruck#Dalton-Gesetz et:Daltoni seadus When proving a meter using a manually controlled bell, an operator must first fill the bell with a controlled air supply or raise it manually by opening a valve and pulling a chained mechanism, seal the bell and meter and check the sealed system for leaks, determine the flow rate needed for the meter, install a special flow-rate cap on the meter outlet, note the starting points of both the bell scale and meter index, release the bell valve to pass air through the meter, observe the meter index and calculate the time it takes to pass the predetermined amount of air, then manually calculate the meter's proof accounting for bell air and meter temperature and in some cases other environmental factors.	-6.42	0.66666666666	15.0	8.3147	1260	D
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The standard enthalpy of combustion of solid phenol $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}\right)$ is $-3054 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298 \mathrm{~K}_{\text {and }}$ its standard molar entropy is $144.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. Calculate the standard Gibbs energy of formation of phenol at $298 \mathrm{~K}$.	Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. However the standard enthalpy of combustion is readily measurable using bomb calorimetry. The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? :ΔG˚ = -RTln(Keq) :ΔG˚ = (2.303)RT(pKeq) :ΔG˚ = -nFE˚1/2 Useful conversion factors: :-23.06 (kcal/mol)(e−)−1(V)−1 :1.37(pKeq) kcal/mol :1.37[-log(Keq)] kcal/mol == References == Category:Thermodynamic cycles Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. The NIST Chemistry WebBook (see link below) is an online resource that contains standard enthalpy of formation for various compounds along with the standard absolute entropy for these compounds from which the standard Gibbs free energy of formation can be calculated. J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). The standard Gibbs free energy of formation (Gf°) of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 1 bar of pressure and the specified temperature, usually 298.15 K or 25 °C). For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol . == Hess's law == For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. The standard enthalpy of formation is then determined using Hess's law. In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absorbed in any changes between different crystal structures). == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. The table below lists the standard Gibbs function of formation for several elements and chemical compounds and is taken from Lange's Handbook of Chemistry. However O2 is an element in its standard state, so that \Delta_{\text{f}} H^{\ominus }(\text{O}_2) = 0, and the heat of reaction is simplified to :\Delta_{\text{r}} H^{\ominus } = [\Delta_{\text{f}} H^{\ominus }(\text{CO}_2) + 2\Delta_{\text{f}} H^{\ominus } (\text{H}_2{}\text{O})] - \Delta_{\text{f}} H^{\ominus }(\text{CH}_4), which is the equation in the previous section for the enthalpy of combustion \Delta_{\text{comb}}H^{\ominus }. == Key concepts for enthalpy calculations == When a reaction is reversed, the magnitude of ΔH stays the same, but the sign changes.	-50	0.3085	537.0	200	258.14	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \mathrm{~mol} \mathrm{CO}_2(\mathrm{~g})$, initially at $25^{\circ} \mathrm{C}$ and $10 \mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \mathrm{~m}}=28.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and calculate $\Delta U$.	In the second case, the gas will both heat and expand, causing the piston to do mechanical work on the atmosphere. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. We assume the expansion occurs without exchange of heat (adiabatic expansion). The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. To return to the target temperature (still with a free piston), the air must be heated, but is no longer under constant volume, since the piston is free to move as the gas is reheated. Consider the difference between adding heat to the gas with a locked piston and adding heat with a piston free to move, so that pressure remains constant. The piston is now freed and moves outwards, stopping as the pressure inside the chamber reaches atmospheric pressure. For real gases the equation of state will depart from the simpler one, and the result above derived for an ideal gas will only be a good approximation provided that (a) the typical size of the molecule is negligible compared to the average distance between the individual molecules, and (b) the short range behavior of the inter-molecular potential can be neglected, i.e., when the molecules can be considered to rebound elastically off each other during molecular collisions. The heat that is added to the gas goes only partly into heating the gas, while the rest is transformed into the mechanical work performed by the piston. Since the piston cannot move, the volume is constant. CO-0.40-0.22 is a high velocity compact gas cloud near the centre of the Milky Way. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. The temperature dependence at constant pressure is \left(\frac{\partial \ln f}{\partial T}\right)_P = \frac{\Delta H_\mathrm{m}}{R T^2}, where is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum. The fugacities commonly obey a similar law called the Lewis and Randall rule: f_i = y_i f^*_i, where is the fugacity that component would have if the entire gas had that composition at the same temperature and pressure. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. thumb\|Jets of liquid carbon dioxide Liquid carbon dioxide is the liquid state of carbon dioxide (), which cannot occur under atmospheric pressure. The solubility turned out to be very low: from 0.02 to 0.10 %. thumb\|Carbon dioxide pressure-temperature phase diagram == Uses == thumb\|219x219px\|Fire extinguisher Uses of liquid carbon dioxide include the preservation of food, in fire extinguishers, and in commercial food processes. Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures.	−1.642876	0.042	16.0	-59.24	-20	E
A manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid. Suppose the liquid is water, the external pressure is 770 Torr, and the open side is $10.0 \mathrm{cm}$ lower than the side connected to the apparatus. What is the pressure in the apparatus? (The density of water at $25^{\circ} \mathrm{C}$ is $0.99707 \mathrm{g} \mathrm{cm}^{-3}$.)	The open end of the manometer is then connected to a pressure measuring device. Therefore, the pressure difference between the applied pressure Pa and the reference pressure P0 in a U-tube manometer can be found by solving . The pressure at the bottom of the barometer, Point B, is equal to the atmospheric pressure. It consists of a submerged manometer and container holding the substance whose vapor pressure is being measured. Manometric measurement is the subject of pressure head calculations. A single-limb liquid-column manometer has a larger reservoir instead of one side of the U-tube and has a scale beside the narrower column. Simple hydrostatic gauges can measure pressures ranging from a few torrs (a few 100 Pa) to a few atmospheres (approximately ). Bourdon tube pressure gauges. If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired, except when measuring differential pressure of a fluid (for example, across an orifice plate or venturi), in which case the density ρ should be corrected by subtracting the density of the fluid being measured. There are three different types of pressuremeters. The difference in liquid levels represents the applied pressure. The pressuremeter has two major components. Typically, atmospheric pressure is measured between and of Hg. A very simple version is a U-shaped tube half-full of liquid, one side of which is connected to the region of interest while the reference pressure (which might be the atmospheric pressure or a vacuum) is applied to the other. They have poor dynamic response. ====Piston==== Piston-type gauges counterbalance the pressure of a fluid with a spring (for example tire- pressure gauges of comparatively low accuracy) or a solid weight, in which case it is known as a deadweight tester and may be used for calibration of other gauges. ====Liquid column (manometer)==== thumb\|upright\|The difference in fluid height in a liquid-column manometer is proportional to the pressure difference: h = \frac{P_a - P_o}{g \rho} Liquid-column gauges consist of a column of liquid in a tube whose ends are exposed to different pressures. The pressure inside the probe is held constant for a specific period of time and the increase in volume required to maintain the pressure is recorded. thumb\|Barometer A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Gauges that rely on a change in capacitance are often referred to as capacitance manometers. ====Bourdon tube==== thumb\|Membrane-type manometer The Bourdon pressure gauge uses the principle that a flattened tube tends to straighten or regain its circular form in cross-section when pressurized. A pressuremeter is a meter constructed to measure the “at-rest horizontal earth pressure”. The word "gauge" or "vacuum" may be added to such a measurement to distinguish between a pressure above or below the atmospheric pressure. Pressure instruments connected to the system will indicate pressures relative to the current atmospheric pressure. It has a pressure resolution of approximately 1mm of water when measuring pressure at a depth of several kilometers.	32	0.9984	102.0	-100	4.8	C
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The standard enthalpy of formation of the metallocene bis(benzene)chromium was measured in a calorimeter. It was found for the reaction $\mathrm{Cr}\left(\mathrm{C}_6 \mathrm{H}_6\right)_2(\mathrm{~s}) \rightarrow \mathrm{Cr}(\mathrm{s})+2 \mathrm{C}_6 \mathrm{H}_6(\mathrm{~g})$ that $\Delta_{\mathrm{r}} U^{\bullet}(583 \mathrm{~K})=+8.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Find the corresponding reaction enthalpy and estimate the standard enthalpy of formation of the compound at $583 \mathrm{~K}$. The constant-pressure molar heat capacity of benzene is $136.1 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ in its liquid range and $81.67 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ as a gas.	Regardless, if each reactant and product can be prepared in its respective standard state, then the contribution of each species is equal to its molar enthalpy of formation multiplied by its stoichiometric coefficient in the reaction, and the enthalpy of reaction at constant (standard) pressure P^{\ominus} and constant temperature (usually 298 K) may be written as : Q_{P^{\ominus}} = \Delta_{\text {rxn}} H^\ominus = \sum_{products,~p} u_{p}\Delta_{\text {f}} H_{p}^{\ominus} - \sum_{reactants,~r} u_{r}\Delta_{\text {f}} H_{r}^{\ominus} As shown above, at constant pressure the heat of the reaction is exactly equal to the enthalpy change, \Delta_{\text {rxn}} H, of the reacting system. == Variation with temperature or pressure == The variation of the enthalpy of reaction with temperature is given by Kirchhoff's Law of Thermochemistry, which states that the temperature derivative of ΔH for a chemical reaction is given by the difference in heat capacity (at constant pressure) between products and reactants: :\left(\frac{\partial \Delta H}{\partial T}\right)_p = \Delta C_p. For a generic chemical reaction : u_{\text {A}} \text {A} + u_{\,\text {B}} \text {B} ~+ ~... \rightarrow u_{\,\text {X}} \text {X} + u_{\text {Y}} \text {Y} ~+ ~... the standard enthalpy of reaction \Delta_{\text {rxn}} H^\ominus is related to the standard enthalpy of formation \Delta_{\text {f}} H^\ominus values of the reactants and products by the following equation: : \Delta_{\text {rxn}} H^\ominus = \sum_{products,~p} u_p\Delta_{\text {f}} H_{p}^{\ominus} - \sum_{reactants,~r} u_r\Delta_{\text {f}} H_{r}^{\ominus} In this equation, u_p and u_r are the stoichiometric coefficients of each product p and reactant r. Petrucci, Harwood and Herring, pages 241–243 Finally the reaction enthalpy may be estimated using bond energies for the bonds which are broken and formed in the reaction of interest. Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. The standard enthalpy of reaction (denoted \Delta_{\text {rxn}} H^\ominus or \Delta H_{\text {reaction}}^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. The enthalpy of formation of one mole of ethane gas refers to the reaction 2 C (graphite) + 3 H2 (g) → C2H6 (g). The standard enthalpy of formation is then determined using Hess's law. * Standard enthalpy of formation is the enthalpy change when one mole of any compound is formed from its constituent elements in their standard states. For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol . == Hess's law == For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). For example, the standard enthalpy of combustion of ethane gas refers to the reaction C2H6 (g) + (7/2) O2 (g) → 2 CO2 (g) + 3 H2O (l). If the enthalpies for each step can be measured, then their sum gives the enthalpy of the overall single reaction. The standard enthalpy of formation, which has been determined for a vast number of substances, is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states. This calculation has a tacit assumption of ideal solution between reactants and products where the enthalpy of mixing is zero. The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products Elements in their standard states make no contribution to the enthalpy calculations for the reaction, since the enthalpy of an element in its standard state is zero. Accordingly, the calculation of standard enthalpy of reaction is the most established way of quantifying the conversion of chemical potential energy into thermal energy. ==Enthalpy of reaction for standard conditions defined and measured== The standard enthalpy of a reaction is defined so as to depend simply upon the standard conditions that are specified for it, not simply on the conditions under which the reactions actually occur. It is also possible to evaluate the enthalpy of one reaction from the enthalpies of a number of other reactions whose sum is the reaction of interest, and these not need be formation reactions. Since enthalpy is a state function, its value is the same for any path between given initial and final states, so that the measured ΔH is the same as if the temperature stayed constant during the combustion.Engel and Reid p.65 For reactions which are incomplete, the equilibrium constant can be determined as a function of temperature. It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method. == Use in calculation for other reactions == The standard enthalpy change of any reaction can be calculated from the standard enthalpies of formation of reactants and products using Hess's law. However the standard enthalpy of combustion is readily measurable using bomb calorimetry.	+17.7	3.38	0.2553	0.11	1.95	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the Carnot efficiency of a primitive steam engine operating on steam at $100^{\circ} \mathrm{C}$ and discharging at $60^{\circ} \mathrm{C}$.	Latest generation gas turbine engines have achieved an efficiency of 46% in simple cycle and 61% when used in combined cycle. ==External combustion engines== ===Steam engine=== ::See also: Steam engine#Efficiency ::See also: Timeline of steam power ====Piston engine==== Steam engines and turbines operate on the Rankine cycle which has a maximum Carnot efficiency of 63% for practical engines, with steam turbine power plants able to achieve efficiency in the mid 40% range. While gasoline-powered ICE cars have an operational thermal efficiency of 15% to 30%, early automotive steam units were capable of only about half this efficiency. Its theoretical efficiency depends on the compression ratio r of the engine and the specific heat ratio γ of the gas in the combustion chamber. \eta_{\rm th} = 1 - \frac{1}{r^{\gamma-1}} Thus, the efficiency increases with the compression ratio. The thermal efficiency of modern steam turbine plants with reheat cycles can reach 47%, and in combined cycle plants, in which a steam turbine is powered by exhaust heat from a gas turbine, it can approach 60%. For example, if an automobile engine burns gasoline at a temperature of T_{\rm H} = 816^\circ \text{C} = 1500^\circ \text{F} = 1089 \text{K} and the ambient temperature is T_{\rm C} = 21^\circ \text{C} = 70^\circ \text{F} = 294 \text{K}, then its maximum possible efficiency is: :\eta_{\rm th} \le \left (1 - \frac{294 K}{1089 K} \right ) 100\% = 73.0\% It can be seen that since T_{\rm C} is fixed by the environment, the only way for a designer to increase the Carnot efficiency of an engine is to increase T_{\rm H}, the temperature at which the heat is added to the engine. The efficiency depends largely on the ratio of the pressure inside the combustion chamber p2 to the pressure outside p1 \eta_{\rm th} = 1 - \left(\frac{p_2}{p_1}\right)^\frac{1-\gamma}{\gamma} ===Other inefficiencies=== One should not confuse thermal efficiency with other efficiencies that are used when discussing engines. Steam engine efficiency improved as the operating principles were discovered, which led to the development of the science of thermodynamics. The efficiency of steam engines is primarily related to the steam temperature and pressure and the number of stages or expansions. See graph:Steam Engine Efficiency In earliest steam engines the boiler was considered part of the engine. So, for a boiler that produces 210 kW (or 700,000 BTU/h) output for each 300 kW (or 1,000,000 BTU/h) heat-equivalent input, its thermal efficiency is 210/300 = 0.70, or 70%. There is an overall theoretical limit to the efficiency of any heat engine due to temperature, called the Carnot efficiency. The first piston steam engine, developed by Thomas Newcomen around 1710, was slightly over one half percent (0.5%) efficient. Some steam enthusiasts feel steam has not received its share of attention in the field of automobile efficiency. A very well-designed and built steam locomotive used to get around 7-8% efficiency in its heyday. The above efficiency formulas are based on simple idealized mathematical models of engines, with no friction and working fluids that obey simple thermodynamic rules called the ideal gas law. Today they are considered separate, so it is necessary to know whether stated efficiency is overall, which includes the boiler, or just of the engine. Comparisons of efficiency and power of the early steam engines is difficult for several reasons: 1) there was no standard weight for a bushel of coal, which could be anywhere from 82 to 96 pounds (37 to 44 kg). The Carnot cycle achieves maximum efficiency because all the heat is added to the working fluid at the maximum temperature T_{\rm H}, and removed at the minimum temperature T_{\rm C}. From Carnot's theorem, for any engine working between these two temperatures: :\eta_{\rm th} \le 1 - \frac{T_{\rm C}}{T_{\rm H}} This limiting value is called the Carnot cycle efficiency because it is the efficiency of an unattainable, ideal, reversible engine cycle called the Carnot cycle. Practical engine cycles are irreversible and thus have inherently lower efficiency than the Carnot efficiency when operated between the same temperatures T_{\rm H} and T_{\rm C}. For example, the average automobile engine is less than 35% efficient. Thermal efficiency is defined as :\eta_{\rm th} \equiv \frac{\|W_{\rm out}\|}{Q_{\rm in}} = \frac{ {Q_{\rm in}} - \|Q_{\rm out}\|} {Q_{\rm in}} = 1 - \frac{\|Q_{\rm out}\|}{Q_{\rm in}} The efficiency of even the best heat engines is low; usually below 50% and often far below.	52	5.51	4500.0	129	0.11	E
In an industrial process, nitrogen is heated to $500 \mathrm{~K}$ at a constant volume of $1.000 \mathrm{~m}^3$. The gas enters the container at $300 \mathrm{~K}$ and $100 \mathrm{~atm}$. The mass of the gas is $92.4 \mathrm{~kg}$. Use the van der Waals equation to determine the approximate pressure of the gas at its working temperature of $500 \mathrm{~K}$. For nitrogen, $a=1.352 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}, b=0.0387 \mathrm{dm}^3 \mathrm{~mol}^{-1}$.	Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and b (volume occupied by molecules) values, then a and b for the mixture can be calculated as :m = total number of moles of gas present, :for each i, m_i = number of moles of gas i present, and x_i = \frac{m_i}{m} :a = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{a_i a_j}) :b = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{b_i b_j}) and the rule of adding partial pressures becomes invalid if the numerical result of the equation \left(p + ({n^2 a}/{V^2})\right)\left(V-nb\right) = nRT is significantly different from the ideal gas equation pV = nRT . ===Reduced form=== The Van der Waals equation can also be expressed in terms of reduced properties: :\left(P_r + \frac{3}{V_r^2}\right)\left(V_r-\frac{1}{3}\right) = \frac{8}{3}T_r The equation in reduced form is exactly the same for every gas, this is consistent with the Theorem of corresponding states. Indeed, there is no reason to assume that the van der Waals radius is a fixed property of the atom in all circumstances: rather, it tends to vary with the particular chemical environment of the atom in any given case. === Van der Waals equation of state === The van der Waals equation of state is the simplest and best-known modification of the ideal gas law to account for the behaviour of real gases: \left (p + a\left (\frac{n}{\tilde{V}}\right )^2\right ) (\tilde{V} - nb) = nRT, where is pressure, is the number of moles of the gas in question and and depend on the particular gas, \tilde{V} is the volume, is the specific gas constant on a unit mole basis and the absolute temperature; is a correction for intermolecular forces and corrects for finite atomic or molecular sizes; the value of equals the van der Waals volume per mole of the gas. The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. In the derivation of ideal gas laws on the basis of kinetic theory of gases some assumption have been made. ===Compressibility factor=== The compressibility factor for the Van der Waals equation is: : Z = \frac{P V_m}{RT} = \frac{V_m}{V_m-b} - \frac{a}{V_m RT} Or in reduced form by substitution of P_r=P/P_c, T_r=T/T_c, V_r=V_m/V_c: : Z = \frac{V_r}{V_r-\frac{1}{3}} - \frac{9}{8 V_r T_r} At the critical point: : Z_c = \frac{P_c V_c}{RT_c} = \frac{3}{8} = 0.375 ==Validity== The Van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.. Gas d (Å) b (cmmol) V (Å) r (Å) Hydrogen 0.74611 26.61 44.19 2.02 Nitrogen 1.0975 39.13 64.98 2.25 Oxygen 1.208 31.83 52.86 2.06 Chlorine 1.988 56.22 93.36 2.39 van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. The ideal gas law states that the volume V occupied by n moles of any gas has a pressure P at temperature T given by the following relationship, where R is the gas constant: :PV=nRT To account for the volume occupied by real gas molecules, the Van der Waals equation replaces V/n in the ideal gas law with (V_m-b), where Vm is the molar volume of the gas and b is the volume occupied by the molecules of one mole: :P(V_m - b)=R T thumb\|Van der Waals equation on a wall in Leiden The second modification made to the ideal gas law accounts for interaction between molecules of the gas. Hence the molar van der Waals volume, which only counts the volume occupied by the atoms or molecules, is usually about times smaller than the molar volume for a gas at standard temperature and pressure. ==Table of van der Waals radii== == Methods of determination == Van der Waals radii may be determined from the mechanical properties of gases (the original method), from the critical point, from measurements of atomic spacing between pairs of unbonded atoms in crystals or from measurements of electrical or optical properties (the polarizability and the molar refractivity). The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. D-166. b = 23.7 cm/mol. Helium is a monatomic gas, and each mole of helium contains atoms (the Avogadro constant, N): V_{\rm w} = {b\over{N_{\rm A}}} Therefore, the van der Waals volume of a single atom V = 39.36 Å, which corresponds to r = 2.11 Å (≈ 200 picometers). The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. Above the critical temperature, TC, the Van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region. However, near the phase transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the Van der Waals equation fails to accurately model observed experimental behavior. * Analytical calculation of Van der Waals surfaces and volumes. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the Avogadro constant N. The van der Waals constant b volume can be used to calculate the van der Waals volume of an atom or molecule with experimental data derived from measurements on gases. The van der Waals volume is given by V_{\rm w} = \frac{\pi V_{\rm m}}{N_{\rm A}\sqrt{18}} where the factor of π/√18 arises from the packing of spheres: V = = 23.0 Å, corresponding to a van der Waals radius r = 1.76 Å. === Molar refractivity === The molar refractivity of a gas is related to its refractive index by the Lorentz–Lorenz equation: A = \frac{R T (n^2 - 1)}{3p} The refractive index of helium n = at 0 °C and 101.325 kPa,Kaye & Laby Tables, Refractive index of gases. which corresponds to a molar refractivity A = . Since: :p=-\left(\frac{\partial A}{\partial V}\right)_{T,N} where A is the Helmholtz free energy, it follows that the equal area rule can be expressed as: :p_V=\frac{A(V_L,T,N)-A(V_G,T,N)}{V_G-V_L}is Since the gas and liquid volumes are functions of pV and T only, this equation is then solved numerically to obtain pV as a function of temperature (and number of particles N), which may then be used to determine the gas and liquid volumes. thumb\|800px\|Locus of coexistence for two phases of Van der Waals fluid A pseudo-3D plot of the locus of liquid and vapor volumes versus temperature and pressure is shown in the accompanying figure. An isotherm of the Van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal. == Other parameters, forms and applications == ===Other thermodynamic parameters=== We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for the finite size of the molecules. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. In this case specific volume changes are small and it can be written in a simplified form: :(p+A)(V-B)=CT, \, where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters. == See also == * Gas laws * Ideal gas * Inversion temperature * Iteration * Maxwell construction * Real gas * Theorem of corresponding states * Van der Waals constants (data page) * Redlich–Kwong equation of state ==References== ==Further reading== * * .	-11.875	140	131.0	655	13.45	B
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. Silylene $\left(\mathrm{SiH}_2\right)$ is a key intermediate in the thermal decomposition of silicon hydrides such as silane $\left(\mathrm{SiH}_4\right)$ and disilane $\left(\mathrm{Si}_2 \mathrm{H}_6\right)$. Moffat et al. (J. Phys. Chem. 95, 145 (1991)) report $\Delta_{\mathrm{f}} H^{\ominus}\left(\mathrm{SiH}_2\right)=+274 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\Delta_{\mathrm{f}} H^{\ominus}\left(\mathrm{SiH}_4\right)=+34.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta_{\mathrm{f}} H^{\ominus}\left(\mathrm{Si}_2 \mathrm{H}_6\right)=+80.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$(CRC Handbook (2008)), compute the standard enthalpies of the following reaction: $\mathrm{SiH}_4 (\mathrm{g}) \rightarrow \mathrm{SiH}_2(\mathrm{g})+\mathrm{H}_2(\mathrm{g})$	Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? \\!\| cdf =\| mean =\mu + \frac{\delta \beta K_{\lambda+1}(\delta \gamma)}{\gamma K_\lambda(\delta\gamma)}\| median =\| mode =\| variance =\frac{\delta K_{\lambda+1}(\delta \gamma)}{\gamma K_\lambda(\delta\gamma)} + \frac{\beta^2\delta^2}{\gamma^2}\left( \frac{K_{\lambda+2}(\delta\gamma)}{K_{\lambda}(\delta\gamma)} - \frac{K_{\lambda+1}^2(\delta\gamma)}{K_{\lambda}^2(\delta\gamma)} \right)\| skewness =\| kurtosis =\| entropy =\| mgf =\frac{e^{\mu z}\gamma^\lambda}{(\sqrt{\alpha^2 -(\beta +z)^2})^\lambda} \frac{K_\lambda(\delta \sqrt{\alpha^2 -(\beta +z)^2})}{K_\lambda (\delta \gamma)}\| char =\| }} The generalised hyperbolic distribution (GH) is a continuous probability distribution defined as the normal variance-mean mixture where the mixing distribution is the generalized inverse Gaussian distribution (GIG). J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? {{OrganicBox complete \|wiki_name=Lysine \|image=110px\|Skeletal structure of L-lysine 130px\|3D structure of L-lysine \|name=-2,6-Diaminohexanoic acid \|C=6 \|H=14 \|N=2 \|O=2 \|mass=146.19 \|abbreviation=K, Lys \|synonyms= \|SMILES=NCCCCC(N)C(=O)O \|InChI=1/C6H14N2O2/c7-4-2-1-3-5(8)6(9)10/h5H,1-4,7-8H2,(H,9,10)/f/h9H \|CAS=56-87-1 \|DrugBank= \|EINECS=200-294-2 \|PubChem=866 (DL) , 5962 (L) \|index_of_refraction= \|abbe_number= \|dielectric_constant= \|magnetic_susceptibility= \|lambda_max= \|extinction_coefficient= \|absorption_bands= \|proton_NMR= \|carbon_NMR= \|other_NMR= \|mass_spectrometry= \|triple_point_K= \|triple_point_C= \|triple_point_Pa= \|criticle_point_K= \|criticle_point_C= \|criticle_point_Pa= \|delta_fus_H_o= \|delta_fus_S_o= \|delta_vap_H_o= \|delta_vap_S_o= \|delta_f_H_o= \|S_o_solid= \|heat_capacity_solid= \|density_solid= \|melting_point_C=224 \|melting_point_F= \|melting_point_K= \|delta_f_H_o_liquid= \|S_o_liquid= \|heat_capacity_liquid= \|density_liquid= \|viscosity_liquid= \|boiling_point_C= \|boiling_point_F= \|boiling_point_K= \|delta_f_H_o_gas= \|S_o_gas= \|heat_capacity_gas= \|viscosity_gas= \|MSDS= \|main_hazards= \|nfpa_health= \|nfpa_flammability= \|nfpa_reactivity= \|nfpa_special= \|flash_point= \|r_phrases= \|s_phrases= \|RTECS_number= \|XLogP=-2.926 \|isoelectric_point=9.74 \|disociation_constant=2.15, 9.16, 10.67 \|tautomers= \|H_bond_donor=3 \|H_bond_acceptor=4 }} ==References== # (Lysine) # (DL-Lysine) # (L-Lysine) Category:Chemical data pages Category:Chemical data pages cleanup In fluid dynamics, the general equation of heat transfer is a nonlinear partial differential equation describing specific entropy production in a Newtonian fluid subject to thermal conduction and viscous forces:}_{\text{Heat Gain}} = \underbrace{ abla\cdot (\kappa abla T)}_{\text{Thermal Conduction}} + \underbrace{{\mu\over{2}}\left( {\partial v_{i}\over{\partial x_{j}}} + {\partial v_{j}\over{\partial x_{i}}} - {2\over{3}}\delta_{ij} abla\cdot {\bf v} \right)^{2} + \zeta( abla\cdot {\bf v})^{2}}_{\text{Viscous Dissipation}} \|border colour=#0073CF\|background colour=#F5FFFA}}where s is the specific entropy, \rho is the fluid's density, T is the fluid's temperature, D/Dt is the material derivative, \kappa is the thermal conductivity, \mu is the dynamic viscosity, \zeta is the second Lamé parameter, {\bf v} is the flow velocity, abla is the del operator used to characterize the gradient and divergence, and \delta_{ij} is the Kronecker delta. \frac{1}{\sqrt{1 + \left(\frac{x-\xi}{\lambda}\right)^2}} e^{-\frac{1}{2}\left(\gamma+\delta \sinh^{-1} \left(\frac{x-\xi}{\lambda}\right)\right)^2} \| cdf = \Phi \left(\gamma + \delta \sinh^{-1} \left( \frac{x-\xi}{\lambda} \right) \right) \| mean = \xi - \lambda \exp \frac{\delta^{-2}}{2} \sinh\left(\frac{\gamma}{\delta}\right) \| median = \xi + \lambda \sinh \left( - \frac{\gamma}{\delta} \right) \| mode = \| variance = \frac{\lambda^2}{2} (\exp(\delta^{-2})-1) \left( \exp(\delta^{-2}) \cosh \left(\frac{2\gamma}{\delta} \right) +1 \right) \| skewness = -\frac{\lambda^3\sqrt{e^{\delta^{-2}}}(e^{\delta^{-2}}-1)^{2}((e^{\delta^{-2}})(e^{\delta^{-2}}+2)\sinh(\frac{3\gamma}{\delta})+3\sinh(\frac{2\gamma}{\delta}))}{4(\operatorname{Variance}X)^{1.5}} \| kurtosis = \frac{\lambda^4(e^{\delta^{-2}}-1)^2(K_{1}+K_2+K_3)}{8(\operatorname{Variance}X)^2} K_{1}=\left( e^{\delta^{-2}} \right)^{2}\left( \left( e^{\delta^{-2}} \right)^{4}+2\left( e^{\delta^{-2}} \right)^{3}+3\left( e^{\delta^{-2}} \right)^{2}-3 \right)\cosh\left( \frac{4\gamma}{\delta} \right) K_2=4\left( e^{\delta^{-2}} \right)^2 \left( \left( e^{\delta^{-2}} \right)+2 \right)\cosh\left( \frac{3\gamma}{\delta} \right) K_3=3\left( 2\left( e^{\delta^{-2}} \right)+1 \right) \| entropy = \| pgf = \| mgf = \| char = }} The Johnson's SU-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? ==Thermal conductivity== 1 H hydrogen use 180.5 mW/(m·K) CR2 (P=0) 186.9 mW/(m·K) LNG 0.1805 W/(m·K) WEL 0.1805 W/(m·K) 2 He helium use 151.3 mW/(m·K) CR2 (P=0) 156.7 mW/(m·K) LNG 0.1513 W/(m·K) WEL 0.1513 W/(m·K) 3 Li lithium use 84.8 W/(m·K) CRC 0.847 W/(cm·K) LNG 84.8 W/(m·K) WEL 85 W/(m·K) 4 Be beryllium use 200 W/(m·K) CRC 2.00 W/(cm·K) LNG 200 W/(m·K) WEL 190 W/(m·K) 5 B boron use 27.4 W/(m·K) LNG 27.4 W/(m·K) WEL 27 W/(m·K) 6 C carbon (graphite) use (graphite) (119-165) W/(m·K) LNG (119-165) W/(m·K) LNG (amorphous) 1.59 W/(m·K) WEL 140 W/(m·K) CRC pyrolytic graphite (parallel to the layer planes) 19.5 W/(cm·K) (perpendicular) 0.0570 W/(cm·K) 6 C carbon (diamond) use (diamond) (900-2320) W/(m·K) LNG (900-2320) W/(m·K) CRC (type I) 8.95 W/(cm·K) (type IIa) 23.0 W/(cm·K) (type IIb) 13.5 W/(cm·K) 7 N nitrogen use 25.83 mW/(m·K) CR2 26.0 mW/(m·K) LNG 0.02583 W/(m·K) WEL 0.02583 W/(m·K) 8 O oxygen use 26.58 mW/(m·K) CR2 26.3 mW/(m·K) LNG (gas) 0.02658 W/(m·K) LNG (liquid) 0.149 W/(m·K) WEL 0.02658 W/(m·K) 9 F fluorine use 27.7 mW/(m·K) LNG 0.0277 W/(m·K) WEL 0.0277 W/(m·K) 10 Ne neon use 49.1 mW/(m·K) CR2 (P=0) 49.8 mW/(m·K) LNG 0.0491 W/(m·K) WEL 0.0491 W/(m·K) 11 Na sodium use 142 W/(m·K) CRC 1.41 W/(cm·K) LNG 142 W/(m·K) WEL 140 W/(m·K) 12 Mg magnesium use 156 W/(m·K) CRC 1.56 W/(cm·K) LNG 156 W/(m·K) WEL 160 W/(m·K) 13 Al aluminium use 237 W/(m·K) CRC 2.37 W/(cm·K) LNG 237 W/(m·K) WEL 235 W/(m·K) 14 Si silicon use 149 W/(m·K) LNG 149 W/(m·K) WEL 150 W/(m·K) 15 P phosphorus use (white) 0.236 W/(m·K) LNG (white) 0.23617 W/(m·K) [sic] WEL 0.236 W/(m·K) 16 S sulfur use (amorphous) 0.205 W/(m·K) LNG (amorphous) 0.205 W/(m·K) WEL 0.205 W/(m·K) 17 Cl chlorine use 8.9 mW/(m·K) LNG 0.0089 W/(m·K) WEL 0.0089 W/(m·K) 18 Ar argon use 17.72 mW/(m·K) CR2 17.9 mW/(m·K) LNG 0.01772 W/(m·K) WEL 0.01772 W/(m·K) 19 K potassium use 102.5 W/(m·K) CRC 1.024 W/(cm·K) LNG 102.5 W/(m·K) WEL 100 W/(m·K) 20 Ca calcium use 201 W/(m·K) CRC 2.00 W/(cm·K) LNG 201 W/(m·K) WEL 200 W/(m·K) 21 Sc scandium use 15.8 W/(m·K) CRC 0.158 W/(cm·K) LNG 15.8 W/(m·K) WEL 16 W/(m·K) 22 Ti titanium use 21.9 W/(m·K) CRC 0.219 W/(cm·K) LNG 21.9 W/(m·K) WEL 22 W/(m·K) 23 V vanadium use 30.7 W/(m·K) CRC 0.307 W/(cm·K) LNG 30.7 W/(m·K) WEL 31 W/(m·K) 24 Cr chromium use 93.9 W/(m·K) CRC 0.937 W/(cm·K) LNG 93.9 W/(m·K) WEL 94 W/(m·K) 25 Mn manganese use 7.81 W/(m·K) CRC 0.0782 W/(cm·K) LNG 7.81 W/(m·K) WEL 7.8 W/(m·K) 26 Fe iron use 80.4 W/(m·K) CRC 0.802 W/(cm·K) LNG 80.4 W/(m·K) WEL 80 W/(m·K) 27 Co cobalt use 100 W/(m·K) CRC 1.00 W/(cm·K) LNG 100 W/(m·K) WEL 100 W/(m·K) 28 Ni nickel use 90.9 W/(m·K) CRC 0.907 W/(cm·K) LNG 90.9 W/(m·K) WEL 91 W/(m·K) 29 Cu copper use 401 W/(m·K) CRC 4.01 W/(cm·K) LNG 401 W/(m·K) WEL 400 W/(m·K) 30 Zn zinc use 116 W/(m·K) CRC 1.16 W/(cm·K) LNG 116 W/(m·K) WEL 120 W/(m·K) 31 Ga gallium use 40.6 W/(m·K) CRC 0.406 W/(cm·K) LNG (liquid) 29.4 W/(m·K) LNG (solid) 40.6 W/(m·K) WEL 29 W/(m·K) 32 Ge germanium use 60.2 W/(m·K) LNG 60.2 W/(m·K) WEL 60 W/(m·K) 33 As arsenic use 50.2 W/(m·K) LNG 50.2 W/(m·K) WEL 50 W/(m·K) 34 Se selenium use (amorphous) 0.519 W/(m·K) LNG (amorphous) 0.519 W/(m·K) WEL 0.52 W/(m·K) 35 Br bromine use 0.122 W/(m·K) LNG 0.122 W/(m·K) WEL 0.12 W/(m·K) 36 Kr krypton use 9.43 mW/(m·K) CR2 (P=0) 9.5 mW/(m·K) LNG 9.43 W/(m·K) [sic] WEL 0.00943 W/(m·K) 37 Rb rubidium use 58.2 W/(m·K) CRC 0.582 W/(cm·K) LNG 58.2 W/(m·K) WEL 58 W/(m·K) 38 Sr strontium use 35.4 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.4 W/(m·K) WEL 35 W/(m·K) 39 Y yttrium use 17.2 W/(m·K) CRC 0.172 W/(cm·K) LNG 17.2 W/(m·K) WEL 17 W/(m·K) 40 Zr zirconium use 22.6 W/(m·K) CRC 0.227 W/(cm·K) LNG 22.6 W/(m·K) WEL 23 W/(m·K) 41 Nb niobium use 53.7 W/(m·K) CRC 0.537 W/(cm·K) LNG 53.7 W/(m·K) WEL 54 W/(m·K) 42 Mo molybdenum use 138 W/(m·K) CRC 1.38 W/(cm·K) LNG 138 W/(m·K) WEL 139 W/(m·K) 43 Tc technetium use 50.6 W/(m·K) CRC 0.506 W/(cm·K) LNG 50.6 W/(m·K) WEL 51 W/(m·K) 44 Ru ruthenium use 117 W/(m·K) CRC 1.17 W/(cm·K) LNG 117 W/(m·K) WEL 120 W/(m·K) 45 Rh rhodium use 150 W/(m·K) CRC 1.50 W/(cm·K) LNG 150 W/(m·K) WEL 150 W/(m·K) 46 Pd palladium use 71.8 W/(m·K) CRC 0.718 W/(cm·K) LNG 71.8 W/(m·K) WEL 72 W/(m·K) 47 Ag silver use 429 W/(m·K) CRC 4.29 W/(cm·K) LNG 429 W/(m·K) WEL 430 W/(m·K) 48 Cd cadmium use 96.6 W/(m·K) CRC 0.968 W/(cm·K) LNG 96.6 W/(m·K) WEL 97 W/(m·K) 49 In indium use 81.8 W/(m·K) CRC 0.816 W/(cm·K) LNG 81.8 W/(m·K) WEL 82 W/(m·K) 50 Sn tin use 66.8 W/(m·K) CRC 0.666 W/(cm·K) LNG 66.8 W/(m·K) WEL 67 W/(m·K) 51 Sb antimony use 24.4 W/(m·K) CRC 0.243 W/(cm·K) LNG 24.4 W/(m·K) WEL 24 W/(m·K) 52 Te tellurium use (1.97-3.38) W/(m·K) LNG (1.97-3.38) W/(m·K) WEL 3 W/(m·K) 53 I iodine use 0.449 W/(m·K) CRC (300 K) 0.45 W/(m·K) LNG 449 W/(m·K) [sic] WEL 0.449 W/(m·K) 54 Xe xenon use 5.65 mW/(m·K) CR2 (P=0) 5.5 mW/(m·K) LNG 0.00565 W/(m·K) WEL 0.00565 W/(m·K) 55 Cs caesium use 35.9 W/(m·K) CRC 0.359 W/(cm·K) LNG 35.9 W/(m·K) WEL 36 W/(m·K) 56 Ba barium use 18.4 W/(m·K) CRC 0.184 W/(cm·K) LNG 18.4 W/(m·K) WEL 18 W/(m·K) 57 La lanthanum use 13.4 W/(m·K) CRC 0.134 W/(cm·K) LNG 13.4 W/(m·K) WEL 13 W/(m·K) 58 Ce cerium use 11.3 W/(m·K) CRC 0.113 W/(cm·K) LNG 11.3 W/(m·K) WEL 11 W/(m·K) 59 Pr praseodymium use 12.5 W/(m·K) CRC 0.125 W/(cm·K) LNG 12.5 W/(m·K) WEL 13 W/(m·K) 60 Nd neodymium use 16.5 W/(m·K) CRC 0.165 W/(cm·K) LNG 16.5 W/(m·K) WEL 17 W/(m·K) 61 Pm promethium use 17.9 W/(m·K) CRC (est.) 0.15 W/(cm·K) LNG 17.9 W/(m·K) WEL 15 W/(m·K) 62 Sm samarium use 13.3 W/(m·K) CRC 0.133 W/(cm·K) LNG 13.3 W/(m·K) WEL 13 W/(m·K) 63 Eu europium use (est.) 13.9 W/(m·K) CRC (est.) 0.139 W/(cm·K) LNG 13.9 W/(m·K) WEL 14 W/(m·K) 64 Gd gadolinium use 10.6 W/(m·K) (300 K) 10.6 W/(m·K) CRC (100 °C) 0.105 W/(cm·K) LNG 10.5 W/(m·K) WEL 11 W/(m·K) 65 Tb terbium use 11.1 W/(m·K) CRC 0.111 W/(cm·K) LNG 11.1 W/(m·K) WEL 11 W/(m·K) 66 Dy dysprosium use 10.7 W/(m·K) CRC 0.107 W/(cm·K) LNG 10.7 W/(m·K) WEL 11 W/(m·K) 67 Ho holmium use 16.2 W/(m·K) CRC 0.162 W/(cm·K) LNG 16.2 W/(m·K) WEL 16 W/(m·K) 68 Er erbium use 14.5 W/(m·K) CRC 0.145 W/(cm·K) LNG 14.5 W/(m·K) WEL 15 W/(m·K) 69 Tm thulium use 16.9 W/(m·K) CRC 0.169 W/(cm·K) LNG 16.9 W/(m·K) WEL 17 W/(m·K) 70 Yb ytterbium use 38.5 W/(m·K) CRC 0.385 W/(cm·K) LNG 38.5 W/(m·K) WEL 39 W/(m·K) 71 Lu lutetium use 16.4 W/(m·K) CRC 0.164 W/(cm·K) LNG 16.4 W/(m·K) WEL 16 W/(m·K) 72 Hf hafnium use 23.0 W/(m·K) CRC 0.230 W/(cm·K) LNG 23.0 W/(m·K) WEL 23 W/(m·K) 73 Ta tantalum use 57.5 W/(m·K) CRC 0.575 W/(cm·K) LNG 57.5 W/(m·K) WEL 57 W/(m·K) 74 W tungsten use 173 W/(m·K) CRC 1.74 W/(cm·K) LNG 173 W/(m·K) WEL 170 W/(m·K) 75 Re rhenium use 48.0 W/(m·K) CRC 0.479 W/(cm·K) LNG 48.0 W/(m·K) WEL 48 W/(m·K) 76 Os osmium use 87.6 W/(m·K) CRC 0.876 W/(cm·K) LNG 87.6 W/(m·K) WEL 88 W/(m·K) 77 Ir iridium use 147 W/(m·K) CRC 1.47 W/(cm·K) LNG 147 W/(m·K) WEL 150 W/(m·K) 78 Pt platinum use 71.6 W/(m·K) CRC 0.716 W/(cm·K) LNG 71.6 W/(m·K) WEL 72 W/(m·K) 79 Au gold use 318 W/(m·K) CRC 3.17 W/(cm·K) LNG 318 W/(m·K) WEL 320 W/(m·K) 80 Hg mercury use 8.30 W/(m·K) CRC 0.0834 W/(cm·K) LNG 8.30 W/(m·K) WEL 8.3 W/(m·K) 81 Tl thallium use 46.1 W/(m·K) CRC 0.461 W/(cm·K) LNG 46.1 W/(m·K) WEL 46 W/(m·K) 82 Pb lead use 35.3 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.3 W/(m·K) WEL 35 W/(m·K) 83 Bi bismuth use 7.97 W/(m·K) CRC 0.0787 W/(cm·K) LNG 7.97 W/(m·K) WEL 8 W/(m·K) 84 Po polonium use CRC 0.20 W/(cm·K) LNG 0.2 W/(m·K) 85 At astatine use 1.7 W/(m·K) LNG 1.7 W/(m·K) WEL 2 W/(m·K) 86 Rn radon use 3.61 mW/(m·K) LNG 0.00361 W/(m·K) WEL 0.00361 W/(m·K) 88 Ra radium use 18.6 W/(m·K) LNG 18.6 W/(m·K) WEL 19 W/(m·K) 89 Ac actinium use 12 W/(m·K) LNG 12 W/(m·K) WEL 12 W/(m·K) 90 Th thorium use 54.0 W/(m·K) CRC 0.540 W/(cm·K) LNG 54.0 W/(m·K) WEL 54 W/(m·K) 91 Pa protactinium use 47 W/(m·K) LNG 47 W/(m·K) WEL 47 W/(m·K) 92 U uranium use 27.5 W/(m·K) CRC 0.276 W/(cm·K) LNG 27.5 W/(m·K) WEL 27 W/(m·K) 93 Np neptunium use 6.3 W/(m·K) CRC 0.063 W/(cm·K) LNG 6.3 W/(m·K) WEL 6 W/(m·K) 94 Pu plutonium use 6.74 W/(m·K) CRC 0.0674 W/(cm·K) LNG 6.74 W/(m·K) WEL 6 W/(m·K) 95 Am americium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) 97 Bk berkelium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) ==Notes== * Ref. CRC: Values refer to 27 °C unless noted. Then the general equation for conservation of energy is:{\partial\over{\partial t}}\left[ \rho (k+\varepsilon) \right] + abla\cdot \left[ \rho {\bf v}(k+ h) - \kappa abla T - \sigma\cdot {\bf v} \right] = 0 === Equation for entropy production === Note that the thermodynamic relations for the internal energy and enthalpy are given by:\begin{aligned} \rho d\varepsilon &= \rho Tds + {p\over{\rho}}d\rho \\\ \rho dh &= \rho Tds + dp \end{aligned}We may also obtain an equation for the kinetic energy by taking the dot product of the Navier-Stokes equation with the flow velocity {\bf v} to yield:\rho {Dk\over{Dt}} = -{\bf v}\cdot abla p + v_{i}{\partial\sigma_{ij}\over{\partial x_{j}}} The second term on the righthand side may be expanded to read:\begin{aligned} v_{i} {\partial \sigma_{ij}\over{\partial x_{j}}} &= {\partial\over{\partial x_{j}}}\left(\sigma_{ij}v_{i} \right ) - \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} \\\ &\equiv abla\cdot (\sigma \cdot {\bf v}) - \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} \end{aligned} With the aid of the thermodynamic relation for enthalpy and the last result, we may then put the kinetic energy equation into the form:\rho {Dk\over{Dt}} = -\rho {\bf v}\cdot abla h + \rho T {\bf v}\cdot abla s + abla\cdot (\sigma \cdot {\bf v}) - \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} Now expanding the time derivative of the total energy, we have:{\partial\over{\partial t}}\left[ \rho (k+\varepsilon) \right] = \rho {\partial k\over{\partial t}} + \rho {\partial\varepsilon\over{\partial t}} + (k+\varepsilon) {\partial \rho\over{\partial t}} Then by expanding each of these terms, we find that:\begin{aligned} \rho {\partial k\over{\partial t}} &= -\rho {\bf v}\cdot abla k - \rho {\bf v}\cdot abla h + \rho T{\bf v}\cdot abla s + abla\cdot(\sigma\cdot {\bf v}) - \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} \\\ \rho {\partial\varepsilon\over{\partial t}} &= \rho T {\partial s\over{\partial t}} - {p\over{\rho}} abla\cdot(\rho {\bf v}) \\\ (k+\varepsilon){\partial\rho\over{\partial t}} &= -(k+\varepsilon) abla\cdot (\rho {\bf v}) \end{aligned} And collecting terms, we are left with:{\partial\over{\partial t}}\left[\rho(k+\varepsilon) \right ] + abla \cdot\left[\rho {\bf v}(k+h) - \sigma\cdot {\bf v} \right ] = \rho T {Ds\over{Dt}} - \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} Now adding the divergence of the heat flux due to thermal conduction to each side, we have that:{\partial\over{\partial t}}\left[\rho(k+\varepsilon) \right ] + abla \cdot\left[\rho {\bf v}(k+h) - \kappa abla T - \sigma\cdot {\bf v} \right ] = \rho T {Ds\over{Dt}} - abla\cdot(\kappa abla T) - \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} However, we know that by the conservation of energy on the lefthand side is equal to zero, leaving us with:\rho T {Ds\over{Dt}} = abla\cdot(\kappa abla T) + \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} The product of the viscous stress tensor and the velocity gradient can be expanded as:\begin{aligned} \sigma_{ij}{\partial v_{i}\over{\partial x_{j}}} &= \mu\left( {\partial v_{i}\over{\partial x_{j}}} + {\partial v_{j}\over{\partial x_{i}}} - {2\over{3}}\delta_{ij} abla\cdot {\bf v} \right){\partial v_{i}\over{\partial x_{j}}} + \zeta \delta_{ij}{\partial v_{i}\over{\partial x_{j}}} abla\cdot {\bf v} \\\ &= {\mu\over{2}}\left( {\partial v_{i}\over{\partial x_{j}}} + {\partial v_{j}\over{\partial x_{i}}} - {2\over{3}}\delta_{ij} abla\cdot {\bf v} \right)^{2} + \zeta( abla \cdot {\bf v})^{2} \end{aligned} Thus leading to the final form of the equation for specific entropy production:\rho T {Ds\over{Dt}} = abla\cdot(\kappa abla T) + {\mu\over{2}}\left( {\partial v_{i}\over{\partial x_{j}}} + {\partial v_{j}\over{\partial x_{i}}} - {2\over{3}}\delta_{ij} abla\cdot {\bf v} \right)^{2} + \zeta( abla \cdot {\bf v})^{2} In the case where thermal conduction and viscous forces are absent, the equation for entropy production collapses to Ds/Dt=0 \- showing that ideal fluid flow is isentropic. == Application == This equation is derived in Section 49, at the opening of the chapter on "Thermal Conduction in Fluids" in the sixth volume of L.D. Landau and E.M. Lifshitz's Course of Theoretical Physics. Boca Raton, Florida, 2003; Section 6, Fluid Properties; Thermal Conductivity of Gases ===LNG=== As quoted from this source in an online version of: J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 4; Table 4.1, Electronic Configuration and Properties of the Elements * Ho, C. Y., Powell, R. W., and Liley, P. E., J. Phys. Chem. Ref. Data 3:Suppl. 1 (1974) ===WEL=== As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? K (? °C), ? K (? °C), ? * A.M. James and M.P. Lord in Macmillan's Chemical and Physical Data, Macmillan, London, UK, 1992. ==See also== * List of thermal conductivities Category:Properties of chemical elements Category:Chemical element data pages LNG: Values refer to 300 K. * Ref. WEL: Values refer to 25 °C. ==References== ===CRC=== As quoted from various sources in an online version of: * David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. J/(mol K) Heat capacity cp ? J/(mol K) Heat capacity cp ? J/(mol K) Heat capacity cp ? * J.A. Dean (ed) in Lange's Handbook of Chemistry, McGraw-Hill, New York, USA, 14th edition, 1992. This page provides supplementary chemical data on Lutetium(III) oxide == Thermodynamic properties == Phase behavior Triple point ? * X \sim \mathrm{GH}(1, \alpha, \beta, \delta, \mu)\, has a hyperbolic distribution.	5.1	240	'-8.0'	2.25	0.9731	B
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A sample of $4.50 \mathrm{~g}$ of methane occupies $12.7 \mathrm{dm}^3$ at $310 \mathrm{~K}$. Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by $3.3 \mathrm{dm}^3$.	In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. The heat that is added to the gas goes only partly into heating the gas, while the rest is transformed into the mechanical work performed by the piston. Consider the difference between adding heat to the gas with a locked piston and adding heat with a piston free to move, so that pressure remains constant. Work in compressed air, compressed air work or hyperbaric work is occupational activity in an enclosed atmosphere at a controlled ambient pressure significantly higher than the adjacent normal atmospheric pressure. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Despite this, if the density is fairly low and intermolecular forces are negligible, the two heat capacities may still continue to differ from each other by a fixed constant (as above, ), which reflects the relatively constant difference in work done during expansion for constant pressure vs. constant volume conditions. In the second case, the gas will both heat and expand, causing the piston to do mechanical work on the atmosphere. Therefore, the heat capacity ratio in this example is 1.4. A methane reformer is a device based on steam reforming, autothermal reforming or partial oxidation and is a type of chemical synthesis which can produce pure hydrogen gas from methane using a catalyst. A gas heater is a space heater used to heat a room or outdoor area by burning natural gas, liquefied petroleum gas, propane, or butane. Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. thumb\|Large propane torch used for construction A propane torch is a tool normally used for the application of flame or heat which uses propane, a hydrocarbon gas, for its fuel and ambient air as its combustion medium. We assume the expansion occurs without exchange of heat (adiabatic expansion). Conventional steam reforming plants operate at pressures between 200 and 600 psi with outlet temperatures in the range of 815 to 925 °C. In the first, constant-volume case (locked piston), there is no external motion, and thus no mechanical work is done on the atmosphere; is used. To return to the target temperature (still with a free piston), the air must be heated, but is no longer under constant volume, since the piston is free to move as the gas is reheated. The stoichiometric equation for complete combustion of propane with 100% oxygen is: :C3H8 \+ 5 (O2) → 4 (H2O) + 3 (CO2) In this case, the only products are CO2 and water. The balanced equation shows to use 1 mole of propane for every 5 moles of oxygen. An example of incomplete combustion that uses 1 mole of propane for every 4 moles of oxygen: :C3H8 \+ 4 (O2) → 4 (H2O) + 2 (CO2) + 1 C The extra carbon product will cause soot to form, and the less oxygen used, the more soot will form. Oxygen-fed torches can be much hotter at up to . ==See also== * Butane torch * Blowtorch * Thermal lance ==References== ==Bibliography== * * ==External links== * How to Silver Solder Steel with a Propane Torch * How To properly Heat Up Copper Pipe Using A Propane Torch Category:Burners Category:Metalworking tools Category:Welding Torch Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures. Another way of understanding the difference between and is that applies if work is done to the system, which causes a change in volume (such as by moving a piston so as to compress the contents of a cylinder), or if work is done by the system, which changes its temperature (such as heating the gas in a cylinder to cause a piston to move). applies only if P\,\mathrm{d}V = 0, that is, no work is done.	16	3.07	7200.0	15.1	-88	E
The barometric formula relates the pressure of a gas of molar mass $M$ at an altitude $h$ to its pressure $p_0$ at sea level. Derive this relation by showing that the change in pressure $\mathrm{d} p$ for an infinitesimal change in altitude $\mathrm{d} h$ where the density is $\rho$ is $\mathrm{d} p=-\rho g \mathrm{~d} h$. Remember that $\rho$ depends on the pressure. Evaluate the pressure difference between the top and bottom of a laboratory vessel of height 15 cm.	The barometric formula is a formula used to model how the pressure (or density) of the air changes with altitude. == Pressure equations == thumb\|300px\|Pressure as a function of the height above the sea level There are two equations for computing pressure as a function of height. Subscript b Height Above Sea Level (h) Mass Density (\rho) Standard Temperature (T') (K) Temperature Lapse Rate (L) (m) (ft) (kg/m3) (slug/ft3) (K/m) (K/ft) 0 0 0 1.2250 288.15 0.0065 0.0019812 1 11 000 36,089.24 0.36391 216.65 0.0 0.0 2 20 000 65,616.79 0.08803 216.65 -0.001 -0.0003048 3 32 000 104,986.87 0.01322 228.65 -0.0028 -0.00085344 4 47 000 154,199.48 0.00143 270.65 0.0 0.0 5 51 000 167,322.83 0.00086 270.65 0.0028 0.00085344 6 71 000 232,939.63 0.000064 214.65 0.002 0.0006096 ==Derivation== The barometric formula can be derived using the ideal gas law: P = \frac{\rho}{M} {R^} T Assuming that all pressure is hydrostatic: dP = - \rho g\,dz and dividing the dP by the P expression we get: \frac{dP}{P} = - \frac{M g\,dz}{R^T} Integrating this expression from the surface to the altitude z we get: P = P_0 e^{-\int_{0}^{z}{M g dz/R^T}} Assuming linear temperature change T = T_0 - L z and constant molar mass and gravitational acceleration, we get the first barometric formula: P = P_0 \cdot \left[\frac{T}{T_0}\right]^{\textstyle \frac{M g}{R^ L}} Instead, assuming constant temperature, integrating gives the second barometric formula: P = P_0 e^{-M g z/R^T} In this formulation, R is the gas constant, and the term RT/Mg gives the scale height (approximately equal to 8.4 km for the troposphere). This then yields a more accurate formula, of the form P_h = P_0 e^{-\frac{mgh}{kT}}, where is the pressure at height , * is the pressure at reference point 0 (typically referring to sea level), * is the mass per air molecule, * is the acceleration due to gravity, * is height from reference point 0, * is the Boltzmann constant, * is the temperature in kelvins. Subscript b Height above sea level Static pressure Standard temperature (K) Temperature lapse rate Exponent g0 M / R L (m) (ft) (Pa) (inHg) (K/m) (K/ft) 0 0 0 101 325.00 29.92126 288.15 0.0065 0.0019812 5.2558 1 11 000 36,089 22 632.10 6.683245 216.65 0.0 0.0 -- 2 20 000 65,617 5474.89 1.616734 216.65 -0.001 -0.0003048 -34.1626 3 32 000 104,987 868.02 0.2563258 228.65 -0.0028 -0.00085344 -12.2009 4 47 000 154,199 110.91 0.0327506 270.65 0.0 0.0 -- 5 51 000 167,323 66.94 0.01976704 270.65 0.0028 0.00085344 12.2009 6 71 000 232,940 3.96 0.00116833 214.65 0.002 0.0006096 17.0813 ==Density equations== The expressions for calculating density are nearly identical to calculating pressure. Equation 1: \rho = \rho_b \left[\frac{T_b - (h-h_b) L_b}{T_b}\right]^{\left(\frac{g_0 M}{R^* L_b}-1\right)} which is equivalent to the ratio of the relative pressure and temperature changes \rho = \rho_b \frac{P}{T} \frac{T_b}{P_b} Equation 2: \rho =\rho_b \exp\left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right] where {\rho} = mass density (kg/m3) T_b = standard temperature (K) L = standard temperature lapse rate (see table below) (K/m) in ISA h = height above sea level (geopotential meters) R^ = universal gas constant 8.3144598 N·m/(mol·K) g_0 = gravitational acceleration: 9.80665 m/s2 M = molar mass of Earth's air: 0.0289644 kg/mol or, converted to U.S. gravitational foot-pound-second units (no longer used in U.K.): {\rho} = mass density (slug/ft3) {T_b} = standard temperature (K) {L} = standard temperature lapse rate (K/ft) {h} = height above sea level (geopotential feet) {R^} = universal gas constant: 8.9494596×104 ft2/(s·K) {g_0} = gravitational acceleration: 32.17405 ft/s2 {M} = molar mass of Earth's air: 0.0289644 kg/mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. The equation is as follows: \frac{dP}{dh} = - \rho g , where * is pressure, * is density, * is acceleration of gravity, and * is height. When density and gravity are approximately constant (that is, for relatively small changes in height), simply multiplying height difference, gravity, and density will yield a good approximation of pressure difference. Different formulas are presented for different kinds of approximations; for comparison with the previous formula, the first referenced from the article will be the one applying the same constant-temperature approximation; in which case: z = -\frac{RT}{g} \ln \frac{P}{P_0} where (with values used in the article) * is the elevation in meters, * is the specific gas constant = * is the absolute temperature in kelvins = at sea level, * is the acceleration due to gravity = at sea level, * is the pressure at a given point at elevation in Pascals, and * is pressure at the reference point = at sea level. This may seem counter-intuitive, as pressure results from height rather than vice versa, but such a formula can be useful in finding height based on pressure difference when one knows the latter and not the former. However, the vertical variation is especially significant, as it results from the pull of gravity on the fluid; namely, for the same given fluid, a decrease in elevation within it corresponds to a taller column of fluid weighing down on that point. ==Basic formula== A relatively simple version of the vertical fluid pressure variation is simply that the pressure difference between two elevations is the product of elevation change, gravity, and density. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C. where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/ft) in ISA h = height at which pressure is calculated (ft) h_b = height of reference level b (feet; e.g., hb = 36,089 ft) R^* = universal gas constant; using feet, kelvins, and (SI) moles: g_0 = gravitational acceleration: 32.17405 ft/s2 M = molar mass of Earth's air: 28.9644 lb/lb-mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. Vertical pressure variation is the variation in pressure as a function of elevation. Thus water's density can be more reasonably approximated as constant than that of air, and given the same height difference, the pressure differences in water are approximately equal at any height. ==Hydrostatic paradox== thumb\|upright\|Diagram illustrating the hydrostatic paradox The barometric formula depends only on the height of the fluid chamber, and not on its width or length. (The total air mass below a certain altitude is calculated by integrating over the density function.) Image:Liquid ocean atmosphere model.png ===Isothermal-barotropic approximation and scale height=== This atmospheric model assumes both molecular weight and temperature are constant over a wide range of altitude. Assuming density is constant, then a graph of pressure vs altitude will have a retained slope, since the weight of the ocean over head is directly proportional to its depth. An alternative derivation, shown by the Portland State Aerospace Society, is used to give height as a function of pressure instead. This is the recommended formula to use. ==See also== * Barometer * Hypsometric equation * Pascal's barrel * Ruina montium * Pressure gradient * Siphon ==References== * ==External links== Category:Pressure Category:Vertical position For the isothermal-barotropic model, density and pressure turn out to be exponential functions of altitude. If the pressure at one point in a liquid with uniform density ρ is known to be P0, then the pressure at another point is P1: :P_1=P_0 - \rho g (h_1 - h_0) where h1 \- h0 is the vertical distance between the two points.Streeter, Victor L. (1966). The first equation is applicable to the standard model of the troposphere in which the temperature is assumed to vary with altitude at a lapse rate of L_b: P = P_b \left[\frac{T_b - \left(h - h_b\right) L_b}{T_b}\right]^{\tfrac{g_0 M}{R^* L_b}} The second equation is applicable to the standard model of the stratosphere in which the temperature is assumed not to vary with altitude: P = P_b \exp \left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right] where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/m) in ISA h = height at which pressure is calculated (m) h_b = height of reference level b (meters; e.g., hb = 11 000 m) R^* = universal gas constant: 8.3144598 J/(mol·K) g_0 = gravitational acceleration: 9.80665 m/s2 M = molar mass of Earth's air: 0.0289644 kg/mol Or converted to imperial units:Mechtly, E. A., 1973: The International System of Units, Physical Constants and Conversion Factors. Since is negative, an increase in height will correspond to a decrease in pressure, which fits with the previously mentioned reasoning about the weight of a column of fluid.	0.01961	0.00017	0.2553	362880	0.6296296296	B
The mass density of water vapour at $327.6 \mathrm{~atm}$ and $776.4 \mathrm{~K}$ is $133.2 \mathrm{~kg} \mathrm{~m}^{-3}$. Given that for water $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, and $M=18.02 \mathrm{~g} \mathrm{~mol}^{-1}$, calculate the molar volume.	The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). Calculations of the (saturation) vapour pressure of water are commonly used in meteorology. Liquid water path - in units of g/m2 is a measure of the total amount of liquid water present between two points in the atmosphere. thumb\|The Mollier enthalpy–entropy diagram for water and steam. Air is given a vapour density of one. Further g is acceleration due to gravity and ρ is the fluid density. Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. For this use, air has a molecular weight of 28.97 atomic mass units, and all other gas and vapour molecular weights are divided by this number to derive their vapour density.HazMat Math: Calculating Vapor Density . Further ρ is the (constant) fluid density and g is the gravitational acceleration. The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. It may be defined as mass of a certain volume of a substance divided by mass of same volume of hydrogen. :vapour density = mass of n molecules of gas / mass of n molecules of hydrogen gas . :vapour density = molar mass of gas / molar mass of H2 :vapour density = molar mass of gas / 2.016 :vapour density = × molar mass (and thus: molar mass = ~2 × vapour density) For example, vapour density of mixture of NO2 and N2O4 is 38.3. U.S. Geological Survey Water-Supply Paper 1541-B' An example of a double mass analysis is a "double mass plot", or "double mass curve".Wilson, E.M. (1983) Engineering Hydrology, 3rd edition. Double mass analysis is a simple graphical method to evaluate the consistency of hydrological data. The first equation is derived from mass conservation, the second two from momentum conservation. ===Non-conservative form=== Expanding the derivatives in the above using the product rule, the non-conservative form of the shallow-water equations is obtained. In the case of a horizontal bed, with negligible Coriolis forces, frictional and viscous forces, the shallow-water equations are: \begin{align} \frac{\partial (\rho \eta) }{\partial t} &\+ \frac{\partial (\rho \eta u)}{\partial x} + \frac{\partial (\rho \eta v)}{\partial y} = 0,\\\\[3pt] \frac{\partial (\rho \eta u)}{\partial t} &\+ \frac{\partial}{\partial x}\left( \rho \eta u^2 + \frac{1}{2}\rho g \eta^2 \right) + \frac{\partial (\rho \eta u v)}{\partial y} = 0,\\\\[3pt] \frac{\partial (\rho \eta v)}{\partial t} &\+ \frac{\partial}{\partial y}\left(\rho \eta v^2 + \frac{1}{2}\rho g \eta ^2\right) + \frac{\partial (\rho \eta uv)}{\partial x} = 0. \end{align} Here η is the total fluid column height (instantaneous fluid depth as a function of x, y and t), and the 2D vector (u,v) is the fluid's horizontal flow velocity, averaged across the vertical column. For nadir observations and whole atmospheric column we have :LWP=\int_{z=0}^\infty \rho_{air} r_L dz' where is the liquid water mixing ratio and is the density of air (including water loading). X gives the fraction (by mass) of gaseous substance in the wet region, the remainder being colloidal liquid droplets. The Mollier diagram coordinates are enthalpy h and humidity ratio x. thumb\|491px\|right\|Output from a shallow-water equation model of water in a bathtub. The shallow- water equations are thus derived.	-1.32	-9.54	'-13.598'	4.49	0.1353	E
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \mathrm{~mol} \mathrm{CO}_2(\mathrm{~g})$, initially at $25^{\circ} \mathrm{C}$ and $10 \mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \mathrm{~m}}=28.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and calculate $q$.	If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. For light-duty CNG cars to become a viable short-term climate strategy, methane leakage would need to be kept below 1.6% of total natural gas produced (approximately half the current amount for well to wheels – note difference from well to city)." However, CNG requires a much larger volume to store the energy equivalent of petrol and the use of very high pressures (3000 to 4000 psi, or 205 to 275 bar). ** The lifecycle greenhouse gas emissions for CNG compressed from California's pipeline natural gas is given a value of 67.70 grams of -equivalent per megajoule (gCO2e/MJ) by CARB (the California Air Resources Board), approximately 28 percent lower than the average petrol fuel in that market (95.86 gCO2e/MJ). Compressed natural gas (CNG) is a fuel gas mainly composed of methane (CH4), compressed to less than 1% of the volume it occupies at standard atmospheric pressure. A 2012 study of the effects for the original hypothesis, based on a coupled climate–carbon cycle model (GCM) assessed a 1000-fold (from <1 to 1000 ppmv) methane increase—within a single pulse, from methane hydrates (based on carbon amount estimates for the PETM, with ~2000 GtC), and concluded it would increase atmospheric temperatures by more than 6 °C within 80 years. * Being a gaseous fuel, CNG mixes easily and evenly in air. A carbon dioxide generator or CO2 generator is a machine used to enhance carbon dioxide levels in order to promote plant growth in greenhouses or other enclosed areas. thumb\|upright=1.6\|Methane clathrate is released as gas into the surrounding water column or soils when ambient temperature increases thumb\|upright=1.6\|The impact of CH4 atmospheric methane concentrations on global temperature increase may be far greater than previously estimated. [http://regmorrison.edublogs.org/files/2013/02/METHANE-2-1sca3tx.pdf] The clathrate gun hypothesis is a proposed explanation for the periods of rapid warming during the Quaternary. The estimated amount of methane hydrate in this slope is 2.5 gigatonnes (about 0.2% of the amount required to cause the PETM), and it is unclear if the methane could reach the atmosphere. This would have had an immediate impact on the global temperature, as methane is a much more powerful greenhouse gas than carbon dioxide. In a fire, the pressure in a gas cylinder rises in direct proportion to its temperature. A release on this scale would increase the methane content of the planet's atmosphere by a factor of twelve, equivalent in greenhouse effect to a doubling in the 2008 level of . Especially, for the CNG Type 1 and Type 2 cylinders, many countries are able to make reliable and cost effective cylinders for conversion need. ==Energy density== CNG's energy density is the same as liquefied natural gas at 53.6 MJ/kg. Natural gas is being experimentally stored at lower pressure in a form known as an ANG (adsorbed natural gas) cylinder, where it is adsorbed at 35 bar (500 psi, the pressure of gas in natural gas pipelines) in various sponge-like materials, such as carbon and MOFs (metal-organic frameworks). ** CNG produced from landfill biogas was found by CARB to have the lowest greenhouse gas emissions of any fuel analyzed, with a value of 11.26 gCO2e/MJ (more than 88 percent lower than conventional petrol) in the low-carbon fuel standard that went into effect on January 12, 2010. Gastric tonometry describes the measurement of the carbon dioxide level inside the stomach in order to assess the degree of blood flow to the stomach and bowel. Normocapnia or normocarbia is a state of normal arterial carbon dioxide pressure, usually about 40 mmHg. == See also == * * * == References == *The Free Dictionary - Normocapnia Category:Diving medicine Category:Pulmonology Since it is a compressed gas, rather than a liquid like petrol, CNG takes up more space for each GGE (petrol gallon equivalent). Accumulation of carbon dioxide is predominantly a result of hypoperfusion and not hypoxia. For gases that are liquid under storage, e.g., propane, the outlet pressure is dependent on the vapor pressure of the gas, and does not fall until the cylinder is nearly exhausted, although it will vary according to the temperature of the cylinder contents. In this process known as high pressure ANG, a high pressure CNG tank is filled by absorbers such as activated carbon (which is an adsorbent with high surface area) and stores natural gas by both CNG and ANG mechanisms.	0	1000	0.18	-1.5	1855	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \mathrm{~mol}$ of diatomic perfect gas molecules at $200 \mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \mathrm{~K}$. Given that $C_{V, \mathrm{~m}}=27.5 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, calculate $\Delta S$.	Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. A calorically perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, and enthalpy H that are functions of temperature only, i.e., U = U(T), H = H(T) * has heat capacities C_V, C_P that are constant, i.e., dU = C_V dT, dH = C_P dT and \Delta U = C_V \Delta T, \Delta H = C_P \Delta T, where \Delta is any finite (non-differential) change in each quantity. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). For a diatomic gas, often 5 degrees of freedom are assumed to contribute at room temperature since each molecule has 3 translational and 2 rotational degrees of freedom, and the single vibrational degree of freedom is often not included since vibrations are often not thermally active except at high temperatures, as predicted by quantum statistical mechanics. From both statistical mechanics and the simpler kinetic theory of gases, we expect the heat capacity of a monatomic ideal gas to be constant, since for such a gas only kinetic energy contributes to the internal energy and to within an arbitrary additive constant U = (3/2) n R T , and therefore C_V = (3/2) n R , a constant. == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. Compressed natural gas (CNG) is a fuel gas mainly composed of methane (CH4), compressed to less than 1% of the volume it occupies at standard atmospheric pressure. Nomenclature 1 Nomenclature 2 Heat capacity at constant V, C_V, or constant P, C_P Ideal-gas law PV = nRT and C_P - C_V = nR Calorically perfect Perfect Thermally perfect Semi-perfect Ideal Imperfect Imperfect, or non-ideal === Thermally and calorically perfect gas === Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. A conversion factor is included into the original first coefficients of the equations to provide the pressure in pascals (CR2: 5.006, SMI: -0.875). The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. It can be proved that an ideal gas (i.e. satisfying the ideal gas equation of state, PV = nRT ) is either calorically perfect or thermally perfect. Thus we observe that for a monatomic gas, with 3 translational degrees of freedom per atom: : \gamma = \frac{5}{3} = 1.6666\ldots, As an example of this behavior, at 273 K (0 °C) the noble gases He, Ne, and Ar all have nearly the same value of , equal to 1.664. But even if the heat capacity is strictly a function of temperature for a given gas, it might be assumed constant for purposes of calculation if the temperature and heat capacity variations are not too large, which would lead to the assumption of a calorically perfect gas (see below). In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. This temperature limit depends on the chemical composition of the gas and how accurate the calculations need to be, since molecular dissociation may be important at a higher or lower temperature which is intrinsically dependent on the molecular nature of the gas. For an imperfect or non-ideal gas, Chandrasekhar defined three different adiabatic indices so that the adiabatic relations can be written in the same form as above; these are used in the theory of stellar structure: : \begin{align} \Gamma_1 &= \left.\frac{\partial \ln P}{\partial \ln \rho}\right\|_{S}, \\\\[2pt] \frac{\Gamma_2 - 1}{\Gamma_2} &= \left.\frac{\partial \ln T}{\partial \ln P}\right\|_{S}, \\\\[2pt] \Gamma_3 - 1 &= \left.\frac{\partial \ln T}{\partial \ln \rho}\right\|_{S}. \end{align} All of these are equal to \gamma in the case of an ideal gas. == See also == * Relations between heat capacities * Heat capacity * Specific heat capacity * Speed of sound * Thermodynamic equations * Thermodynamics * Volumetric heat capacity == References == == Notes == Category:Thermodynamic properties Category:Physical quantities Category:Ratios Category:Thought experiments in physics Sometimes, other distinctions are made, such as between thermally perfect gas and calorically perfect gas, or between imperfect, semi-perfect, and perfect gases, and as well as the characteristics of ideal gases. In addition, other factors come into play and dominate during a compression cycle if they have a greater impact on the final calculated result than whether or not C_P was held constant. (i) Indicates values calculated from ideal gas thermodynamic functions.	0	650000	4.68	0.925	-0.38	A
Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. Find an expression for the fugacity coefficient of a gas that obeys the equation of state $p V_{\mathrm{m}}=R T\left(1+B / V_{\mathrm{m}}+C / V_{\mathrm{m}}^2\right)$. Use the resulting expression to estimate the fugacity of argon at 1.00 atm and $100 \mathrm{~K}$ using $B=-21.13 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$ and $C=1054 \mathrm{~cm}^6 \mathrm{~mol}^{-2}$.	For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure. The fugacity coefficient is . Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. Using , where is the fugacity coefficient, f = \varphi_\mathrm{sat}P_\mathrm{sat}\exp\left(\frac{V\left(P-P_\mathrm{sat}\right)}{R T}\right). This error is corrected in the above equation. ==Measurement== The fugacity can be deduced from measurements of volume as a function of pressure at constant temperature. In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. When using a fugacity capacity approach to calculate the concentrations of a chemical in each of several medias/phases/compartments, it is often convenient to calculate the prevailing fugacity of the system using the following equation if the total mass of target chemical (MT) and the volume of each compartment (Vm) are known: :f = M_T / \Sigma_m (V_m Z_m) Alternatively, if the target chemical is present as a pure phase at equilibrium, its vapor pressure will be the prevailing fugacity of the system. ==See also== * Multimedia fugacity model ==References== Category:Chemical thermodynamics Category:Environmental chemistry Category:Equilibrium chemistry The real gas pressure and fugacity are related through the dimensionless fugacity coefficient . \varphi = \frac{f}{P} For an ideal gas, fugacity and pressure are equal and so . If the chemical potential of each gas is expressed as a function of fugacity, the equilibrium condition may be transformed into the familiar reaction quotient form (or law of mass action) except that the pressures are replaced by fugacities. Numerical example: Nitrogen gas (N2) at 0 °C and a pressure of atmospheres (atm) has a fugacity of atm. In addition, there are natural reference states for fugacity (for example, an ideal gas makes a natural reference state for gas mixtures since the fugacity and pressure converge at low pressure). ===Gases=== In a mixture of gases, the fugacity of each component has a similar definition, with partial molar quantities instead of molar quantities (e.g., instead of and instead of ): dG_i = R T \,d \ln f_i and \lim_{P\to 0} \frac{f_i}{P_i} = 1, where is the partial pressure of component . :C_m = Z_m \cdot f where Z is a proportional constant, termed fugacity capacity. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. Fugacities are determined experimentally or estimated from various models such as a Van der Waals gas that are closer to reality than an ideal gas. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). The constant of proportionality (a measured Henry's constant) depends on whether the concentration is represented by the mole fraction, molality or molarity. ==Temperature and pressure dependence== The pressure dependence of fugacity (at constant temperature) is given by \left(\frac{\partial \ln f}{\partial P}\right)_T = \frac{V_\mathrm{m}}{R T} and is always positive. The fugacities commonly obey a similar law called the Lewis and Randall rule: f_i = y_i f^*_i, where is the fugacity that component would have if the entire gas had that composition at the same temperature and pressure. Hemond and Hechner-Levy (2000) describe how to utilize the fugacity capacity to calculate the concentration of a chemical in a system. Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures.	6.6	0.03	0.9974	-4564.7	2.3613	C
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the maximum non-expansion work per mole that may be obtained from a fuel cell in which the chemical reaction is the combustion of methane at $298 \mathrm{~K}$.	For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. Even more restricted is the calorically perfect gas for which, in addition, the heat capacity is assumed to be constant. From both statistical mechanics and the simpler kinetic theory of gases, we expect the heat capacity of a monatomic ideal gas to be constant, since for such a gas only kinetic energy contributes to the internal energy and to within an arbitrary additive constant U = (3/2) n R T , and therefore C_V = (3/2) n R , a constant. This temperature limit depends on the chemical composition of the gas and how accurate the calculations need to be, since molecular dissociation may be important at a higher or lower temperature which is intrinsically dependent on the molecular nature of the gas. A calorically perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, and enthalpy H that are functions of temperature only, i.e., U = U(T), H = H(T) * has heat capacities C_V, C_P that are constant, i.e., dU = C_V dT, dH = C_P dT and \Delta U = C_V \Delta T, \Delta H = C_P \Delta T, where \Delta is any finite (non-differential) change in each quantity. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. ==References== ==External links== * Ideal gas calculator – Ideal gas calculator provides the correct information for the moles of gas involved. But even if the heat capacity is strictly a function of temperature for a given gas, it might be assumed constant for purposes of calculation if the temperature and heat capacity variations are not too large, which would lead to the assumption of a calorically perfect gas (see below). Instead of a mole the constant can be expressed by considering the normal cubic meter. * Individual Gas Constants and the Universal Gas Constant – Engineering Toolbox Category:Ideal gas Category:Physical constants Category:Amount of substance Category:Statistical mechanics Category:Thermodynamics The contribution of nonideality to the molar Gibbs energy of a real gas is equal to . Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB): R = N_{\rm A} k. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. Pressure gain combustion is a combustion process whereby gas expansion by heat release is constrained, causing a rise in stagnation pressure and allowing work extraction by expansion to the initial pressure. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. Mayer's relation relates the specific gas constant to the specific heat capacities for a calorically perfect gas and a thermally perfect gas. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = .	54.7	91.7	'-233.0'	817.90	0	D
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. Silylene $\left(\mathrm{SiH}_2\right)$ is a key intermediate in the thermal decomposition of silicon hydrides such as silane $\left(\mathrm{SiH}_4\right)$ and disilane $\left(\mathrm{Si}_2 \mathrm{H}_6\right)$. Moffat et al. (J. Phys. Chem. 95, 145 (1991)) report $\Delta_{\mathrm{f}} H^{\ominus}\left(\mathrm{SiH}_2\right)=+274 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\Delta_{\mathrm{f}} H^{\ominus}\left(\mathrm{SiH}_4\right)=+34.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta_{\mathrm{f}} H^{\ominus}\left(\mathrm{Si}_2 \mathrm{H}_6\right)=+80.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$(CRC Handbook (2008)), compute the standard enthalpies of the following reaction: $\mathrm{Si}_2 \mathrm{H}_6(\mathrm{g}) \rightarrow \mathrm{SiH}_2(\mathrm{g})+\mathrm{SiH}_4(\mathrm{g})$	Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? ==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.18 1.293 65 KAL 33.2 1.297 65.0 SMI −239.9 13.2 kgf/cm² 0.0310 1 H hydrogen (equilibrium) LNG −240.17 1.294 12.77 atm 65.4 0.0308 1 H hydrogen (normal) LNG −239.91 1.297 12.8 atm 65.0 0.0310 1 D deuterium KAL 38.2 1.65 60 1 D deuterium (equilibrium) LNG −234.8 1.650 16.28 atm 60.4 0.0668 1 D deuterium (normal) LNG −234.7 1.665 16.43 atm 60.3 0.0669 2 He helium use 5.19 −267.96 0.227 CRC.a 5.19 −267.96 0.227 57 KAL 5.19 0.227 57.2 SMI −267.9 2.34 kgf/cm² 0.0693 2 He helium (equilibrium) LNG −267.96 0.2289 2.261 atm 0.06930 2 He helium-3 LNG −269.85 0.1182 1.13 atm 72.5 0.0414 2 He helium-4 LNG −267.96 0.227 2.24 atm 57.3 0.0698 3 Li lithium use (3223) (2950) (67) CRC.b (3223) 2950 (67) (66) 7 N nitrogen use 126.21 −146.94 3.39 CRC.a 126.21 −146.94 3.39 90 KAL 126.2 3.39 89.5 SMI −147.1 34.7 kgf/cm² 0.3110 7 N nitrogen-14 LNG −146.94 3.39 33.5 atm 89.5 0.313 7 N nitrogen-15 LNG −146.8 3.39 33.5 atm 90.4 0.332 8 O oxygen use 154.59 −118.56 5.043 CRC.a 154.59 −118.56 5.043 73 LNG −118.56 5.043 49.77 atm 73.4 0.436 KAL 154.6 5.04 73.4 SMI −118.8 51.4 kgf/cm² 0.430 9 F fluorine use 144.13 −129.02 5.172 CRC.a 144.13 −129.02 5.172 66 LNG −129.0 5.215 51.47 atm 66.2 0.574 KAL 144.3 5.22 66 10 Ne neon use 44.4 −228.7 2.76 CRC.a 44.4 −228.7 2.76 42 LNG −228.71 2.77 27.2 atm 41.7 0.4835 KAL 44.4 2.76 41.7 SMI −228.7 26.8 kgf/cm² 0.484 11 Na sodium use (2573) (2300) (35) CRC.b (2573) 2300 (35) (116) 15 P phosphorus use 994 721 CRC.a 994 721 LNG 721 16 S sulfur use 1314 1041 20.7 CRC.a 1314 1041 20.7 LNG 1041 11.7 116 atm KAL 1314 20.7 SMI 1040 17 Cl chlorine use 416.9 143.8 7.991 CRC.a 416.9 143.8 7.991 123 LNG 143.8 7.71 76.1 atm 124 0.573 KAL 416.9 7.98 124 SMI 144.0 78.7 kgf/cm² 0.573 18 Ar argon use 150.87 −122.28 4.898 CRC.a 150.87 −122.28 4.898 75 LNG −122.3 4.87 48.1 atm 74.6 0.536 KAL 150.9 4.90 74.6 SMI −122 49.7 kgf/cm² 0.531 19 K potassium use (2223) (1950) (16) CRC.b (2223) 1950 (16) (209) 33 As arsenic use 1673 1400 CRC.a 1673 1400 35 LNG 1400 34 Se selenium use 1766 1493 27.2 CRC.a 1766 1493 27.2 LNG 1493 35 Br bromine use 588 315 10.34 CRC.a 588 315 10.34 127 LNG 315 10.3 102 atm 135 1.184 KAL 588 10.3 127 SMI 302 1.18 36 Kr krypton use 209.41 −63.74 5.50 CRC.a 209.41 −63.74 5.50 91 LNG −63.75 5.50 54.3 atm 91.2 0.9085 KAL 209.4 5.50 91.2 37 Rb rubidium use (2093) (1820) (16) CRC.b (2093) 1820 (16) (247) LNG 1832 250 0.34 53 I iodine use 819 546 11.7 CRC.a 819 546 155 LNG 546 11.7 115 atm 155 0.164 KAL 819 155 SMI 553 54 Xe xenon use 289.77 16.62 5.841 CRC.c 289.77 16.62 5.841 118 LNG 16.583 5.84 57.64 atm 118 1.105 KAL 289.7 5.84 118 SMI 16.6 60.2 kgf/cm² 1.155 55 Cs caesium use 1938 1665 9.4 CRC.d 1938 1665 9.4 341 LNG 1806 300 0.44 80 Hg mercury use 1750 1477 172.00 CRC.a 1750 1477 172.00 43 LNG 1477 160.8 1587 atm KAL 1750 172 42.7 SMI 1460±20 1640±50 kgf/cm² 0.5 86 Rn radon use 377 104 6.28 CRC.a 377 104 6.28 LNG 104 6.28 62 atm 139 1.6 KAL 377 6.3 SMI 104 64.1 kgf/cm² ==References== ===CRC.a-d=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 85th Edition, online version. J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? :(d) N.B. Vargaftik, Int. J. Thermophys. 11, 467, (1990). ===LNG=== J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6; Table 6.5 Critical Properties ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; D. Ambrose, M.B. Ewing, M.L. McGlashan, Critical constants and second virial coefficients of gases (retrieved Dec 2005) ===SMI=== W.E. Forsythe (ed.), Smithsonian Physical Tables 9th ed., online version (1954; Knovel 2003). :(c) O. Sifner, J. Klomfar, J. Phys. Chem. Ref. Data 23, 63, (1994). J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? {{OrganicBox complete \|wiki_name=Lysine \|image=110px\|Skeletal structure of L-lysine 130px\|3D structure of L-lysine \|name=-2,6-Diaminohexanoic acid \|C=6 \|H=14 \|N=2 \|O=2 \|mass=146.19 \|abbreviation=K, Lys \|synonyms= \|SMILES=NCCCCC(N)C(=O)O \|InChI=1/C6H14N2O2/c7-4-2-1-3-5(8)6(9)10/h5H,1-4,7-8H2,(H,9,10)/f/h9H \|CAS=56-87-1 \|DrugBank= \|EINECS=200-294-2 \|PubChem=866 (DL) , 5962 (L) \|index_of_refraction= \|abbe_number= \|dielectric_constant= \|magnetic_susceptibility= \|lambda_max= \|extinction_coefficient= \|absorption_bands= \|proton_NMR= \|carbon_NMR= \|other_NMR= \|mass_spectrometry= \|triple_point_K= \|triple_point_C= \|triple_point_Pa= \|criticle_point_K= \|criticle_point_C= \|criticle_point_Pa= \|delta_fus_H_o= \|delta_fus_S_o= \|delta_vap_H_o= \|delta_vap_S_o= \|delta_f_H_o= \|S_o_solid= \|heat_capacity_solid= \|density_solid= \|melting_point_C=224 \|melting_point_F= \|melting_point_K= \|delta_f_H_o_liquid= \|S_o_liquid= \|heat_capacity_liquid= \|density_liquid= \|viscosity_liquid= \|boiling_point_C= \|boiling_point_F= \|boiling_point_K= \|delta_f_H_o_gas= \|S_o_gas= \|heat_capacity_gas= \|viscosity_gas= \|MSDS= \|main_hazards= \|nfpa_health= \|nfpa_flammability= \|nfpa_reactivity= \|nfpa_special= \|flash_point= \|r_phrases= \|s_phrases= \|RTECS_number= \|XLogP=-2.926 \|isoelectric_point=9.74 \|disociation_constant=2.15, 9.16, 10.67 \|tautomers= \|H_bond_donor=3 \|H_bond_acceptor=4 }} ==References== # (Lysine) # (DL-Lysine) # (L-Lysine) Category:Chemical data pages Category:Chemical data pages cleanup ==Thermal conductivity== 1 H hydrogen use 180.5 mW/(m·K) CR2 (P=0) 186.9 mW/(m·K) LNG 0.1805 W/(m·K) WEL 0.1805 W/(m·K) 2 He helium use 151.3 mW/(m·K) CR2 (P=0) 156.7 mW/(m·K) LNG 0.1513 W/(m·K) WEL 0.1513 W/(m·K) 3 Li lithium use 84.8 W/(m·K) CRC 0.847 W/(cm·K) LNG 84.8 W/(m·K) WEL 85 W/(m·K) 4 Be beryllium use 200 W/(m·K) CRC 2.00 W/(cm·K) LNG 200 W/(m·K) WEL 190 W/(m·K) 5 B boron use 27.4 W/(m·K) LNG 27.4 W/(m·K) WEL 27 W/(m·K) 6 C carbon (graphite) use (graphite) (119-165) W/(m·K) LNG (119-165) W/(m·K) LNG (amorphous) 1.59 W/(m·K) WEL 140 W/(m·K) CRC pyrolytic graphite (parallel to the layer planes) 19.5 W/(cm·K) (perpendicular) 0.0570 W/(cm·K) 6 C carbon (diamond) use (diamond) (900-2320) W/(m·K) LNG (900-2320) W/(m·K) CRC (type I) 8.95 W/(cm·K) (type IIa) 23.0 W/(cm·K) (type IIb) 13.5 W/(cm·K) 7 N nitrogen use 25.83 mW/(m·K) CR2 26.0 mW/(m·K) LNG 0.02583 W/(m·K) WEL 0.02583 W/(m·K) 8 O oxygen use 26.58 mW/(m·K) CR2 26.3 mW/(m·K) LNG (gas) 0.02658 W/(m·K) LNG (liquid) 0.149 W/(m·K) WEL 0.02658 W/(m·K) 9 F fluorine use 27.7 mW/(m·K) LNG 0.0277 W/(m·K) WEL 0.0277 W/(m·K) 10 Ne neon use 49.1 mW/(m·K) CR2 (P=0) 49.8 mW/(m·K) LNG 0.0491 W/(m·K) WEL 0.0491 W/(m·K) 11 Na sodium use 142 W/(m·K) CRC 1.41 W/(cm·K) LNG 142 W/(m·K) WEL 140 W/(m·K) 12 Mg magnesium use 156 W/(m·K) CRC 1.56 W/(cm·K) LNG 156 W/(m·K) WEL 160 W/(m·K) 13 Al aluminium use 237 W/(m·K) CRC 2.37 W/(cm·K) LNG 237 W/(m·K) WEL 235 W/(m·K) 14 Si silicon use 149 W/(m·K) LNG 149 W/(m·K) WEL 150 W/(m·K) 15 P phosphorus use (white) 0.236 W/(m·K) LNG (white) 0.23617 W/(m·K) [sic] WEL 0.236 W/(m·K) 16 S sulfur use (amorphous) 0.205 W/(m·K) LNG (amorphous) 0.205 W/(m·K) WEL 0.205 W/(m·K) 17 Cl chlorine use 8.9 mW/(m·K) LNG 0.0089 W/(m·K) WEL 0.0089 W/(m·K) 18 Ar argon use 17.72 mW/(m·K) CR2 17.9 mW/(m·K) LNG 0.01772 W/(m·K) WEL 0.01772 W/(m·K) 19 K potassium use 102.5 W/(m·K) CRC 1.024 W/(cm·K) LNG 102.5 W/(m·K) WEL 100 W/(m·K) 20 Ca calcium use 201 W/(m·K) CRC 2.00 W/(cm·K) LNG 201 W/(m·K) WEL 200 W/(m·K) 21 Sc scandium use 15.8 W/(m·K) CRC 0.158 W/(cm·K) LNG 15.8 W/(m·K) WEL 16 W/(m·K) 22 Ti titanium use 21.9 W/(m·K) CRC 0.219 W/(cm·K) LNG 21.9 W/(m·K) WEL 22 W/(m·K) 23 V vanadium use 30.7 W/(m·K) CRC 0.307 W/(cm·K) LNG 30.7 W/(m·K) WEL 31 W/(m·K) 24 Cr chromium use 93.9 W/(m·K) CRC 0.937 W/(cm·K) LNG 93.9 W/(m·K) WEL 94 W/(m·K) 25 Mn manganese use 7.81 W/(m·K) CRC 0.0782 W/(cm·K) LNG 7.81 W/(m·K) WEL 7.8 W/(m·K) 26 Fe iron use 80.4 W/(m·K) CRC 0.802 W/(cm·K) LNG 80.4 W/(m·K) WEL 80 W/(m·K) 27 Co cobalt use 100 W/(m·K) CRC 1.00 W/(cm·K) LNG 100 W/(m·K) WEL 100 W/(m·K) 28 Ni nickel use 90.9 W/(m·K) CRC 0.907 W/(cm·K) LNG 90.9 W/(m·K) WEL 91 W/(m·K) 29 Cu copper use 401 W/(m·K) CRC 4.01 W/(cm·K) LNG 401 W/(m·K) WEL 400 W/(m·K) 30 Zn zinc use 116 W/(m·K) CRC 1.16 W/(cm·K) LNG 116 W/(m·K) WEL 120 W/(m·K) 31 Ga gallium use 40.6 W/(m·K) CRC 0.406 W/(cm·K) LNG (liquid) 29.4 W/(m·K) LNG (solid) 40.6 W/(m·K) WEL 29 W/(m·K) 32 Ge germanium use 60.2 W/(m·K) LNG 60.2 W/(m·K) WEL 60 W/(m·K) 33 As arsenic use 50.2 W/(m·K) LNG 50.2 W/(m·K) WEL 50 W/(m·K) 34 Se selenium use (amorphous) 0.519 W/(m·K) LNG (amorphous) 0.519 W/(m·K) WEL 0.52 W/(m·K) 35 Br bromine use 0.122 W/(m·K) LNG 0.122 W/(m·K) WEL 0.12 W/(m·K) 36 Kr krypton use 9.43 mW/(m·K) CR2 (P=0) 9.5 mW/(m·K) LNG 9.43 W/(m·K) [sic] WEL 0.00943 W/(m·K) 37 Rb rubidium use 58.2 W/(m·K) CRC 0.582 W/(cm·K) LNG 58.2 W/(m·K) WEL 58 W/(m·K) 38 Sr strontium use 35.4 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.4 W/(m·K) WEL 35 W/(m·K) 39 Y yttrium use 17.2 W/(m·K) CRC 0.172 W/(cm·K) LNG 17.2 W/(m·K) WEL 17 W/(m·K) 40 Zr zirconium use 22.6 W/(m·K) CRC 0.227 W/(cm·K) LNG 22.6 W/(m·K) WEL 23 W/(m·K) 41 Nb niobium use 53.7 W/(m·K) CRC 0.537 W/(cm·K) LNG 53.7 W/(m·K) WEL 54 W/(m·K) 42 Mo molybdenum use 138 W/(m·K) CRC 1.38 W/(cm·K) LNG 138 W/(m·K) WEL 139 W/(m·K) 43 Tc technetium use 50.6 W/(m·K) CRC 0.506 W/(cm·K) LNG 50.6 W/(m·K) WEL 51 W/(m·K) 44 Ru ruthenium use 117 W/(m·K) CRC 1.17 W/(cm·K) LNG 117 W/(m·K) WEL 120 W/(m·K) 45 Rh rhodium use 150 W/(m·K) CRC 1.50 W/(cm·K) LNG 150 W/(m·K) WEL 150 W/(m·K) 46 Pd palladium use 71.8 W/(m·K) CRC 0.718 W/(cm·K) LNG 71.8 W/(m·K) WEL 72 W/(m·K) 47 Ag silver use 429 W/(m·K) CRC 4.29 W/(cm·K) LNG 429 W/(m·K) WEL 430 W/(m·K) 48 Cd cadmium use 96.6 W/(m·K) CRC 0.968 W/(cm·K) LNG 96.6 W/(m·K) WEL 97 W/(m·K) 49 In indium use 81.8 W/(m·K) CRC 0.816 W/(cm·K) LNG 81.8 W/(m·K) WEL 82 W/(m·K) 50 Sn tin use 66.8 W/(m·K) CRC 0.666 W/(cm·K) LNG 66.8 W/(m·K) WEL 67 W/(m·K) 51 Sb antimony use 24.4 W/(m·K) CRC 0.243 W/(cm·K) LNG 24.4 W/(m·K) WEL 24 W/(m·K) 52 Te tellurium use (1.97-3.38) W/(m·K) LNG (1.97-3.38) W/(m·K) WEL 3 W/(m·K) 53 I iodine use 0.449 W/(m·K) CRC (300 K) 0.45 W/(m·K) LNG 449 W/(m·K) [sic] WEL 0.449 W/(m·K) 54 Xe xenon use 5.65 mW/(m·K) CR2 (P=0) 5.5 mW/(m·K) LNG 0.00565 W/(m·K) WEL 0.00565 W/(m·K) 55 Cs caesium use 35.9 W/(m·K) CRC 0.359 W/(cm·K) LNG 35.9 W/(m·K) WEL 36 W/(m·K) 56 Ba barium use 18.4 W/(m·K) CRC 0.184 W/(cm·K) LNG 18.4 W/(m·K) WEL 18 W/(m·K) 57 La lanthanum use 13.4 W/(m·K) CRC 0.134 W/(cm·K) LNG 13.4 W/(m·K) WEL 13 W/(m·K) 58 Ce cerium use 11.3 W/(m·K) CRC 0.113 W/(cm·K) LNG 11.3 W/(m·K) WEL 11 W/(m·K) 59 Pr praseodymium use 12.5 W/(m·K) CRC 0.125 W/(cm·K) LNG 12.5 W/(m·K) WEL 13 W/(m·K) 60 Nd neodymium use 16.5 W/(m·K) CRC 0.165 W/(cm·K) LNG 16.5 W/(m·K) WEL 17 W/(m·K) 61 Pm promethium use 17.9 W/(m·K) CRC (est.) 0.15 W/(cm·K) LNG 17.9 W/(m·K) WEL 15 W/(m·K) 62 Sm samarium use 13.3 W/(m·K) CRC 0.133 W/(cm·K) LNG 13.3 W/(m·K) WEL 13 W/(m·K) 63 Eu europium use (est.) 13.9 W/(m·K) CRC (est.) 0.139 W/(cm·K) LNG 13.9 W/(m·K) WEL 14 W/(m·K) 64 Gd gadolinium use 10.6 W/(m·K) (300 K) 10.6 W/(m·K) CRC (100 °C) 0.105 W/(cm·K) LNG 10.5 W/(m·K) WEL 11 W/(m·K) 65 Tb terbium use 11.1 W/(m·K) CRC 0.111 W/(cm·K) LNG 11.1 W/(m·K) WEL 11 W/(m·K) 66 Dy dysprosium use 10.7 W/(m·K) CRC 0.107 W/(cm·K) LNG 10.7 W/(m·K) WEL 11 W/(m·K) 67 Ho holmium use 16.2 W/(m·K) CRC 0.162 W/(cm·K) LNG 16.2 W/(m·K) WEL 16 W/(m·K) 68 Er erbium use 14.5 W/(m·K) CRC 0.145 W/(cm·K) LNG 14.5 W/(m·K) WEL 15 W/(m·K) 69 Tm thulium use 16.9 W/(m·K) CRC 0.169 W/(cm·K) LNG 16.9 W/(m·K) WEL 17 W/(m·K) 70 Yb ytterbium use 38.5 W/(m·K) CRC 0.385 W/(cm·K) LNG 38.5 W/(m·K) WEL 39 W/(m·K) 71 Lu lutetium use 16.4 W/(m·K) CRC 0.164 W/(cm·K) LNG 16.4 W/(m·K) WEL 16 W/(m·K) 72 Hf hafnium use 23.0 W/(m·K) CRC 0.230 W/(cm·K) LNG 23.0 W/(m·K) WEL 23 W/(m·K) 73 Ta tantalum use 57.5 W/(m·K) CRC 0.575 W/(cm·K) LNG 57.5 W/(m·K) WEL 57 W/(m·K) 74 W tungsten use 173 W/(m·K) CRC 1.74 W/(cm·K) LNG 173 W/(m·K) WEL 170 W/(m·K) 75 Re rhenium use 48.0 W/(m·K) CRC 0.479 W/(cm·K) LNG 48.0 W/(m·K) WEL 48 W/(m·K) 76 Os osmium use 87.6 W/(m·K) CRC 0.876 W/(cm·K) LNG 87.6 W/(m·K) WEL 88 W/(m·K) 77 Ir iridium use 147 W/(m·K) CRC 1.47 W/(cm·K) LNG 147 W/(m·K) WEL 150 W/(m·K) 78 Pt platinum use 71.6 W/(m·K) CRC 0.716 W/(cm·K) LNG 71.6 W/(m·K) WEL 72 W/(m·K) 79 Au gold use 318 W/(m·K) CRC 3.17 W/(cm·K) LNG 318 W/(m·K) WEL 320 W/(m·K) 80 Hg mercury use 8.30 W/(m·K) CRC 0.0834 W/(cm·K) LNG 8.30 W/(m·K) WEL 8.3 W/(m·K) 81 Tl thallium use 46.1 W/(m·K) CRC 0.461 W/(cm·K) LNG 46.1 W/(m·K) WEL 46 W/(m·K) 82 Pb lead use 35.3 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.3 W/(m·K) WEL 35 W/(m·K) 83 Bi bismuth use 7.97 W/(m·K) CRC 0.0787 W/(cm·K) LNG 7.97 W/(m·K) WEL 8 W/(m·K) 84 Po polonium use CRC 0.20 W/(cm·K) LNG 0.2 W/(m·K) 85 At astatine use 1.7 W/(m·K) LNG 1.7 W/(m·K) WEL 2 W/(m·K) 86 Rn radon use 3.61 mW/(m·K) LNG 0.00361 W/(m·K) WEL 0.00361 W/(m·K) 88 Ra radium use 18.6 W/(m·K) LNG 18.6 W/(m·K) WEL 19 W/(m·K) 89 Ac actinium use 12 W/(m·K) LNG 12 W/(m·K) WEL 12 W/(m·K) 90 Th thorium use 54.0 W/(m·K) CRC 0.540 W/(cm·K) LNG 54.0 W/(m·K) WEL 54 W/(m·K) 91 Pa protactinium use 47 W/(m·K) LNG 47 W/(m·K) WEL 47 W/(m·K) 92 U uranium use 27.5 W/(m·K) CRC 0.276 W/(cm·K) LNG 27.5 W/(m·K) WEL 27 W/(m·K) 93 Np neptunium use 6.3 W/(m·K) CRC 0.063 W/(cm·K) LNG 6.3 W/(m·K) WEL 6 W/(m·K) 94 Pu plutonium use 6.74 W/(m·K) CRC 0.0674 W/(cm·K) LNG 6.74 W/(m·K) WEL 6 W/(m·K) 95 Am americium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) 97 Bk berkelium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) ==Notes== * Ref. CRC: Values refer to 27 °C unless noted. J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? \frac{1}{\sqrt{1 + \left(\frac{x-\xi}{\lambda}\right)^2}} e^{-\frac{1}{2}\left(\gamma+\delta \sinh^{-1} \left(\frac{x-\xi}{\lambda}\right)\right)^2} \| cdf = \Phi \left(\gamma + \delta \sinh^{-1} \left( \frac{x-\xi}{\lambda} \right) \right) \| mean = \xi - \lambda \exp \frac{\delta^{-2}}{2} \sinh\left(\frac{\gamma}{\delta}\right) \| median = \xi + \lambda \sinh \left( - \frac{\gamma}{\delta} \right) \| mode = \| variance = \frac{\lambda^2}{2} (\exp(\delta^{-2})-1) \left( \exp(\delta^{-2}) \cosh \left(\frac{2\gamma}{\delta} \right) +1 \right) \| skewness = -\frac{\lambda^3\sqrt{e^{\delta^{-2}}}(e^{\delta^{-2}}-1)^{2}((e^{\delta^{-2}})(e^{\delta^{-2}}+2)\sinh(\frac{3\gamma}{\delta})+3\sinh(\frac{2\gamma}{\delta}))}{4(\operatorname{Variance}X)^{1.5}} \| kurtosis = \frac{\lambda^4(e^{\delta^{-2}}-1)^2(K_{1}+K_2+K_3)}{8(\operatorname{Variance}X)^2} K_{1}=\left( e^{\delta^{-2}} \right)^{2}\left( \left( e^{\delta^{-2}} \right)^{4}+2\left( e^{\delta^{-2}} \right)^{3}+3\left( e^{\delta^{-2}} \right)^{2}-3 \right)\cosh\left( \frac{4\gamma}{\delta} \right) K_2=4\left( e^{\delta^{-2}} \right)^2 \left( \left( e^{\delta^{-2}} \right)+2 \right)\cosh\left( \frac{3\gamma}{\delta} \right) K_3=3\left( 2\left( e^{\delta^{-2}} \right)+1 \right) \| entropy = \| pgf = \| mgf = \| char = }} The Johnson's SU-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. Boca Raton, Florida, 2003; Section 6, Fluid Properties; Thermal Conductivity of Gases ===LNG=== As quoted from this source in an online version of: J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 4; Table 4.1, Electronic Configuration and Properties of the Elements * Ho, C. Y., Powell, R. W., and Liley, P. E., J. Phys. Chem. Ref. Data 3:Suppl. 1 (1974) ===WEL=== As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. J/(mol·K) Solid properties Std enthalpy change of formation ΔfH ~~o~~ solid −118 kJ/mol Standard molar entropy S ~~o~~ solid ? J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? :*(b) I.G. Dillon, P.A. Nelson, B.S. Swanson, J. Chem. Phys. 44, 4229, (1966). K (? °C), ? K (? °C), ? K (? °C), ? K (? °C), ?	+37	0.9522	3.2	228	22.2036033112	D
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \mathrm{~mol} \mathrm{CO}_2(\mathrm{~g})$, initially at $25^{\circ} \mathrm{C}$ and $10 \mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \mathrm{~m}}=28.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and calculate $\Delta S$.	In the second case, the gas will both heat and expand, causing the piston to do mechanical work on the atmosphere. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975 allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known. == Equations == : \ln P_{\rm r} = f^{(0)} + \omega \cdot f^{(1)} : f^{(0)}=5.92714 - \frac{6.09648}{T_{\rm r}} - 1.28862 \cdot \ln T_{\rm r} + 0.169347 \cdot T_{\rm r}^6 : f^{(1)}=15.2518 - \frac{15.6875}{T_{\rm r}}-13.4721 \cdot \ln T_{\rm r} + 0.43577 \cdot T_{\rm r}^6 with :P_{\rm r}=\frac{P}{P_{\rm c}} (reduced pressure) and T_{\rm r}=\frac{T}{T_{\rm c}} (reduced temperature). == Typical errors == The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. We assume the expansion occurs without exchange of heat (adiabatic expansion). To return to the target temperature (still with a free piston), the air must be heated, but is no longer under constant volume, since the piston is free to move as the gas is reheated. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Consider the difference between adding heat to the gas with a locked piston and adding heat with a piston free to move, so that pressure remains constant. If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. Since the piston cannot move, the volume is constant. The piston is now freed and moves outwards, stopping as the pressure inside the chamber reaches atmospheric pressure. The heat that is added to the gas goes only partly into heating the gas, while the rest is transformed into the mechanical work performed by the piston. However, CNG requires a much larger volume to store the energy equivalent of petrol and the use of very high pressures (3000 to 4000 psi, or 205 to 275 bar). For light-duty CNG cars to become a viable short-term climate strategy, methane leakage would need to be kept below 1.6% of total natural gas produced (approximately half the current amount for well to wheels – note difference from well to city)." Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures. Compressed natural gas (CNG) is a fuel gas mainly composed of methane (CH4), compressed to less than 1% of the volume it occupies at standard atmospheric pressure. Auflage, McGraw-Hill, 1988 == Example calculation == For benzene with * Tc = 562.12 KBrunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006 * Pc = 4898 kPa * Tb = 353.15 KSilva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006 * ω = 0.2120Dortmund Data Bank the following calculation for T=Tb results: * Tr = 353.15 / 562.12 = 0.628247 * f(0) = -3.167428 * f(1) = -3.429560 * Pr = exp( f(0) \+ ω f(1) ) = 0.020354 * P = Pr * Pc = 99.69 kPa The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. * Being a gaseous fuel, CNG mixes easily and evenly in air. ** The lifecycle greenhouse gas emissions for CNG compressed from California's pipeline natural gas is given a value of 67.70 grams of -equivalent per megajoule (gCO2e/MJ) by CARB (the California Air Resources Board), approximately 28 percent lower than the average petrol fuel in that market (95.86 gCO2e/MJ). In a fire, the pressure in a gas cylinder rises in direct proportion to its temperature. Natural gas is being experimentally stored at lower pressure in a form known as an ANG (adsorbed natural gas) cylinder, where it is adsorbed at 35 bar (500 psi, the pressure of gas in natural gas pipelines) in various sponge-like materials, such as carbon and MOFs (metal-organic frameworks). Especially, for the CNG Type 1 and Type 2 cylinders, many countries are able to make reliable and cost effective cylinders for conversion need. ==Energy density== CNG's energy density is the same as liquefied natural gas at 53.6 MJ/kg.	30	+0.60	0.2553	0.14	0.1792	B
The mass density of water vapour at $327.6 \mathrm{~atm}$ and $776.4 \mathrm{~K}$ is $133.2 \mathrm{~kg} \mathrm{~m}^{-3}$. Given that for water $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, and $M=18.02 \mathrm{~g} \mathrm{~mol}^{-1}$, calculate the compression factor from the virial expansion of the van der Waals equation.	Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and b (volume occupied by molecules) values, then a and b for the mixture can be calculated as :m = total number of moles of gas present, :for each i, m_i = number of moles of gas i present, and x_i = \frac{m_i}{m} :a = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{a_i a_j}) :b = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{b_i b_j}) and the rule of adding partial pressures becomes invalid if the numerical result of the equation \left(p + ({n^2 a}/{V^2})\right)\left(V-nb\right) = nRT is significantly different from the ideal gas equation pV = nRT . ===Reduced form=== The Van der Waals equation can also be expressed in terms of reduced properties: :\left(P_r + \frac{3}{V_r^2}\right)\left(V_r-\frac{1}{3}\right) = \frac{8}{3}T_r The equation in reduced form is exactly the same for every gas, this is consistent with the Theorem of corresponding states. In the derivation of ideal gas laws on the basis of kinetic theory of gases some assumption have been made. ===Compressibility factor=== The compressibility factor for the Van der Waals equation is: : Z = \frac{P V_m}{RT} = \frac{V_m}{V_m-b} - \frac{a}{V_m RT} Or in reduced form by substitution of P_r=P/P_c, T_r=T/T_c, V_r=V_m/V_c: : Z = \frac{V_r}{V_r-\frac{1}{3}} - \frac{9}{8 V_r T_r} At the critical point: : Z_c = \frac{P_c V_c}{RT_c} = \frac{3}{8} = 0.375 ==Validity== The Van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. The first form of the Van der Waals equation of state given above can be recast in the following reduced form: :\left(p_R + \frac{3}{v_R^2}\right)(3v_R - 1) = (8 T_R) This equation is invariant for all fluids; that is, the same reduced form equation of state applies, no matter what a and b may be for the particular fluid. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. Since: :p=-\left(\frac{\partial A}{\partial V}\right)_{T,N} where A is the Helmholtz free energy, it follows that the equal area rule can be expressed as: :p_V=\frac{A(V_L,T,N)-A(V_G,T,N)}{V_G-V_L}is Since the gas and liquid volumes are functions of pV and T only, this equation is then solved numerically to obtain pV as a function of temperature (and number of particles N), which may then be used to determine the gas and liquid volumes. thumb\|800px\|Locus of coexistence for two phases of Van der Waals fluid A pseudo-3D plot of the locus of liquid and vapor volumes versus temperature and pressure is shown in the accompanying figure. An isotherm of the Van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal. == Other parameters, forms and applications == ===Other thermodynamic parameters=== We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). Therefore, expressing the enthalpy and the Gibbs energy as functions of their natural variables will be complicated. ===Reduced form=== Although the material constant a and b in the usual form of the Van der Waals equation differs for every single fluid considered, the equation can be recast into an invariant form applicable to all fluids. Even with its acknowledged shortcomings, the pervasive use of the Van der Waals equation in standard university physical chemistry textbooks makes clear its importance as a pedagogic tool to aid understanding fundamental physical chemistry ideas involved in developing theories of vapour–liquid behavior and equations of state. However, near the phase transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the Van der Waals equation fails to accurately model observed experimental behavior. The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. This apparent discrepancy is resolved in the context of vapour–liquid equilibrium: at a particular temperature, there exist two points on the Van der Waals isotherm that have the same chemical potential, and thus a system in thermodynamic equilibrium will appear to traverse a straight line on the p–V diagram as the ratio of vapour to liquid changes. In this case specific volume changes are small and it can be written in a simplified form: :(p+A)(V-B)=CT, \, where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters. == See also == * Gas laws * Ideal gas * Inversion temperature * Iteration * Maxwell construction * Real gas * Theorem of corresponding states * Van der Waals constants (data page) * Redlich–Kwong equation of state ==References== ==Further reading== * * . A variety of empirical formulas exist for this quantity; the most used reference formula is the Goff-Gratch equation for the SVP over liquid water below zero degrees Celsius: :\begin{align} \log_{10} \left( p \right) = & -7.90298 \left( \frac{373.16}{T}-1 \right) + 5.02808 \log_{10} \frac{373.16}{T} \\\ & \- 1.3816 \times 10^{-7} \left( 10^{11.344 \left( 1-\frac{T}{373.16} \right)} -1 \right) \\\ & \+ 8.1328 \times 10^{-3} \left( 10^{-3.49149 \left( \frac{373.16}{T}-1 \right)} -1 \right) \\\ & \+ \log_{10} \left( 1013.246 \right) \end{align} where , temperature of the moist air, is given in units of kelvin, and is given in units of millibars (hectopascals). Therefore, they will respond to changes in roughly the same way, even though their measurable physical characteristics may differ significantly. ===Cubic equation=== The Van der Waals equation is a cubic equation of state; in the reduced formulation the cubic equation is: :{v_R^3}-\frac{1}{3}\left({1+\frac{8T_R}{p_R}}\right){v_R^2} +\frac{3}{p_R}v_R- \frac{1}{p_R}= 0 At the critical temperature, where T_R=p_R=1 we get as expected :{v_R^3}-3v_R^2 +3v_R- 1=\left(v_R -1\right)^3 = 0 \quad \Longleftrightarrow \quad v_R=1 For TR < 1, there are 3 values for vR. Above the critical temperature, TC, the Van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region. The corrected equation becomes : p = \frac{RT}{V_\mathrm{m}-b}.	-167	0.7158	0.18	9.8	0.123	B
Express the van der Waals parameters $a=0.751 \mathrm{~atm} \mathrm{dm}^6 \mathrm{~mol}^{-2}$ in SI base units.	* Analytical calculation of Van der Waals surfaces and volumes. Petitjean, On the Analytical Calculation of Van der Waals Surfaces and Volumes: Some Numerical Aspects, Journal of Computational Chemistry, Volume 15, Number 5, 1994, pp. 507–523. == External links == * VSAs for various molecules by Anton Antonov, The Wolfram Demonstrations Project, 2007. These various methods give values for the van der Waals radius which are similar (1–2 Å, 100–200 pm) but not identical. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the Avogadro constant N. The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances, and angles) are known. Useful tabulated values of Van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will be seen to present different values for the Van der Waals radius of the same atom. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Gas d (Å) b (cmmol) V (Å) r (Å) Hydrogen 0.74611 26.61 44.19 2.02 Nitrogen 1.0975 39.13 64.98 2.25 Oxygen 1.208 31.83 52.86 2.06 Chlorine 1.988 56.22 93.36 2.39 van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. The van der Waals constant b volume can be used to calculate the van der Waals volume of an atom or molecule with experimental data derived from measurements on gases. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. Van der Waals volumes of a single atom or molecules are arrived at by dividing the macroscopically determined volumes by the Avogadro constant. D-166. b = 23.7 cm/mol. Helium is a monatomic gas, and each mole of helium contains atoms (the Avogadro constant, N): V_{\rm w} = {b\over{N_{\rm A}}} Therefore, the van der Waals volume of a single atom V = 39.36 Å, which corresponds to r = 2.11 Å (≈ 200 picometers). Tabulated values of van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will often have different values for the van der Waals radius of the same atom. Blaney and G. E. Ewing, Annual Review of Physical Chemistry, Vol. 27, pp. 553-586 (1976): Van der Waals Molecules. Hence the molar van der Waals volume, which only counts the volume occupied by the atoms or molecules, is usually about times smaller than the molar volume for a gas at standard temperature and pressure. ==Table of van der Waals radii== == Methods of determination == Van der Waals radii may be determined from the mechanical properties of gases (the original method), from the critical point, from measurements of atomic spacing between pairs of unbonded atoms in crystals or from measurements of electrical or optical properties (the polarizability and the molar refractivity).	0.0761	0.3359	2.3	0.0625	9.30	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Estimate the change in the Gibbs energy of $1.0 \mathrm{dm}^3$ of benzene when the pressure acting on it is increased from $1.0 \mathrm{~atm}$ to $100 \mathrm{~atm}$.	Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in). Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . thumb\|2D model of a benzene molecule. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. As pressure is defined as force per area of measurement, the gas equation can also be written as: :R = \frac{ \dfrac{\mathrm{force}}{\mathrm{area}} \times \mathrm{volume} } { \mathrm{amount} \times \mathrm{temperature} } Area and volume are (length)2 and (length)3 respectively. The standard Gibbs free energy of formation (Gf°) of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 1 bar of pressure and the specified temperature, usually 298.15 K or 25 °C). Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. ==References== ==External links== * Ideal gas calculator – Ideal gas calculator provides the correct information for the moles of gas involved. However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other exactly defined physical constants. ==Specific gas constant== Rspecific for dry air Unit 287.052874 J⋅kg−1⋅K−1 53.3523 ft⋅lbf⋅lb−1⋅°R−1 1,716.46 ft⋅lbf⋅slug−1⋅°R−1 The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture. The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Uses formula: \scriptstyle \log_e P_{mmHg} =\scriptstyle \log_e (\frac {760} {101.325}) - 8.433613\log_e(T+273.15) - \frac {6281.040} {T+273.15} + 71.10718 + 6.198413 \times 10^{-06} (T+273.15)^2 obtained from CHERIC Note: yellow area is the region where the formula disagrees with tabulated data above. ==Distillation data== {\| border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border- collapse: collapse; border-color: #C0C090;" Vapor-liquid Equilibrium for Benzene/Ethanol P = 760 mm Hg BP Temp. °C % by mole ethanol liquid vapor 70.8 8.6 26.5 69.8 11.2 28.2 69.6 12.0 30.8 69.1 15.8 33.5 68.5 20.0 36.8 67.7 30.8 41.0 67.7 44.2 44.6 68.1 60.4 50.5 69.6 77.0 59.0 70.4 81.5 62.8 70.9 84.1 66.5 72.7 89.8 74.4 73.8 92.4 78.2 == Spectral data == UV-Vis Ionization potential 9.24 eV (74525.6 cm−1) S1 4.75 eV (38311.3 cm−1) S2 6.05 eV (48796.5 cm−1) λmax 255 nm Extinction coefficient, ε ? This page provides supplementary chemical data on benzene. == Material Safety Data Sheet == The handling of this chemical may incur notable safety precautions. (i) Indicates values calculated from ideal gas thermodynamic functions. == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == *Values are given in terms of temperature necessary to reach the specified pressure. On the elasticity of gases. 1875 (in Russian) Mendeleev also calculated it with high precision, within 0.3% of its modern value. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, i.e. the pressure–volume product, rather than energy per temperature increment per particle. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB): R = N_{\rm A} k. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance.	0.1591549431	+10	1.33	35.64	0.0024	B
The mass density of water vapour at $327.6 \mathrm{~atm}$ and $776.4 \mathrm{~K}$ is $133.2 \mathrm{~kg} \mathrm{~m}^{-3}$. Given that for water $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, and $M=18.02 \mathrm{~g} \mathrm{~mol}^{-1}$, calculate the compression factor from the data.	The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). Regarding the measurement of upper-air humidity, this publication also reads (in Section 12.5.1): The saturation with respect to water cannot be measured much below –50 °C, so manufacturers should use one of the following expressions for calculating saturation vapour pressure relative to water at the lowest temperatures – Wexler (1976, 1977), reported by Flatau et al. (1992)., Hyland and Wexler (1983) or Sonntag (1994) – and not the Goff- Gratch equation recommended in earlier WMO publications. ==Experimental correlation== The original Goff–Gratch (1945) experimental correlation reads as follows: : \log\ e^\ = -7.90298(T_\mathrm{st}/T-1)\ +\ 5.02808\ \log(T_\mathrm{st}/T) -\ 1.3816\times10^{-7}(10^{11.344(1-T/T_\mathrm{st})}-1) +\ 8.1328\times10^{-3}(10^{-3.49149(T_\mathrm{st}/T-1)}-1)\ +\ \log\ e^_\mathrm{st} where: :log refers to the logarithm in base 10 :e* is the saturation water vapor pressure (hPa) :T is the absolute air temperature in kelvins :Tst is the steam-point (i.e. boiling point at 1 atm.) temperature (373.15 K) :est is e at the steam-point pressure (1 atm = 1013.25 hPa) Similarly, the correlation for the saturation water vapor pressure over ice is: : \log\ e^_i\ = -9.09718(T_0/T-1)\ -\ 3.56654\ \log(T_0/T) +\ 0.876793(1-T/T_0) +\ \log\ e^_{i0} where: :log stands for the logarithm in base 10 :ei is the saturation water vapor pressure over ice (hPa) :T is the air temperature (K) :T0 is the ice-point (triple point) temperature (273.16 K) :ei0 is e* at the ice-point pressure (6.1173 hPa) ==See also== Vapour pressure of water Antoine equation Arden Buck equation Tetens equation Lee–Kesler method ==References== Goff, J. A., and Gratch, S. (1946) Low- pressure properties of water from −160 to 212 °F, in Transactions of the American Society of Heating and Ventilating Engineers, pp 95–122, presented at the 52nd annual meeting of the American Society of Heating and Ventilating Engineers, New York, 1946. Calculations of the (saturation) vapour pressure of water are commonly used in meteorology. * * ;Notes ==External links== * * Free Windows Program, Moisture Units Conversion Calculator w/Goff-Gratch equation — PhyMetrix Category:Atmospheric thermodynamics Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. For this use, air has a molecular weight of 28.97 atomic mass units, and all other gas and vapour molecular weights are divided by this number to derive their vapour density.HazMat Math: Calculating Vapor Density . Air is given a vapour density of one. Further g is acceleration due to gravity and ρ is the fluid density. The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. The Goff–Gratch equation is one (arguably the first reliable in history) amongst many experimental correlation proposed to estimate the saturation water vapor pressure at a given temperature. thumb\|The Mollier enthalpy–entropy diagram for water and steam. Further ρ is the (constant) fluid density and g is the gravitational acceleration. * Goff, J. A. (1957) Saturation pressure of water on the new Kelvin temperature scale, Transactions of the American Society of Heating and Ventilating Engineers, pp 347–354, presented at the semi-annual meeting of the American Society of Heating and Ventilating Engineers, Murray Bay, Que. Canada. * After correction, repeat this process until all data points have the same slope. ==See also== Statistics ==Notes== ==Further reading== Dubreuil P. (1974) Initiation à l'analyse hydrologique Masson& Cie et ORSTOM, Paris. In the case of a horizontal bed, with negligible Coriolis forces, frictional and viscous forces, the shallow-water equations are: \begin{align} \frac{\partial (\rho \eta) }{\partial t} &\+ \frac{\partial (\rho \eta u)}{\partial x} + \frac{\partial (\rho \eta v)}{\partial y} = 0,\\\\[3pt] \frac{\partial (\rho \eta u)}{\partial t} &\+ \frac{\partial}{\partial x}\left( \rho \eta u^2 + \frac{1}{2}\rho g \eta^2 \right) + \frac{\partial (\rho \eta u v)}{\partial y} = 0,\\\\[3pt] \frac{\partial (\rho \eta v)}{\partial t} &\+ \frac{\partial}{\partial y}\left(\rho \eta v^2 + \frac{1}{2}\rho g \eta ^2\right) + \frac{\partial (\rho \eta uv)}{\partial x} = 0. \end{align} Here η is the total fluid column height (instantaneous fluid depth as a function of x, y and t), and the 2D vector (u,v) is the fluid's horizontal flow velocity, averaged across the vertical column. Another similar equation based on more recent data is the Arden Buck equation. ==Historical note== This equation is named after the authors of the original scientific article who described how to calculate the saturation water vapor pressure above a flat free water surface as a function of temperature (Goff and Gratch, 1946). Double mass analysis is a simple graphical method to evaluate the consistency of hydrological data. The Mollier diagram coordinates are enthalpy h and humidity ratio x. The temperature-vapour pressure relation inversely describes the relation between the boiling point of water and the pressure. An understanding of vapour pressure is also relevant in explaining high altitude breathing and cavitation. ==Approximation formulas == There are many published approximations for calculating saturated vapour pressure over water and over ice.	+93.4	2.3	1.0	0.6957	311875200	D
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in Gibbs energy of $35 \mathrm{~g}$ of ethanol (mass density $0.789 \mathrm{~g} \mathrm{~cm}^{-3}$ ) when the pressure is increased isothermally from $1 \mathrm{~atm}$ to $3000 \mathrm{~atm}$.	Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of nitrogen as an ideal gas at . The temperature dependence at constant pressure is \left(\frac{\partial \ln f}{\partial T}\right)_P = \frac{\Delta H_\mathrm{m}}{R T^2}, where is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). The partial pressures obey Dalton's law: P_i = y_i P, where is the total pressure and is the mole fraction of the component (so the partial pressures add up to the total pressure). It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas. The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. Taken at the same temperature and pressure, the difference between the molar Gibbs free energies of a real gas and the corresponding ideal gas is equal to . The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. In a pure substance, is equal to the Gibbs energy for a mole of the substance, and d\mu = dG_\mathrm{m} = -S_\mathrm{m}dT + V_\mathrm{m}dP, where and are the temperature and pressure, is the volume per mole and is the entropy per mole. ===Gas=== For an ideal gas the equation of state can be written as V_\mathrm{m}^\text{ideal} = \frac{RT}{P}, where is the ideal gas constant. Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. The differential change of the chemical potential between two states of slightly different pressures but equal temperature (i.e., ) is given by d\mu = V_\mathrm{m}dP = RT \, \frac{dP}{P} = R T\, d \ln P,where ln p is the natural logarithm of p. At standard pressure , the value is denoted as and normally expressed in joules per mole-kelvin, J/(mol·K). == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure. Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. The contribution of nonideality to the molar Gibbs energy of a real gas is equal to . The Reid vapor pressure (RVP) can differ substantially from the true vapor pressure (TVP) of a liquid mixture, since (1) RVP is the vapor pressure measured at 37.8 °C (100 °F) and the TVP is a function of the temperature; (2) RVP is defined as being measured at a vapor-to-liquid ratio of 4:1, whereas the TVP of mixtures can depend on the actual vapor-to-liquid ratio; (3) RVP will include the pressure associated with the presence of dissolved water and air in the sample (which is excluded by some but not all definitions of TVP); and (4) the RVP method is applied to a sample which has had the opportunity to volatilize somewhat prior to measurement: i.e., the sample container is required to be only 70-80% full of liquid ASTM D323-15a, Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method), Section 8.3(so that whatever volatilizes into the container headspace is lost prior to analysis); the sample then again volatilizes into the headspace of the D323 test chamber before it is heated to 37.8 degrees Celsius.Conversion between the two measures can be found here, from p. 7.1-54 onwards. ==See also== Crude oil assay * Gasoline volatility * Vapor pressure ==External links== * ASTM D323 - 06 Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method) * Reid Vapor Pressure Requirements for Ethanol Congressional Research Service * USA's Environmental Protection Agency (EPA) publication AP-42, Compilation of Air Pollutant Emissions. Reid vapor pressure (RVP) is a common measure of the volatility of gasoline and other petroleum products.ASTM D323-15a, Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method), Section 1.1 It is defined as the absolute vapor pressure exerted by the vapor of the liquid and any dissolved gases/moisture at 37.8 °C (100 °F) as determined by the test method ASTM-D-323, which was first developed in 1930 ASTM D323-15a, Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method), footnote 1 and has been revised several times (the latest version is ASTM D323-15a).ASTM D323-15a, Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method) The test method measures the vapor pressure of gasoline, volatile crude oil, jet fuels, naphtha, and other volatile petroleum products but is not applicable for liquefied petroleum gases.ASTM D323-15a, Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method), Sections 1.1 and 1.6 ASTM D323-15a requires that the sample be chilled to 0 to 1 degrees Celsius and then poured into the apparatus;ASTM D323-15a, Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method), Sections 11.1 and 11.1.2 for any material that solidifies at this temperature, this step cannot be performed.	5	0.68	152.67	-167	12	E
The densities of air at $-85^{\circ} \mathrm{C}, 0^{\circ} \mathrm{C}$, and $100^{\circ} \mathrm{C}$ are $1.877 \mathrm{~g} \mathrm{dm}^{-3}, 1.294 \mathrm{~g}$ $\mathrm{dm}^{-3}$, and $0.946 \mathrm{~g} \mathrm{dm}^{-3}$, respectively. From these data, and assuming that air obeys Charles's law, determine a value for the absolute zero of temperature in degrees Celsius.	Rounding up 1.98°C to 2°C, this approximation simplifies to become :\begin{align} \text{DA} & \approx \text{PA} + 118.8 ~ \frac{\text{ft}}{^\circ \text{C}} \left[ T_\text{OA} + \frac{\text{PA}}{500 ~ \text{ft}} {^\circ \text{C}} - 15 ~ {^\circ \text{C}} \right] \\\\[3pt] & = 1.2376 \, \text{PA} + 118.8 ~ \frac{\text{ft}}{{}^\circ \text{C}} \, T_\text{OA} - 1782 ~ \text{ft}. \end{align} ==See also== Outside air temperature Barometric formula Density of air Hot and high List of longest runways == Notes == ==References== * * Advisory Circular AC 61-23C, Pilot's Handbook of Aeronautical Knowledge, U.S. Federal Aviation Administration, Revised 1997 * http://www.tpub.com/content/aerographer/14269/css/14269_74.htm * ==External links== Density Altitude Calculator Density Altitude influence on aircraft performance NewByte Atmospheric Calculator Category:Altitudes in aviation Category:Atmospheric thermodynamics Unaware of the inaccuracies of mercury thermometers at the time, which were divided into equal portions between the fixed points, Dalton, after concluding in Essay II that in the case of vapours, “any elastic fluid expands nearly in a uniform manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat”, was unable to confirm it for gases. ==Relation to absolute zero== Charles's law appears to imply that the volume of a gas will descend to zero at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or −273.15 °C. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C. where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/ft) in ISA h = height at which pressure is calculated (ft) h_b = height of reference level b (feet; e.g., hb = 36,089 ft) R^ = universal gas constant; using feet, kelvins, and (SI) moles: g_0 = gravitational acceleration: 32.17405 ft/s2 M = molar mass of Earth's air: 28.9644 lb/lb-mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In this formula, : \text{DA} , density altitude in meters (m); : P , (static) atmospheric pressure; : P_\text{SL} , standard sea-level atmospheric pressure, International Standard Atmosphere (ISA): 1013.25 hectopascals (hPa), or U.S. Standard Atmosphere: 29.92 inches of mercury (inHg); : T , outside air temperature in kelvins (K); : T_\text{SL} = 288.15K, ISA sea-level air temperature; : \Gamma = 0.0065K/m, ISA temperature lapse rate (below 11km); : R ≈ 8.3144598J/mol·K, ideal gas constant; : g ≈ 9.80665m/s, gravitational acceleration; : M ≈ 0.028964kg/mol, molar mass of dry air. ===The National Weather Service (NWS) formula=== The National Weather Service uses the following dry-air approximation to the formula for the density altitude above in its standard: : \text{DA}_\text{NWS} = 145442.16 ~ \text{ft} \left( 1 - \left[ 17.326 ~ \frac{^\circ \text{F}}{\text{inHg}} \ \frac{P}{459.67 ~ {{}^\circ \text{F}} + T} \right]^{0.235} \right). Subscript b Height above sea level Static pressure Standard temperature (K) Temperature lapse rate Exponent g0 M / R L (m) (ft) (Pa) (inHg) (K/m) (K/ft) 0 0 0 101 325.00 29.92126 288.15 0.0065 0.0019812 5.2558 1 11 000 36,089 22 632.10 6.683245 216.65 0.0 0.0 -- 2 20 000 65,617 5474.89 1.616734 216.65 -0.001 -0.0003048 -34.1626 3 32 000 104,987 868.02 0.2563258 228.65 -0.0028 -0.00085344 -12.2009 4 47 000 154,199 110.91 0.0327506 270.65 0.0 0.0 -- 5 51 000 167,323 66.94 0.01976704 270.65 0.0028 0.00085344 12.2009 6 71 000 232,940 3.96 0.00116833 214.65 0.002 0.0006096 17.0813 ==Density equations== The expressions for calculating density are nearly identical to calculating pressure. (Before going further, I should inform [you] that although I had recognized many times that the gases oxygen, nitrogen, hydrogen, and carbonic acid [i.e., carbon dioxide], and atmospheric air also expand from 0° to 80°, citizen Charles had noticed 15 years ago the same property in these gases; but having never published his results, it is by the merest chance that I knew of them.) although he credited the discovery to unpublished work from the 1780s by Jacques Charles. This equation does not contain the temperature and so is not what became known as Charles's Law. Equation 1: \rho = \rho_b \left[\frac{T_b - (h-h_b) L_b}{T_b}\right]^{\left(\frac{g_0 M}{R^* L_b}-1\right)} which is equivalent to the ratio of the relative pressure and temperature changes \rho = \rho_b \frac{P}{T} \frac{T_b}{P_b} Equation 2: \rho =\rho_b \exp\left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right] where {\rho} = mass density (kg/m3) T_b = standard temperature (K) L = standard temperature lapse rate (see table below) (K/m) in ISA h = height above sea level (geopotential meters) R^ = universal gas constant 8.3144598 N·m/(mol·K) g_0 = gravitational acceleration: 9.80665 m/s2 M = molar mass of Earth's air: 0.0289644 kg/mol or, converted to U.S. gravitational foot-pound-second units (no longer used in U.K.): {\rho} = mass density (slug/ft3) {T_b} = standard temperature (K) {L} = standard temperature lapse rate (K/ft) {h} = height above sea level (geopotential feet) {R^} = universal gas constant: 8.9494596×104 ft2/(s·K) {g_0} = gravitational acceleration: 32.17405 ft/s2 {M} = molar mass of Earth's air: 0.0289644 kg/mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In this formula, : \text{PA} , pressure altitude in feet (ft) \approx \text{station elevation in feet} + 27 ~ \frac{\text{ft}}{\text{mb}} (1013 ~ \text{mb} - \text{QNH}) ; : \text{QNH} , atmospheric pressure in millibars (mb) adjusted to mean sea level; : T_\text{OA}, outside air temperature in degrees Celsius (°C); : T_\text{ISA} \approx 15 ~ {{}^\circ \text{C}} - 1.98 ~ {{}^\circ \text{C}} \, \frac{\text{PA}}{1000 ~ \text{ft}} , assuming that the outside air temperature falls at the rate of 1.98°C per 1,000ft of altitude until the tropopause (at ) is reached. The first equation is applicable to the standard model of the troposphere in which the temperature is assumed to vary with altitude at a lapse rate of L_b: P = P_b \left[\frac{T_b - \left(h - h_b\right) L_b}{T_b}\right]^{\tfrac{g_0 M}{R^* L_b}} The second equation is applicable to the standard model of the stratosphere in which the temperature is assumed not to vary with altitude: P = P_b \exp \left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right] where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/m) in ISA h = height at which pressure is calculated (m) h_b = height of reference level b (meters; e.g., hb = 11 000 m) R^* = universal gas constant: 8.3144598 J/(mol·K) g_0 = gravitational acceleration: 9.80665 m/s2 M = molar mass of Earth's air: 0.0289644 kg/mol Or converted to imperial units:Mechtly, E. A., 1973: The International System of Units, Physical Constants and Conversion Factors. In the absence of a firm record, the gas law relating volume to temperature cannot be attributed to Charles. A modern statement of Charles' law is: > When the pressure on a sample of a dry gas is held constant, the Kelvin > temperature and the volume will be in direct proportion.. Thomson did not assume that this was equal to the "zero-volume point" of Charles's law, merely that Charles's law provided the minimum temperature which could be attained. The first mention of a temperature at which the volume of a gas might descend to zero was by William Thomson (later known as Lord Kelvin) in 1848:. > This is what we might anticipate when we reflect that infinite cold must > correspond to a finite number of degrees of the air-thermometer below zero; > since if we push the strict principle of graduation, stated above, > sufficiently far, we should arrive at a point corresponding to the volume of > air being reduced to nothing, which would be marked as −273° of the scale > (−100/.366, if .366 be the coefficient of expansion); and therefore −273° of > the air-thermometer is a point which cannot be reached at any finite > temperature, however low. The values used for M, g0 and R* are in accordance with the U.S. Standard Atmosphere, 1976, and that the value for R* in particular does not agree with standard values for this constant. Subscript b Height Above Sea Level (h) Mass Density (\rho) Standard Temperature (T') (K) Temperature Lapse Rate (L) (m) (ft) (kg/m3) (slug/ft3) (K/m) (K/ft) 0 0 0 1.2250 288.15 0.0065 0.0019812 1 11 000 36,089.24 0.36391 216.65 0.0 0.0 2 20 000 65,616.79 0.08803 216.65 -0.001 -0.0003048 3 32 000 104,986.87 0.01322 228.65 -0.0028 -0.00085344 4 47 000 154,199.48 0.00143 270.65 0.0 0.0 5 51 000 167,322.83 0.00086 270.65 0.0028 0.00085344 6 71 000 232,939.63 0.000064 214.65 0.002 0.0006096 ==Derivation== The barometric formula can be derived using the ideal gas law: P = \frac{\rho}{M} {R^} T Assuming that all pressure is hydrostatic: dP = - \rho g\,dz and dividing the dP by the P expression we get: \frac{dP}{P} = - \frac{M g\,dz}{R^T} Integrating this expression from the surface to the altitude z we get: P = P_0 e^{-\int_{0}^{z}{M g dz/R^T}} Assuming linear temperature change T = T_0 - L z and constant molar mass and gravitational acceleration, we get the first barometric formula: P = P_0 \cdot \left[\frac{T}{T_0}\right]^{\textstyle \frac{M g}{R^ L}} Instead, assuming constant temperature, integrating gives the second barometric formula: P = P_0 e^{-M g z/R^T} In this formulation, R is the gas constant, and the term RT/Mg gives the scale height (approximately equal to 8.4 km for the troposphere). The values used for M, g0, and R are in accordance with the U.S. Standard Atmosphere, 1976, and the value for R* in particular does not agree with standard values for this constant.U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976. Note that the NWS standard specifies that the density altitude should be rounded to the nearest 100ft. ===Approximation formula for calculating the density altitude from the pressure altitude=== This is an easier formula to calculate (with great approximation) the density altitude from the pressure altitude and the ISA temperature deviation: : \text{DA} \approx \text{PA} + 118.8 ~ \frac{\text{ft}}{{^\circ \text{C}}} \left(T_\text{OA} - T_\text{ISA}\right). To derive Charles's law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average kinetic energy of the gas molecules, k: :T \propto \bar{E_{\rm k}}.\, Under this definition, the demonstration of Charles's law is almost trivial. This will depend on the latent heat release as: T_e \approx T + \frac{L_v}{c_{pd}} r where: * L_v : latent heat of evaporation (2400 kJ/kg at 25°C to 2600 kJ/kg at −40°C) * c_{pd} : specific heat at constant pressure for air (≈ 1004 J/(kg·K)) Tables exist for exact values of the last two coefficients. == See also == * Wet-bulb temperature * Potential temperature * Atmospheric thermodynamics * Equivalent potential temperature ==Bibliography== * M Robitzsch, Aequivalenttemperatur und Aequivalentthemometer, Meteorologische Zeitschrift, 1928, pp. 313-315. In this formula, : \text{DA}_\text{NWS} , National Weather Service density altitude in feet ( \text{ft} ); : P , station pressure (static atmospheric pressure) in inches of mercury (inHg); : T , station temperature (outside air temperature) in degrees Fahrenheit (°F). * Review of Amontons' findings: "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre" (On a new property of the air and a new construction of thermometer), Histoire de l'Académie Royale des Sciences, 1–8 (submitted: 1702; published: 1743). and Francis Hauksbee* Englishman Francis Hauksbee (1660–1713) independently also discovered Charles's law: Francis Hauksbee (1708) "An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate," Philosophical Transactions of the Royal Society of London 26(315): 93–96. a century earlier.	-100	-273	4.946	-7.5	+65.49	B
A certain gas obeys the van der Waals equation with $a=0.50 \mathrm{~m}^6 \mathrm{~Pa}$ $\mathrm{mol}^{-2}$. Its volume is found to be $5.00 \times 10^{-4} \mathrm{~m}^3 \mathrm{~mol}^{-1}$ at $273 \mathrm{~K}$ and $3.0 \mathrm{MPa}$. From this information calculate the van der Waals constant $b$. What is the compression factor for this gas at the prevailing temperature and pressure?	The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and b (volume occupied by molecules) values, then a and b for the mixture can be calculated as :m = total number of moles of gas present, :for each i, m_i = number of moles of gas i present, and x_i = \frac{m_i}{m} :a = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{a_i a_j}) :b = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{b_i b_j}) and the rule of adding partial pressures becomes invalid if the numerical result of the equation \left(p + ({n^2 a}/{V^2})\right)\left(V-nb\right) = nRT is significantly different from the ideal gas equation pV = nRT . ===Reduced form=== The Van der Waals equation can also be expressed in terms of reduced properties: :\left(P_r + \frac{3}{V_r^2}\right)\left(V_r-\frac{1}{3}\right) = \frac{8}{3}T_r The equation in reduced form is exactly the same for every gas, this is consistent with the Theorem of corresponding states. The table below for a selection of gases uses the following conventions: * T_c: critical temperature [K] * P_c: critical pressure [Pa] * v_c: critical specific volume [m3⋅kg−1] * R: gas constant (8.314 J⋅K−1⋅mol−1) * \mu: Molar mass [kg⋅mol−1] Substance P_c [Pa] T_c [K] v_c [m3/kg] Z_c H2O 647.3 0.23 4He 5.2 0.31 He 5.2 0.30 H2 33.2 0.30 Ne 44.5 0.29 N2 126.2 0.29 Ar 150.7 0.29 Xe 289.7 0.29 O2 154.8 0.291 CO2 304.2 0.275 SO2 430.0 0.275 CH4 190.7 0.285 C3H8 370.0 0.267 ==See also== Van der Waals equation Equation of state Compressibility factors Johannes Diderik van der Waals equation Noro- Frenkel law of corresponding states ==References== ==External links== Properties of Natural Gases. The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. In the derivation of ideal gas laws on the basis of kinetic theory of gases some assumption have been made. ===Compressibility factor=== The compressibility factor for the Van der Waals equation is: : Z = \frac{P V_m}{RT} = \frac{V_m}{V_m-b} - \frac{a}{V_m RT} Or in reduced form by substitution of P_r=P/P_c, T_r=T/T_c, V_r=V_m/V_c: : Z = \frac{V_r}{V_r-\frac{1}{3}} - \frac{9}{8 V_r T_r} At the critical point: : Z_c = \frac{P_c V_c}{RT_c} = \frac{3}{8} = 0.375 ==Validity== The Van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.. An isotherm of the Van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal. == Other parameters, forms and applications == ===Other thermodynamic parameters=== We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. Since: :p=-\left(\frac{\partial A}{\partial V}\right)_{T,N} where A is the Helmholtz free energy, it follows that the equal area rule can be expressed as: :p_V=\frac{A(V_L,T,N)-A(V_G,T,N)}{V_G-V_L}is Since the gas and liquid volumes are functions of pV and T only, this equation is then solved numerically to obtain pV as a function of temperature (and number of particles N), which may then be used to determine the gas and liquid volumes. thumb\|800px\|Locus of coexistence for two phases of Van der Waals fluid A pseudo-3D plot of the locus of liquid and vapor volumes versus temperature and pressure is shown in the accompanying figure. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. In this case specific volume changes are small and it can be written in a simplified form: :(p+A)(V-B)=CT, \, where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters. == See also == * Gas laws * Ideal gas * Inversion temperature * Iteration * Maxwell construction * Real gas * Theorem of corresponding states * Van der Waals constants (data page) * Redlich–Kwong equation of state ==References== ==Further reading== * * . The excluded volume b is not just equal to the volume occupied by the solid, finite-sized particles, but actually four times the total molecular volume for one mole of a Van der waals' gas. It is of some historical interest to point out that Van der Waals, in his Nobel prize lecture, gave credit to Laplace for the argument that pressure is reduced proportional to the square of the density. ===Statistical thermodynamics derivation=== The canonical partition function Z of an ideal gas consisting of N = nNA identical (non-interacting) particles, is: : Z = \frac{z^N}{N!}\quad \hbox{with}\quad z = \frac{V}{\Lambda^3} where \Lambda is the thermal de Broglie wavelength, : \Lambda = \sqrt{\frac{h^2}{2\pi m k T}} with the usual definitions: h is the Planck constant, m the mass of a particle, k the Boltzmann constant and T the absolute temperature. For example, methyl chloride, a highly polar molecule and therefore with significant intermolecular forces, the experimental value for the compressibility factor is Z=0.9152 at a pressure of 10 atm and temperature of 100 °C. page 3-268 For air (small non-polar molecules) at approximately the same conditions, the compressibility factor is only Z=1.0025 (see table below for 10 bars, 400 K). ===Compressibility of air=== Normal air comprises in crude numbers 80 percent nitrogen and 20 percent oxygen . Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts that plot Z as a function of pressure at constant temperature. For an ideal gas the compressibility factor is Z=1 per definition. In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for the finite size of the molecules. The ideal gas law states that the volume V occupied by n moles of any gas has a pressure P at temperature T given by the following relationship, where R is the gas constant: :PV=nRT To account for the volume occupied by real gas molecules, the Van der Waals equation replaces V/n in the ideal gas law with (V_m-b), where Vm is the molar volume of the gas and b is the volume occupied by the molecules of one mole: :P(V_m - b)=R T thumb\|Van der Waals equation on a wall in Leiden The second modification made to the ideal gas law accounts for interaction between molecules of the gas. The first form of the Van der Waals equation of state given above can be recast in the following reduced form: :\left(p_R + \frac{3}{v_R^2}\right)(3v_R - 1) = (8 T_R) This equation is invariant for all fluids; that is, the same reduced form equation of state applies, no matter what a and b may be for the particular fluid. Experimental values for the compressibility factor confirm this. According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. page 141 Material constants that vary for each type of material are eliminated, in a recast reduced form of a constitutive equation. Above the critical temperature, TC, the Van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region.	0.0761	7.136	4.0	2	0.66	E
Calculate the pressure exerted by $1.0 \mathrm{~mol} \mathrm{Xe}$ when it is confined to $1.0 \mathrm{dm}^3$ at $25^{\circ} \mathrm{C}$.	The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. :P=\frac {2 \sigma_\theta s} {D}thumb\|252x252px\|Cylinder, where :P : internal pressure, :\sigma_\theta : allowable stress, :s : wall thickness, :D : outside diameter. Derivation of this equation This is derived from the definitions of pressure and weight density. Pressure is related to energy density and may be expressed in units such as joules per cubic metre (J/m3, which is equal to Pa). With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with :\text{pressure} = \text{weight density} \times \text{depth}. Presently or formerly popular pressure units include the following: atmosphere (atm) manometric units: centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury, height of equivalent column of water, including millimetre (mm ), centimetre (cm ), metre, inch, and foot of water; imperial and customary units: kip, short ton-force, long ton-force, pound- force, ounce-force, and poundal per square inch, short ton-force and long ton-force per square inch, fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression; non-SI metric units: bar, decibar, millibar, msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression, kilogram-force, or kilopond, per square centimetre (technical atmosphere), gram-force and tonne-force (metric ton- force) per square centimetre, barye (dyne per square centimetre), kilogram-force and tonne-force per square metre, sthene per square metre (pieze). ===Examples=== 120px\|thumbnail\|right\|The effects of an external pressure of 700 bar on an aluminum cylinder with wall thickness As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation , where g is the gravitational acceleration. thumb\|259x259px\|English Parliament of General Election 1702 The 1702 English general election was the first to be held during the reign of Queen Anne, and was necessitated by the demise of William III. P_0 is the pressure at the surface. * \rho(z) is the density of the material above the depth z. * g is the gravity acceleration in m/s^2 . Pressure is force magnitude applied over an area. Barlow's formula (called "Kesselformel" in German) relates the internal pressure that a pipeOr pressure vessel, or other cylindrical pressure containment structure. can withstand to its dimensions and the strength of its material. The molecular formula C23H21NO (molar mass: 327.42 g/mol, exact mass: 327.1623 u) may refer to: * JWH-015 * JWH-073 * JWH-120 Category:Molecular formulas The molecular formula C13H14O3 (molar mass: 218.248 g/mol, exact mass: 218.0943 u) may refer to: * NCS-382 * Toxol Category:Molecular formulas Pressure force acts in all directions at a point inside a gas. Then we have :\text{pressure} = \frac{\text{force}}{\text{area}} = \frac{\text{weight}}{\text{area}} = \frac{\text{weight density} \times \text{volume}}{\text{area}}, :\text{pressure} = \frac{\text{weight density} \times \text{(area} \times \text{depth)}}{\text{area}}. Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. The negative gradient of pressure is called the force density. The pressure is the scalar proportionality constant that relates the two normal vectors: :d\mathbf{F}_n = -p\,d\mathbf{A} = -p\,\mathbf{n}\,dA. It is a fundamental parameter in thermodynamics, and it is conjugate to volume. ===Units=== thumb\|right\|Mercury column The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m2, or kg·m−1·s−2). In a stratigraphic layer that is in hydrostatic equilibrium; the overburden pressure at a depth z, assuming the magnitude of the gravity acceleration is approximately constant, is given by: P(z) = P_0 + g \int_{0}^{z} \rho(z) \, dz Where: * z is the depth in meters. This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere.	21	4152	'-20.0'	24	-0.347	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the total change in entropy, when a sample of nitrogen gas of mass $14 \mathrm{~g}$ at $298 \mathrm{~K}$ and $1.00 \mathrm{bar}$ doubles its volume in an isothermal reversible expansion.	The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absorbed in any changes between different crystal structures). However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings: :(\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings})>0 Molar entropy is not the same for all gases. The entropy of vaporization is then equal to the heat of vaporization divided by the boiling point: : \Delta S_\text{vap} = \frac{\Delta H_\text{vap}}{T_\text{vap}}. ISO 15971 is an ISO standard for calorific value measurement of natural gas and its substitutes. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows. The limit of this sum as N \rightarrow \infty becomes an integral: :S^\circ = \sum_{k=1}^N \Delta S_k = \sum_{k=1}^N \frac{dQ_k}{T} \rightarrow \int _0 ^{T_2} \frac{dS}{dT} dT = \int _0 ^{T_2} \frac {C_{p_k}}{T} dT In this example, T_2 =298.15 K and C_{p_k} is the molar heat capacity at a constant pressure of the substance in the reversible process . However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other exactly defined physical constants. ==Specific gas constant== Rspecific for dry air Unit 287.052874 J⋅kg−1⋅K−1 53.3523 ft⋅lbf⋅lb−1⋅°R−1 1,716.46 ft⋅lbf⋅slug−1⋅°R−1 The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture. This quantity relates to the thermodynamic entropy as : \Delta S = 3/2 \ln K . In thermodynamics, the entropy of vaporization is the increase in entropy upon vaporization of a liquid. According to Trouton's rule, the entropy of vaporization (at standard pressure) of most liquids has similar values. When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in). * The heat capacity of the gas from the boiling point to room temperature. As pressure is defined as force per area of measurement, the gas equation can also be written as: :R = \frac{ \dfrac{\mathrm{force}}{\mathrm{area}} \times \mathrm{volume} } { \mathrm{amount} \times \mathrm{temperature} } Area and volume are (length)2 and (length)3 respectively. The entropy of a pure crystalline structure can be 0J⋅mol−1⋅K−1 only at 0K, according to the third law of thermodynamics.	0.25	0	'9.2e-06'	0.2307692308	2	B
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate $\Delta H$ when two copper blocks, each of mass $10.0 \mathrm{~kg}$, one at $100^{\circ} \mathrm{C}$ and the other at $0^{\circ} \mathrm{C}$, are placed in contact in an isolated container. The specific heat capacity of copper is $0.385 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~g}^{-1}$ and may be assumed constant over the temperature range involved.	Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Therefore, the heat capacity ratio in this example is 1.4. Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. The formula is: :\alpha = \frac{ k }{ \rho c_{p} } where * is thermal conductivity (W/(m·K)) * is specific heat capacity (J/(kg·K)) * is density (kg/m3) Together, can be considered the volumetric heat capacity (J/(m3·K)). Hence the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992. In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. The behavior of the heat capacity near the peak is described by the formula C\approx A_\pm t^{-\alpha}+B_\pm where t=\|1-T/T_c\| is the reduced temperature, T_c is the Lambda point temperature, A_\pm,B_\pm are constants (different above and below the transition temperature), and is the critical exponent: \alpha=-0.0127(3). thumb\|250px\|The plot of the specific heat capacity versus temperature. Despite this, if the density is fairly low and intermolecular forces are negligible, the two heat capacities may still continue to differ from each other by a fixed constant (as above, ), which reflects the relatively constant difference in work done during expansion for constant pressure vs. constant volume conditions. Table 363, Evaporation of Metals :The equations are described as reproducing the observed pressures to a satisfactory degree of approximation. However, when the gas density is sufficiently high and intermolecular forces are important, thermodynamic expressions may sometimes be used to accurately describe the relationship between the two heat capacities, as explained below. == Heat of vaporization == kJ/mol 1 H hydrogen (H2) use (H2) 0.904 CRC (H2) 0.90 LNG 0.904 2 He helium use 0.0829 CRC 0.08 LNG 0.0829 WEL 0.083 3 Li lithium use 136 LNG 147.1 WEL 147 Zhang et al. 136 4 Be beryllium use 292 LNG 297 WEL 297 Zhang et al. 292 5 B boron use 508 CRC 480 LNG 480 WEL 507 Zhang et al. 508 6 C carbon use WEL (sublimation) 715 7 N nitrogen (N2) use (N2) 5.57 CRC (N2) 5.57 LNG (N2) 5.577 WEL (per mole N atoms) 2.79 Zhang et al. 5.58 8 O oxygen (O2) use (O2) 6.82 CRC (O2) 6.82 LNG (O2) 6.820 WEL (per mole O atoms) 3.41 Zhang et al. 6.82 9 F fluorine (F2) use (F2) 6.62 CRC (F2) 6.62 LNG (F2) 6.62 WEL (per mole F atoms) 3.27 Zhang et al. 6.32 10 Ne neon use 1.71 CRC 1.71 LNG 1.71 WEL 1.75 Zhang et al. 1.9 11 Na sodium use 97.42 LNG 97.42 WEL 97.7 Zhang et al. 97.4 12 Mg magnesium use 128 LNG 128 WEL 128 Zhang et al. 132 13 Al aluminium use 284 CRC 294 LNG 294.0 WEL 293 Zhang et al. 284 14 Si silicon use 359 LNG 359 WEL 359 Zhang et al. 383 15 P phosphorus use 12.4 CRC 12.4 LNG 12.4 WEL 12.4 Zhang et al. 51.9 (white) 16 S sulfur use (mono) 45 CRC 45 LNG (mono) 45 WEL 9.8 Zhang et al. 45 17 Cl chlorine (Cl2) use (Cl2) 20.41 CRC (Cl2) 20.41 LNG (Cl2) 20.41 WEL (per mole Cl atoms) 10.2 Zhang et al. 20.4 18 Ar argon use 6.53 CRC 6.43 LNG 6.43 WEL 6.5 Zhang et al. 6.53 19 K potassium use 76.90 LNG 76.90 WEL 76.9 Zhang et al. 79.1 20 Ca calcium use 154.7 LNG 154.7 WEL 155 Zhang et al. 153 21 Sc scandium use 332.7 LNG 332.7 WEL 318 Zhang et al. 310 22 Ti titanium use 425 LNG 425 WEL 425 Zhang et al. 427 23 V vanadium use 444 LNG 459 WEL 453 Zhang et al. 451 24 Cr chromium use 339.5 LNG 339.5 WEL 339 Zhang et al. 347 25 Mn manganese use 221 LNG 221 WEL 220 Zhang et al. 225 26 Fe iron use 340 LNG 340 WEL 347 Zhang et al. 354 27 Co cobalt use 377 LNG 377 WEL 375 Zhang et al. 390 28 Ni nickel use 379 LNG 377.5 WEL 378 Zhang et al. 379 29 Cu copper use 300.4 LNG 300.4 WEL 300 Zhang et al. 305 30 Zn zinc use 115 LNG 123.6 WEL 119 Zhang et al. 115 31 Ga gallium use 256 CRC 254 LNG 254 WEL 256 Zhang et al. 256 32 Ge germanium use 334 CRC 334 LNG 334 WEL 334 Zhang et al. 330 33 As arsenic use 32.4 WEL 32.4 (sublimation) Zhang et al. 32.4 34 Se selenium use 95.48 CRC 95.48 LNG 95.48 WEL 26 Zhang et al. 95.5 35 Br bromine (Br2) use (Br2) 29.96 CRC (Br2) 29.96 LNG (Br2) 29.96 WEL (per mole Br atoms) 14.8 Zhang et al. 30 36 Kr krypton use 9.08 CRC 9.08 LNG 9.08 WEL 9.02 Zhang et al. 9.03 37 Rb rubidium use 75.77 LNG 75.77 WEL 72 Zhang et al. 69 38 Sr strontium use 141 LNG 136.9 WEL 137 Zhang et al. 141 39 Y yttrium use 390 LNG 365 WEL 380 Zhang et al. 363 40 Zr zirconium use 573 LNG 573 WEL 580 Zhang et al. 591 41 Nb niobium use 689.9 LNG 689.9 WEL 690 Zhang et al. 682 42 Mo molybdenum use 617 LNG 617 WEL 600 Zhang et al. 617 43 Tc technetium use 585.2 LNG 585.2 WEL 550 44 Ru ruthenium use 619 LNG 591.6 WEL 580 Zhang et al. 619 45 Rh rhodium use 494 LNG 494 WEL 495 Zhang et al. 493 46 Pd palladium use 358 LNG 362 WEL 380 Zhang et al. 358 47 Ag silver use 254 LNG 258 WEL 255 Zhang et al. 254 48 Cd cadmium use 99.87 CRC 99.87 LNG 99.9 WEL 100 Zhang et al. 100 49 In indium use 231.8 LNG 231.8 WEL 230 Zhang et al. 225 50 Sn tin use (white) 296.1 LNG (white) 296.1 WEL 290 Zhang et al. 296 51 Sb antimony use 193.43 LNG 193.43 WEL 68 Zhang et al. 193 52 Te tellurium use 114.1 CRC 114.1 LNG 114.1 WEL 48 Zhang et al. 114 53 I iodine (I2) use (I2) 41.57 CRC (I2) 41.57 LNG (I2) 41.6 WEL (per mole I atoms) 20.9 Zhang et al. 41.6 54 Xe xenon use 12.64 CRC 12.57 LNG 12.64 WEL 12.64 Zhang et al. 12.6 55 Cs caesium use 63.9 LNG 63.9 WEL 65 Zhang et al. 66.1 56 Ba barium use 140.3 CRC 140 LNG 140.3 WEL 140 Zhang et al. 142 57 La lanthanum use 400 LNG 402.1 WEL 400 Zhang et al. 400 58 Ce cerium use 398 LNG 398 WEL 350 Zhang et al. 398 59 Pr praseodymium use 331 LNG 331 WEL 330 Zhang et al. 331 60 Nd neodymium use 289 LNG 289 WEL 285 Zhang et al. 289 61 Pm promethium use 289 LNG 289 WEL 290 62 Sm samarium use 192 LNG 165 WEL 175 Zhang et al. 192 63 Eu europium use 176 LNG 176 WEL 175 Zhang et al. 176 64 Gd gadolinium use 301.3 LNG 301.3 WEL 305 Zhang et al. 301 65 Tb terbium use 391 LNG 293 WEL 295 Zhang et al. 391 66 Dy dysprosium use 280 LNG 280 WEL 280 Zhang et al. 280 67 Ho holmium use 251 LNG 71 WEL 265 Zhang et al. 251 68 Er erbium use 280 LNG 280 WEL 285 Zhang et al. 280 69 Tm thulium use 191 LNG 247 WEL 250 Zhang et al. 191 70 Yb ytterbium use 129 LNG 159 WEL 160 Zhang et al. 129 71 Lu lutetium use 414 LNG 414 WEL 415 Zhang et al. 414 72 Hf hafnium use 648 LNG 571 WEL 630 Zhang et al. 648 73 Ta tantalum use 732.8 LNG 732.8 WEL 735 Zhang et al. 753 74 W tungsten use 806.7 LNG 806.7 WEL 800 Zhang et al. 774 75 Re rhenium use 704 LNG 704 WEL 705 Zhang et al. 707 76 Os osmium use 678 LNG 738 WEL 630 Zhang et al. 678 77 Ir iridium use 564 LNG 231.8 WEL 560 Zhang et al. 564 78 Pt platinum use 510 LNG 469 WEL 490 Zhang et al. 510 79 Au gold use 342 CRC 324 LNG 324 WEL 330 Zhang et al. 342 80 Hg mercury use 59.11 CRC 59.11 LNG 59.1 WEL 59.2 Zhang et al. 58.2 81 Tl thallium use 165 LNG 165 WEL 165 Zhang et al. 162 82 Pb lead use 179.5 CRC 179.5 LNG 179.5 WEL 178 Zhang et al. 177 83 Bi bismuth use 179 CRC 151 LNG 151 WEL 160 Zhang et al. 179 84 Po polonium use 102.91 LNG 102.91 WEL about 100 85 At astatine use 54.39 (At2) GME 54.39 (At2) WEL about 40 86 Rn radon use 18.10 LNG 18.10 WEL 17 87 Fr francium use ca. 65 WEL about 65 88 Ra radium use 113 LNG 113 WEL about 125 89 Ac actinium use 400 WEL 400 90 Th thorium use 514 LNG 514 WEL 530 91 Pa protactinium use 481 LNG 481 WEL 470 92 U uranium use 417.1 LNG 417.1 WEL 420 93 Np neptunium use 336 LNG 336 WEL 335 94 Pu plutonium use 333.5 LNG 333.5 WEL 325 == Notes == Values refer to the enthalpy change in the conversion of liquid to gas at the boiling point (normal, 101.325 kPa). == References == ===Zhang et al.=== ===CRC=== As quoted from various sources in an online version of: * David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 84th Edition. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures. 'At, Astatine', system no. 8a, Springer-Verlag, Berlin, , pp. 116–117 ===LNG=== As quoted from various sources in: * J.A. Dean (ed.), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6, Thermodynamic Properties; Table 6.4, Heats of Fusion, Vaporization, and Sublimation and Specific Heat at Various Temperatures of the Elements and Inorganic Compounds ===WEL=== As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T. H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. See relations between specific heats for the derivation of the thermodynamic relations between the heat capacities. The amount of energy added equals , with representing the change in temperature. Boca Raton, Florida, 2003; Section 4, Properties of the Elements and Inorganic Compounds; Vapor Pressure of the Metallic Elements :The equations reproduce the observed pressures to an accuracy of ±5% or better. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). As quoted from these sources: :a - Lide, D.R., and Kehiaian, H.V., CRC Handbook of Thermophysical and Thermochemical Data, CRC Press, Boca Raton, Florida, 1994. :b - Stull, D., in American Institute of Physics Handbook, Third Edition, Gray, D.E., Ed., McGraw Hill, New York, 1972. :c - Hultgren, R., Desai, P.D., Hawkins, D.T., Gleiser, M., Kelley, K.K., and Wagman, D.D., Selected Values of Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, OH, 1973. :d - TRCVP, Vapor Pressure Database, Version 2.2P, Thermodynamic Research Center, Texas A&M; University, College Station, TX. :e - Barin, I., Thermochemical Data of Pure Substances, VCH Publishers, New York, 1993. :f - Ohse, R.W. Handbook of Thermodynamic and Transport Properties of Alkali Metals, Blackwell Scientific Publications, Oxford, 1994. :g - Gschneidner, K.A., in CRC Handbook of Chemistry and Physics, 77th Edition, p. 4-112, CRC Press, Boca Raton, Florida, 1996. :h - . :*i - Wagner, W., and de Reuck, K.M., International Thermodynamic Tables of the Fluid State, No. 9.	2.3613	0	65.49	14	0.086	B
A perfect gas undergoes isothermal compression, which reduces its volume by $2.20 \mathrm{dm}^3$. The final pressure and volume of the gas are $5.04 \mathrm{bar}$ and $4.65 \mathrm{dm}^3$, respectively. Calculate the original pressure of the gas in atm.	The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture (Dalton's Law). The partial pressures obey Dalton's law: P_i = y_i P, where is the total pressure and is the mole fraction of the component (so the partial pressures add up to the total pressure). It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas. The partial pressure of a gas is a measure of thermodynamic activity of the gas's molecules. That is, the mole fraction x_{\mathrm{i}} of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component: x_{\mathrm{i}} = \frac{p_{\mathrm{i}}}{p} = \frac{n_{\mathrm{i}}}{n} and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression: p_{\mathrm{i}} = x_{\mathrm{i}} \cdot p where: x_{\mathrm{i}} = mole fraction of any individual gas component in a gas mixture p_{\mathrm{i}} = partial pressure of any individual gas component in a gas mixture n_{\mathrm{i}} = moles of any individual gas component in a gas mixture n = total moles of the gas mixture p = total pressure of the gas mixture The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.Frostberg State University's "General Chemistry Online" The ratio of partial pressures relies on the following isotherm relation: \frac{V_{\rm X}}{V_{\rm tot}} = \frac{p_{\rm X}}{p_{\rm tot}} = \frac{n_{\rm X}}{n_{\rm tot}} * VX is the partial volume of any individual gas component (X) * Vtot is the total volume of the gas mixture * pX is the partial pressure of gas X * ptot is the total pressure of the gas mixture * nX is the amount of substance of gas (X) * ntot is the total amount of substance in gas mixture ==Partial volume (Amagat's law of additive volume)== The partial volume of a particular gas in a mixture is the volume of one component of the gas mixture. In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The standard atmosphere (symbol: atm) is a unit of pressure defined as Pa. Using diving terms, partial pressure is calculated as: :partial pressure = (total absolute pressure) × (volume fraction of gas component) For the component gas "i": :pi = P × Fi For example, at underwater, the total absolute pressure is (i.e., 1 bar of atmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen approximately 79% by volume are: :pN2 = 6 bar × 0.79 = 4.7 bar absolute :pO2 = 6 bar × 0.21 = 1.3 bar absolute where: pi = partial pressure of gas component i = P_{\mathrm{i}} in the terms used in this article P = total pressure = P in the terms used in this article Fi = volume fraction of gas component i = mole fraction, x_{\mathrm{i}}, in the terms used in this article pN2 = partial pressure of nitrogen = P_\mathrm{N_2} in the terms used in this article pO2 = partial pressure of oxygen = P_\mathrm{O_2} in the terms used in this article The minimum safe lower limit for the partial pressures of oxygen in a breathing gas mixture for diving is absolute. V_{\rm X} = V_{\rm tot} \times \frac{p_{\rm X}}{p_{\rm tot}} = V_{\rm tot} \times \frac{n_{\rm X}}{n_{\rm tot}} * VX is the partial volume of an individual gas component X in the mixture * Vtot is the total volume of the gas mixture * pX is the partial pressure of gas X * ptot is the total pressure of the gas mixture * nX is the amount of substance of gas X * ntot is the total amount of substance in the gas mixture ==Vapor pressure== thumb\|right\|A log-lin vapor pressure chart for various liquids Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases (i.e., liquid or solid). For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. Typically, the maximum total partial pressure of narcotic gases used when planning for technical diving may be around 4.5 bar absolute, based on an equivalent narcotic depth of . In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of nitrogen as an ideal gas at . In chemistry and in various industries, the reference pressure referred to in standard temperature and pressure was commonly but standards have since diverged; in 1982, the International Union of Pure and Applied Chemistry recommended that for the purposes of specifying the physical properties of substances, standard pressure should be precisely .IUPAC.org, Gold Book, Standard Pressure ==Pressure units and equivalencies == A pressure of 1 atm can also be stated as: :≡ pascals (Pa) :≡ bar :≈ kgf/cm2 :≈ technical atmosphere :≈ m H2O, 4 °CThis is the customarily accepted value for cm–H2O, 4 °C. Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. It is approximately equal to Earth's average atmospheric pressure at sea level. ==History== The standard atmosphere was originally defined as the pressure exerted by 760 mm of mercury at and standard gravity (gn = ). The partial pressure of oxygen also determines the maximum operating depth of a gas mixture. That is, at low pressures is the same as the pressure, so it has the same units as pressure. When calculating the fugacity of the compressed phase, one can generally assume the volume is constant. In a pure substance, is equal to the Gibbs energy for a mole of the substance, and d\mu = dG_\mathrm{m} = -S_\mathrm{m}dT + V_\mathrm{m}dP, where and are the temperature and pressure, is the volume per mole and is the entropy per mole. ===Gas=== For an ideal gas the equation of state can be written as V_\mathrm{m}^\text{ideal} = \frac{RT}{P}, where is the ideal gas constant. In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle.	7.00	3.38	0.4	0.6296296296	+5.41	B
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the total change in entropy, when a sample of nitrogen gas of mass $14 \mathrm{~g}$ at $298 \mathrm{~K}$ and $1.00 \mathrm{bar}$ doubles its volume in an isothermal irreversible expansion against $p_{\mathrm{ex}}=0$.	However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absorbed in any changes between different crystal structures). This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of nitrogen as an ideal gas at . The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings: :(\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings})>0 Molar entropy is not the same for all gases. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. The temperature dependence at constant pressure is \left(\frac{\partial \ln f}{\partial T}\right)_P = \frac{\Delta H_\mathrm{m}}{R T^2}, where is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum. In a pure substance, is equal to the Gibbs energy for a mole of the substance, and d\mu = dG_\mathrm{m} = -S_\mathrm{m}dT + V_\mathrm{m}dP, where and are the temperature and pressure, is the volume per mole and is the entropy per mole. ===Gas=== For an ideal gas the equation of state can be written as V_\mathrm{m}^\text{ideal} = \frac{RT}{P}, where is the ideal gas constant. The entropy of vaporization is then equal to the heat of vaporization divided by the boiling point: : \Delta S_\text{vap} = \frac{\Delta H_\text{vap}}{T_\text{vap}}. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows. The differential change of the chemical potential between two states of slightly different pressures but equal temperature (i.e., ) is given by d\mu = V_\mathrm{m}dP = RT \, \frac{dP}{P} = R T\, d \ln P,where ln p is the natural logarithm of p. This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure. Numerical example: Nitrogen gas (N2) at 0 °C and a pressure of atmospheres (atm) has a fugacity of atm. ISO 15971 is an ISO standard for calorific value measurement of natural gas and its substitutes. In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. In thermodynamics, the entropy of vaporization is the increase in entropy upon vaporization of a liquid. Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. * The heat capacity of the gas from the boiling point to room temperature.	0	-6.9	3.07	34	+2.9	E
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in the molar Gibbs energy of hydrogen gas when its pressure is increased isothermally from $1.0 \mathrm{~atm}$ to 100.0 atm at $298 \mathrm{~K}$.	The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. * The heat capacity of the gas from the boiling point to room temperature. When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in). In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absorbed in any changes between different crystal structures). In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system:A to Z of Thermodynamics Pierre Perrot :\sum_{i=1}^I N_i \mathrm{d}\mu_i = - S \mathrm{d}T + V \mathrm{d}p where N_i is the number of moles of component i, \mathrm{d}\mu_i the infinitesimal increase in chemical potential for this component, S the entropy, T the absolute temperature, V volume and p the pressure. Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. ==References== ==External links== * Ideal gas calculator – Ideal gas calculator provides the correct information for the moles of gas involved. The value of R is then obtained from the relation :c_\mathrm{a}(0, T) = \sqrt{\frac{\gamma_0 R T}{A_\mathrm{r}(\mathrm{Ar}) M_\mathrm{u}}}, where: γ0 is the heat capacity ratio ( for monatomic gases such as argon); T is the temperature, TTPW = 273.16 K by the definition of the kelvin at that time; Ar(Ar) is the relative atomic mass of argon and Mu = as defined at the time. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) *(P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. As pressure is defined as force per area of measurement, the gas equation can also be written as: :R = \frac{ \dfrac{\mathrm{force}}{\mathrm{area}} \times \mathrm{volume} } { \mathrm{amount} \times \mathrm{temperature} } Area and volume are (length)2 and (length)3 respectively. Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB): R = N_{\rm A} k. Consider the difference between adding heat to the gas with a locked piston and adding heat with a piston free to move, so that pressure remains constant.	4.56	0.24995	'-3.8'	+11	0.7854	D
A perfect gas undergoes isothermal compression, which reduces its volume by $2.20 \mathrm{dm}^3$. The final pressure and volume of the gas are $5.04 \mathrm{bar}$ and $4.65 \mathrm{dm}^3$, respectively. Calculate the original pressure of the gas in bar.	The partial pressures obey Dalton's law: P_i = y_i P, where is the total pressure and is the mole fraction of the component (so the partial pressures add up to the total pressure). The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture (Dalton's Law). The partial pressure of a gas is a measure of thermodynamic activity of the gas's molecules. That is, the mole fraction x_{\mathrm{i}} of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component: x_{\mathrm{i}} = \frac{p_{\mathrm{i}}}{p} = \frac{n_{\mathrm{i}}}{n} and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression: p_{\mathrm{i}} = x_{\mathrm{i}} \cdot p where: x_{\mathrm{i}} = mole fraction of any individual gas component in a gas mixture p_{\mathrm{i}} = partial pressure of any individual gas component in a gas mixture n_{\mathrm{i}} = moles of any individual gas component in a gas mixture n = total moles of the gas mixture p = total pressure of the gas mixture The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.Frostberg State University's "General Chemistry Online" The ratio of partial pressures relies on the following isotherm relation: \frac{V_{\rm X}}{V_{\rm tot}} = \frac{p_{\rm X}}{p_{\rm tot}} = \frac{n_{\rm X}}{n_{\rm tot}} * VX is the partial volume of any individual gas component (X) * Vtot is the total volume of the gas mixture * pX is the partial pressure of gas X * ptot is the total pressure of the gas mixture * nX is the amount of substance of gas (X) * ntot is the total amount of substance in gas mixture ==Partial volume (Amagat's law of additive volume)== The partial volume of a particular gas in a mixture is the volume of one component of the gas mixture. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas. In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. V_{\rm X} = V_{\rm tot} \times \frac{p_{\rm X}}{p_{\rm tot}} = V_{\rm tot} \times \frac{n_{\rm X}}{n_{\rm tot}} * VX is the partial volume of an individual gas component X in the mixture * Vtot is the total volume of the gas mixture * pX is the partial pressure of gas X * ptot is the total pressure of the gas mixture * nX is the amount of substance of gas X * ntot is the total amount of substance in the gas mixture ==Vapor pressure== thumb\|right\|A log-lin vapor pressure chart for various liquids Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases (i.e., liquid or solid). Typically, the maximum total partial pressure of narcotic gases used when planning for technical diving may be around 4.5 bar absolute, based on an equivalent narcotic depth of . Using diving terms, partial pressure is calculated as: :partial pressure = (total absolute pressure) × (volume fraction of gas component) For the component gas "i": :pi = P × Fi For example, at underwater, the total absolute pressure is (i.e., 1 bar of atmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen approximately 79% by volume are: :pN2 = 6 bar × 0.79 = 4.7 bar absolute :pO2 = 6 bar × 0.21 = 1.3 bar absolute where: pi = partial pressure of gas component i = P_{\mathrm{i}} in the terms used in this article P = total pressure = P in the terms used in this article Fi = volume fraction of gas component i = mole fraction, x_{\mathrm{i}}, in the terms used in this article pN2 = partial pressure of nitrogen = P_\mathrm{N_2} in the terms used in this article pO2 = partial pressure of oxygen = P_\mathrm{O_2} in the terms used in this article The minimum safe lower limit for the partial pressures of oxygen in a breathing gas mixture for diving is absolute. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C. where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/ft) in ISA h = height at which pressure is calculated (ft) h_b = height of reference level b (feet; e.g., hb = 36,089 ft) R^* = universal gas constant; using feet, kelvins, and (SI) moles: g_0 = gravitational acceleration: 32.17405 ft/s2 M = molar mass of Earth's air: 28.9644 lb/lb-mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. VPT may refer to: * Valor por Tamaulipas * Vermont Public Television * Volume, temperature and pressure, the three parameters in the combined gas law The barometric formula is a formula used to model how the pressure (or density) of the air changes with altitude. == Pressure equations == thumb\|300px\|Pressure as a function of the height above the sea level There are two equations for computing pressure as a function of height. The partial pressure of oxygen also determines the maximum operating depth of a gas mixture. Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. See real gas or perfect gas or gas for further understanding.) ==See also== Hypsometric equation NRLMSISE-00 *Vertical pressure variation == References == Category:Atmosphere Category:Vertical position Category:Pressure That is, at low pressures is the same as the pressure, so it has the same units as pressure. In aeronautical engineering, overall pressure ratio, or overall compression ratio, is the ratio of the stagnation pressure as measured at the front and rear of the compressor of a gas turbine engine. Nomenclature 1 Nomenclature 2 Heat capacity at constant V, C_V, or constant P, C_P Ideal-gas law PV = nRT and C_P - C_V = nR Calorically perfect Perfect Thermally perfect Semi-perfect Ideal Imperfect Imperfect, or non-ideal === Thermally and calorically perfect gas === Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. In a pure substance, is equal to the Gibbs energy for a mole of the substance, and d\mu = dG_\mathrm{m} = -S_\mathrm{m}dT + V_\mathrm{m}dP, where and are the temperature and pressure, is the volume per mole and is the entropy per mole. ===Gas=== For an ideal gas the equation of state can be written as V_\mathrm{m}^\text{ideal} = \frac{RT}{P}, where is the ideal gas constant.	10.7598	5654.86677646	1.43	3.42	2	D
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate $\Delta S$ (for the system) when the state of $3.00 \mathrm{~mol}$ of perfect gas atoms, for which $C_{p, \mathrm{~m}}=\frac{5}{2} R$, is changed from $25^{\circ} \mathrm{C}$ and 1.00 atm to $125^{\circ} \mathrm{C}$ and $5.00 \mathrm{~atm}$. How do you rationalize the $\operatorname{sign}$ of $\Delta S$?	The δ34S (pronounced delta 34 S) value is a standardized method for reporting measurements of the ratio of two stable isotopes of sulfur, 34S:32S, in a sample against the equivalent ratio in a known reference standard. With VCDT as the reference standard, natural δ34S value variations have been recorded between -72‰ and +147‰. The δ34S value refers to a measure of the ratio of the two most common stable sulfur isotopes, 34S:32S, as measured in a sample against that same ratio as measured in a known reference standard. In geochemistry, hydrology, paleoclimatology and paleoceanography, δ15N (pronounced "delta fifteen n") or delta-N-15 is a measure of the ratio of the two stable isotopes of nitrogen, 15N:14N. ==Formulas== Two very similar expressions for are in wide use in hydrology. Thus the step is approximately 13.946 cents, and there are 86.049 steps per octave. :\begin{align} \frac{50\log_2{\left(\frac32\right)} + 28\log_2{\left(\frac54\right)} + 23\log_2{\left(\frac65\right)}}{50^2+28^2+23^2} = 0.011\,621\,2701 \\\ 0.011\,621\,2701 \times 1200 = 13.945\,524\,1627 \end{align} () The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad () and the 9:7:5 "narrow" triad () (rather than the conventional 4:5:6 triad). For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. That value can be calculated in per mil (‰, parts per thousand) as: :\delta \ce{^{34}S} = \left( \frac{\left( \frac\ce{^{34}S}\ce{^{32}S} \right)_\mathrm{sample}}{\left( \frac\ce{^{34}S}\ce{^{32}S} \right)_\mathrm{standard}} - 1 \right) \times 1000 ‰ Less commonly, if the appropriate isotope abundances are measured, similar formulae can be used to quantify ratio variations between 33S and 32S, and 36S and 32S, reported as δ33S and δ36S, respectively. ===Reference standard=== thumb\|right\|Troilite from the Canyon Diablo meteorite was the first reference standard for δ34S.\|alt=A worn brown-red-gold space rock covered in smoothed pock-marks sits mounted in a museum. It can be proved that an ideal gas (i.e. satisfying the ideal gas equation of state, PV = nRT ) is either calorically perfect or thermally perfect. A calorically perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, and enthalpy H that are functions of temperature only, i.e., U = U(T), H = H(T) * has heat capacities C_V, C_P that are constant, i.e., dU = C_V dT, dH = C_P dT and \Delta U = C_V \Delta T, \Delta H = C_P \Delta T, where \Delta is any finite (non-differential) change in each quantity. In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. Since the atmosphere is 99.6337% 14N and 0.3663% 15N, a is 0.003663 in the former case and 0.003663/0.996337 = 0.003676 in the latter. Nomenclature 1 Nomenclature 2 Heat capacity at constant V, C_V, or constant P, C_P Ideal-gas law PV = nRT and C_P - C_V = nR Calorically perfect Perfect Thermally perfect Semi-perfect Ideal Imperfect Imperfect, or non-ideal === Thermally and calorically perfect gas === Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. Both have the form 1000\frac{s-a}a ‰ (‰ = permil or parts per thousand) where s and a are the relative abundances of 15N in respectively the sample and the atmosphere. The lowercase delta character is used by convention, to be consistent with use in other areas of stable isotope chemistry. ISO 15971 is an ISO standard for calorific value measurement of natural gas and its substitutes. However s varies similarly; for example if in the sample 15N is 0.385% and 14N is 99.615%, s is 0.003850 in the former case and 0.00385/0.99615 = 0.003865 in the latter. From both statistical mechanics and the simpler kinetic theory of gases, we expect the heat capacity of a monatomic ideal gas to be constant, since for such a gas only kinetic energy contributes to the internal energy and to within an arbitrary additive constant U = (3/2) n R T , and therefore C_V = (3/2) n R , a constant. The value of 1000\frac{s-a}a is then 51.05‰ in the former case and 51.38‰ in the latter, an insignificant difference in practice given the typical range of -20 to 80 for . ==Applications== One use of 15N is as a tracer to determine the path taken by fertilizers applied to anything from pots to landscapes. However, the idea of a perfect gas model is often invoked as a combination of the ideal gas equation of state with specific additional assumptions regarding the variation (or nonvariation) of the heat capacity with temperature. == Perfect gas nomenclature == The terms perfect gas and ideal gas are sometimes used interchangeably, depending on the particular field of physics and engineering. Sometimes, other distinctions are made, such as between thermally perfect gas and calorically perfect gas, or between imperfect, semi-perfect, and perfect gases, and as well as the characteristics of ideal gases. The δ (delta) scale is a non-octave repeating musical scale. This temperature limit depends on the chemical composition of the gas and how accurate the calculations need to be, since molecular dissociation may be important at a higher or lower temperature which is intrinsically dependent on the molecular nature of the gas.	1.154700538	4.3	'-22.1'	169	2.567	C
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \mathrm{~mol}$ of diatomic perfect gas molecules at $200 \mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \mathrm{~K}$. Given that $C_{V, \mathrm{~m}}=27.5 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, calculate $\Delta H$.	Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. A calorically perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, and enthalpy H that are functions of temperature only, i.e., U = U(T), H = H(T) * has heat capacities C_V, C_P that are constant, i.e., dU = C_V dT, dH = C_P dT and \Delta U = C_V \Delta T, \Delta H = C_P \Delta T, where \Delta is any finite (non-differential) change in each quantity. The temperature dependence at constant pressure is \left(\frac{\partial \ln f}{\partial T}\right)_P = \frac{\Delta H_\mathrm{m}}{R T^2}, where is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum. Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. For a diatomic gas, often 5 degrees of freedom are assumed to contribute at room temperature since each molecule has 3 translational and 2 rotational degrees of freedom, and the single vibrational degree of freedom is often not included since vibrations are often not thermally active except at high temperatures, as predicted by quantum statistical mechanics. This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). From both statistical mechanics and the simpler kinetic theory of gases, we expect the heat capacity of a monatomic ideal gas to be constant, since for such a gas only kinetic energy contributes to the internal energy and to within an arbitrary additive constant U = (3/2) n R T , and therefore C_V = (3/2) n R , a constant. Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. Nomenclature 1 Nomenclature 2 Heat capacity at constant V, C_V, or constant P, C_P Ideal-gas law PV = nRT and C_P - C_V = nR Calorically perfect Perfect Thermally perfect Semi-perfect Ideal Imperfect Imperfect, or non-ideal === Thermally and calorically perfect gas === Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). == Heat of vaporization == kJ/mol 1 H hydrogen (H2) use (H2) 0.904 CRC (H2) 0.90 LNG 0.904 2 He helium use 0.0829 CRC 0.08 LNG 0.0829 WEL 0.083 3 Li lithium use 136 LNG 147.1 WEL 147 Zhang et al. 136 4 Be beryllium use 292 LNG 297 WEL 297 Zhang et al. 292 5 B boron use 508 CRC 480 LNG 480 WEL 507 Zhang et al. 508 6 C carbon use WEL (sublimation) 715 7 N nitrogen (N2) use (N2) 5.57 CRC (N2) 5.57 LNG (N2) 5.577 WEL (per mole N atoms) 2.79 Zhang et al. 5.58 8 O oxygen (O2) use (O2) 6.82 CRC (O2) 6.82 LNG (O2) 6.820 WEL (per mole O atoms) 3.41 Zhang et al. 6.82 9 F fluorine (F2) use (F2) 6.62 CRC (F2) 6.62 LNG (F2) 6.62 WEL (per mole F atoms) 3.27 Zhang et al. 6.32 10 Ne neon use 1.71 CRC 1.71 LNG 1.71 WEL 1.75 Zhang et al. 1.9 11 Na sodium use 97.42 LNG 97.42 WEL 97.7 Zhang et al. 97.4 12 Mg magnesium use 128 LNG 128 WEL 128 Zhang et al. 132 13 Al aluminium use 284 CRC 294 LNG 294.0 WEL 293 Zhang et al. 284 14 Si silicon use 359 LNG 359 WEL 359 Zhang et al. 383 15 P phosphorus use 12.4 CRC 12.4 LNG 12.4 WEL 12.4 Zhang et al. 51.9 (white) 16 S sulfur use (mono) 45 CRC 45 LNG (mono) 45 WEL 9.8 Zhang et al. 45 17 Cl chlorine (Cl2) use (Cl2) 20.41 CRC (Cl2) 20.41 LNG (Cl2) 20.41 WEL (per mole Cl atoms) 10.2 Zhang et al. 20.4 18 Ar argon use 6.53 CRC 6.43 LNG 6.43 WEL 6.5 Zhang et al. 6.53 19 K potassium use 76.90 LNG 76.90 WEL 76.9 Zhang et al. 79.1 20 Ca calcium use 154.7 LNG 154.7 WEL 155 Zhang et al. 153 21 Sc scandium use 332.7 LNG 332.7 WEL 318 Zhang et al. 310 22 Ti titanium use 425 LNG 425 WEL 425 Zhang et al. 427 23 V vanadium use 444 LNG 459 WEL 453 Zhang et al. 451 24 Cr chromium use 339.5 LNG 339.5 WEL 339 Zhang et al. 347 25 Mn manganese use 221 LNG 221 WEL 220 Zhang et al. 225 26 Fe iron use 340 LNG 340 WEL 347 Zhang et al. 354 27 Co cobalt use 377 LNG 377 WEL 375 Zhang et al. 390 28 Ni nickel use 379 LNG 377.5 WEL 378 Zhang et al. 379 29 Cu copper use 300.4 LNG 300.4 WEL 300 Zhang et al. 305 30 Zn zinc use 115 LNG 123.6 WEL 119 Zhang et al. 115 31 Ga gallium use 256 CRC 254 LNG 254 WEL 256 Zhang et al. 256 32 Ge germanium use 334 CRC 334 LNG 334 WEL 334 Zhang et al. 330 33 As arsenic use 32.4 WEL 32.4 (sublimation) Zhang et al. 32.4 34 Se selenium use 95.48 CRC 95.48 LNG 95.48 WEL 26 Zhang et al. 95.5 35 Br bromine (Br2) use (Br2) 29.96 CRC (Br2) 29.96 LNG (Br2) 29.96 WEL (per mole Br atoms) 14.8 Zhang et al. 30 36 Kr krypton use 9.08 CRC 9.08 LNG 9.08 WEL 9.02 Zhang et al. 9.03 37 Rb rubidium use 75.77 LNG 75.77 WEL 72 Zhang et al. 69 38 Sr strontium use 141 LNG 136.9 WEL 137 Zhang et al. 141 39 Y yttrium use 390 LNG 365 WEL 380 Zhang et al. 363 40 Zr zirconium use 573 LNG 573 WEL 580 Zhang et al. 591 41 Nb niobium use 689.9 LNG 689.9 WEL 690 Zhang et al. 682 42 Mo molybdenum use 617 LNG 617 WEL 600 Zhang et al. 617 43 Tc technetium use 585.2 LNG 585.2 WEL 550 44 Ru ruthenium use 619 LNG 591.6 WEL 580 Zhang et al. 619 45 Rh rhodium use 494 LNG 494 WEL 495 Zhang et al. 493 46 Pd palladium use 358 LNG 362 WEL 380 Zhang et al. 358 47 Ag silver use 254 LNG 258 WEL 255 Zhang et al. 254 48 Cd cadmium use 99.87 CRC 99.87 LNG 99.9 WEL 100 Zhang et al. 100 49 In indium use 231.8 LNG 231.8 WEL 230 Zhang et al. 225 50 Sn tin use (white) 296.1 LNG (white) 296.1 WEL 290 Zhang et al. 296 51 Sb antimony use 193.43 LNG 193.43 WEL 68 Zhang et al. 193 52 Te tellurium use 114.1 CRC 114.1 LNG 114.1 WEL 48 Zhang et al. 114 53 I iodine (I2) use (I2) 41.57 CRC (I2) 41.57 LNG (I2) 41.6 WEL (per mole I atoms) 20.9 Zhang et al. 41.6 54 Xe xenon use 12.64 CRC 12.57 LNG 12.64 WEL 12.64 Zhang et al. 12.6 55 Cs caesium use 63.9 LNG 63.9 WEL 65 Zhang et al. 66.1 56 Ba barium use 140.3 CRC 140 LNG 140.3 WEL 140 Zhang et al. 142 57 La lanthanum use 400 LNG 402.1 WEL 400 Zhang et al. 400 58 Ce cerium use 398 LNG 398 WEL 350 Zhang et al. 398 59 Pr praseodymium use 331 LNG 331 WEL 330 Zhang et al. 331 60 Nd neodymium use 289 LNG 289 WEL 285 Zhang et al. 289 61 Pm promethium use 289 LNG 289 WEL 290 62 Sm samarium use 192 LNG 165 WEL 175 Zhang et al. 192 63 Eu europium use 176 LNG 176 WEL 175 Zhang et al. 176 64 Gd gadolinium use 301.3 LNG 301.3 WEL 305 Zhang et al. 301 65 Tb terbium use 391 LNG 293 WEL 295 Zhang et al. 391 66 Dy dysprosium use 280 LNG 280 WEL 280 Zhang et al. 280 67 Ho holmium use 251 LNG 71 WEL 265 Zhang et al. 251 68 Er erbium use 280 LNG 280 WEL 285 Zhang et al. 280 69 Tm thulium use 191 LNG 247 WEL 250 Zhang et al. 191 70 Yb ytterbium use 129 LNG 159 WEL 160 Zhang et al. 129 71 Lu lutetium use 414 LNG 414 WEL 415 Zhang et al. 414 72 Hf hafnium use 648 LNG 571 WEL 630 Zhang et al. 648 73 Ta tantalum use 732.8 LNG 732.8 WEL 735 Zhang et al. 753 74 W tungsten use 806.7 LNG 806.7 WEL 800 Zhang et al. 774 75 Re rhenium use 704 LNG 704 WEL 705 Zhang et al. 707 76 Os osmium use 678 LNG 738 WEL 630 Zhang et al. 678 77 Ir iridium use 564 LNG 231.8 WEL 560 Zhang et al. 564 78 Pt platinum use 510 LNG 469 WEL 490 Zhang et al. 510 79 Au gold use 342 CRC 324 LNG 324 WEL 330 Zhang et al. 342 80 Hg mercury use 59.11 CRC 59.11 LNG 59.1 WEL 59.2 Zhang et al. 58.2 81 Tl thallium use 165 LNG 165 WEL 165 Zhang et al. 162 82 Pb lead use 179.5 CRC 179.5 LNG 179.5 WEL 178 Zhang et al. 177 83 Bi bismuth use 179 CRC 151 LNG 151 WEL 160 Zhang et al. 179 84 Po polonium use 102.91 LNG 102.91 WEL about 100 85 At astatine use 54.39 (At2) GME 54.39 (At2) WEL about 40 86 Rn radon use 18.10 LNG 18.10 WEL 17 87 Fr francium use ca. 65 WEL about 65 88 Ra radium use 113 LNG 113 WEL about 125 89 Ac actinium use 400 WEL 400 90 Th thorium use 514 LNG 514 WEL 530 91 Pa protactinium use 481 LNG 481 WEL 470 92 U uranium use 417.1 LNG 417.1 WEL 420 93 Np neptunium use 336 LNG 336 WEL 335 94 Pu plutonium use 333.5 LNG 333.5 WEL 325 == Notes == Values refer to the enthalpy change in the conversion of liquid to gas at the boiling point (normal, 101.325 kPa). == References == ===Zhang et al.=== ===CRC=== As quoted from various sources in an online version of: * David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 84th Edition. Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. This error is corrected in the above equation. ==Measurement== The fugacity can be deduced from measurements of volume as a function of pressure at constant temperature. When calculating the fugacity of the compressed phase, one can generally assume the volume is constant.	+5.41	0.68	0.59	3.8	58.2	A
A sample of $255 \mathrm{mg}$ of neon occupies $3.00 \mathrm{dm}^3$ at $122 \mathrm{K}$. Use the perfect gas law to calculate the pressure of the gas.	For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. Dalton's law is related to the ideal gas laws. ==Formula== Mathematically, the pressure of a mixture of non-reactive gases can be defined as the summation: p_\text{total} = \sum_{i=1}^n p_i = p_1+p_2+p_3+\cdots+p_n where p1, p2, ..., pn represent the partial pressures of each component. p_{i} = p_\text{total} x_i where xi is the mole fraction of the ith component in the total mixture of n components . ==Volume-based concentration== The relationship below provides a way to determine the volume- based concentration of any individual gaseous component p_i = p_\text{total} c_i where ci is the concentration of component i. Billion cubic meters of natural gas (non SI abbreviation: bcm) or cubic kilometer of natural gas is a measure of natural gas production and trade. thumb\|upright=1.75\|An illustration of Dalton's law using the gases of air at sea level. That means that 1 billion cubic metres of natural gas by the International Energy Agency standard is equivalent to 1.017 billion cubic metres of natural gas by the Russian standard. ==Energy based definitions== Some other organizations use energy equivalent-based standards. Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. The pressure inside is equal to atmospheric pressure. In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. Forming gas is a mixture of hydrogen (mole fraction varies) and nitrogen. 8) or of pressure P (p. 9). From both statistical mechanics and the simpler kinetic theory of gases, we expect the heat capacity of a monatomic ideal gas to be constant, since for such a gas only kinetic energy contributes to the internal energy and to within an arbitrary additive constant U = (3/2) n R T , and therefore C_V = (3/2) n R , a constant. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Thus we observe that for a monatomic gas, with 3 translational degrees of freedom per atom: : \gamma = \frac{5}{3} = 1.6666\ldots, As an example of this behavior, at 273 K (0 °C) the noble gases He, Ne, and Ar all have nearly the same value of , equal to 1.664. Nomenclature 1 Nomenclature 2 Heat capacity at constant V, C_V, or constant P, C_P Ideal-gas law PV = nRT and C_P - C_V = nR Calorically perfect Perfect Thermally perfect Semi-perfect Ideal Imperfect Imperfect, or non-ideal === Thermally and calorically perfect gas === Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. According to the Russian standard, the gas volume is measured at . Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Dalton's law is not strictly followed by real gases, with the deviation increasing with pressure. For example, terrestrial air is primarily made up of diatomic gases (around 78% nitrogen, N2, and 21% oxygen, O2), and at standard conditions it can be considered to be an ideal gas. Cedigaz uses a standard which is equivalent to per billion cubic metres. ==References== Category:Natural gas Category:Units of volume Category:Units of energy Category:Non-SI metric units Category:International Energy Agency Category:BP However, the idea of a perfect gas model is often invoked as a combination of the ideal gas equation of state with specific additional assumptions regarding the variation (or nonvariation) of the heat capacity with temperature. == Perfect gas nomenclature == The terms perfect gas and ideal gas are sometimes used interchangeably, depending on the particular field of physics and engineering. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles.	1.2	0.042	152.67	9.90	0.9984	B
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A chemical reaction takes place in a container of cross-sectional area $100 \mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $10 \mathrm{~cm}$ against an external pressure of $1.0 \mathrm{~atm}$. Calculate the work done by the system.	In this case the work is given by (where is the pressure at the surface, is the increase of the volume of the system). When a system, for example, moles of a gas of volume at pressure and temperature , is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy plus , where is the work done in pushing against the ambient (atmospheric) pressure. The quantity of thermodynamic work is defined as work done by the system on its surroundings. When work, for example pressure–volume work, is done on its surroundings by a closed system that cannot pass heat in or out because it is confined by an adiabatic wall, the work is said to be adiabatic for the system as well as for the surroundings. Given only the initial state and the final state of the system, one can only say what the total change in internal energy was, not how much of the energy went out as heat, and how much as work. Then for a given amount of work transferred, the exchange of volumes involves different pressures, inversely with the piston areas, for mechanical equilibrium. In chemistry, experiments are often conducted at constant atmospheric pressure, and the pressure–volume work represents a small, well-defined energy exchange with the atmosphere, so that is the appropriate expression for the heat of reaction. The work done by the system on its surroundings is calculated from the quantities that constitute the whole cycle.Lavenda, B.H. (2010). For systems at constant pressure, with no external work done other than the work, the change in enthalpy is the heat received by the system. Thermodynamic work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. Work done on a thermodynamic system, by devices or systems in the surroundings, is performed by actions such as compression, and includes shaft work, stirring, and rubbing. Such work done by compression is thermodynamic work as here defined. Thermodynamic work is defined for the purposes of thermodynamic calculations about bodies of material, known as thermodynamic systems. Real gases at common temperatures and pressures often closely approximate this behavior, which simplifies practical thermodynamic design and analysis. ==Definition== The enthalpy of a thermodynamic system is defined as the sum of its internal energy and the product of its pressure and volume: : , where is the internal energy, is pressure, and is the volume of the system; is sometimes referred to as the pressure energy . Thermodynamic work done by a thermodynamic system on its surroundings is defined so as to comply with this principle. The work is due to change of system volume by expansion or contraction of the system. To get an actual and precise physical measurement of a quantity of thermodynamic work, it is necessary to take account of the irreversibility by restoring the system to its initial condition by running a cycle, for example a Carnot cycle, that includes the target work as a step. As a result, the work done by the system also depends on the initial and final states. An Introduction to Thermal Physics, 2000, Addison Wesley Longman, San Francisco, CA, , p. 18 According to the first law of thermodynamics for a closed system, any net change in the internal energy U must be fully accounted for, in terms of heat Q entering the system and work W done by the system: :\Delta U = Q - W.\; Freedman, Roger A., and Young, Hugh D. (2008). 12th Edition. Pressure–volume work is a kind of contact work, because it occurs through direct material contact with the surrounding wall or matter at the boundary of the system. Consequently, thermodynamic work is defined in terms of quantities that describe the states of materials, which appear as the usual thermodynamic state variables, such as volume, pressure, temperature, chemical composition, and electric polarization. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of mass into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of mass out as if it were driving a piston of fluid.	-11.2	-100	6.2	3.54	+93.4	B
Use the van der Waals parameters for chlorine to calculate approximate values of the Boyle temperature of chlorine.	J/(mol K) Enthalpy of combustion –473.2 kJ/mol ΔcH ~~o~~ Heat capacity, cp 114.25 J/(mol K) Gas properties Std enthalpy change of formation, ΔfH ~~o~~ gas –103.18 kJ/mol Standard molar entropy, S ~~o~~ gas 295.6 J/(mol K) at 25 °C Heat capacity, cp 65.33 J/(mol K) at 25 °C van der Waals' constantsLange's Handbook of Chemistry 10th ed, pp. 1522–1524 a = 1537 L2 kPa/mol2 b = 0.1022 liter per mole ==Vapor pressure of liquid== P in mm Hg 1 10 40 100 400 760 1520 3800 7600 15200 30400 45600 T in °C –58.0 –29.7 –7.1 10.4 42.7 61.3 83.9 120.0 152.3 191.8 237.5 — Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. thumb\|812px\|left\|log10 of Chloroform vapor pressure. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. The molecular formula C3H4Cl2O2 (molar mass: 142.97 g/mol, exact mass: 141.9588 u) may refer to: * Chloroethyl chloroformate * Dalapon The Boyle temperature is formally defined as the temperature for which the second virial coefficient, B_{2}(T), becomes zero. Uses formula: \scriptstyle \log_e P_{mmHg} =\scriptstyle \log_e (\frac {760} {101.325}) - 10.07089 \log_e(T+273.15) - \frac {6351.140} {T+273.15} + 81.14393 + 9.127608 \times 10^{-6} (T+273.15)^2 obtained from CHERIC ==Distillation data== {\| border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;" Vapor-liquid Equilibrium for Chloroform/Ethanol P = 101.325 kPa BP Temp. °C % by mole chloroform liquid vapor 78.15 0.0 0.0 78.07 0.52 1.59 77.83 1.02 3.01 76.81 2.21 7.45 74.90 5.80 17.10 74.39 6.72 19.40 73.55 8.38 23.31 72.85 10.57 28.05 72.24 11.80 30.52 71.58 13.18 33.13 69.72 17.65 41.00 68.95 19.62 43.66 68.58 20.71 45.43 67.35 23.86 49.77 65.89 28.54 55.09 64.87 32.35 58.48 63.88 36.07 61.27 63.23 39.34 64.50 62.61 41.38 65.49 62.17 44.41 67.57 61.48 49.97 71.11 61.00 53.92 72.91 60.49 54.76 73.57 60.35 59.65 74.68 60.30 61.60 75.53 60.20 63.04 76.12 60.09 64.48 76.69 59.97 66.90 77.74 59.54 72.01 79.33 59.32 79.07 82.62 59.26 82.99 83.59 59.28 84.97 84.69 59.31 85.96 85.24 59.46 89.92 87.93 59.72 91.10 88.73 59.70 92.44 89.79 59.84 93.90 91.02 59.91 95.26 92.56 60.18 96.13 93.58 60.88 98.89 97.93 61.13 100.00 100.00 == Spectral data == UV-Vis λmax ? nm Extinction coefficient, ε ? Expanding the van der Waals equation in \frac{1}{V_m} one finds that T_b = \frac{a}{Rb}.Verma, K.S. Cengage Physical Chemistry Part 1. Also at Boyle temperature the dip in a PV diagram tends to a straight line over a period of pressure. 100px 100px Two representations of chloroform. This page provides supplementary chemical data on chloroform. == Material Safety Data Sheet == The handling of this chemical may incur notable safety precautions. Several billion kilograms of chlorinated methanes are produced annually, mainly by chlorination of methane: :CH4 \+ x Cl2 → CH4−xClx \+ x HCl The most important is dichloromethane, which is mainly used as a solvent. Organochlorine chemistry is concerned with the properties of organochlorine compounds, or organochlorides, organic compounds containing at least one covalently bonded atom of chlorine. To convert from L^2bar/mol^2 to m^6 Pa/mol^2, divide by 10. a (L2bar/mol2) b (L/mol) Acetic acid 17.7098 0.1065 Acetic anhydride 20.158 0.1263 Acetone 16.02 0.1124 Acetonitrile 17.81 0.1168 Acetylene 4.516 0.0522 Ammonia 4.225 0.0371 Aniline 29.14 0.1486 Argon 1.355 0.03201 Benzene 18.24 0.1193 Bromobenzene 28.94 0.1539 Butane 14.66 0.1226 1-Butanol 20.94 0.1326 2-Butanone 19.97 0.1326 Carbon dioxide 3.640 0.04267 Carbon disulfide 11.77 0.07685 Carbon monoxide 1.505 0.0398500 Carbon tetrachloride 19.7483 0.1281 Chlorine 6.579 0.05622 Chlorobenzene 25.77 0.1453 Chloroethane 11.05 0.08651 Chloromethane 7.570 0.06483 Cyanogen 7.769 0.06901 Cyclohexane 23.11 0.1424 Cyclopropane 8.34 0.0747 Decane 52.74 0.3043 1-Decanol 59.51 0.3086 Diethyl ether 17.61 0.1344 Diethyl sulfide 19.00 0.1214 Dimethyl ether 8.180 0.07246 Dimethyl sulfide 13.04 0.09213 Dodecane 69.38 0.3758 1-Dodecanol 75.70 0.3750 Ethane 5.562 0.0638 Ethanethiol 11.39 0.08098 Ethanol 12.18 0.08407 Ethyl acetate 20.72 0.1412 Ethylamine 10.74 0.08409 Ethylene 4.612 0.0582 Fluorine 1.171 0.0290 Fluorobenzene 20.19 0.1286 Fluoromethane 4.692 0.05264 Freon 10.78 0.0998 Furan 12.74 0.0926 Germanium tetrachloride 22.90 0.1485 Helium 0.0346 0.0238 Heptane 31.06 0.2049 1-Heptanol 38.17 0.2150 Hexane 24.71 0.1735 1-Hexanol 31.79 0.1856 Hydrazine 8.46 0.0462 Hydrogen 0.2476 0.02661 Hydrogen bromide 4.510 0.04431 Hydrogen chloride 3.716 0.04081 Hydrogen cyanide 11.29 0.0881 Hydrogen fluoride 9.565 0.0739 Hydrogen iodide 6.309 0.0530 Hydrogen selenide 5.338 0.04637 Hydrogen sulfide 4.490 0.04287 Isobutane 13.32 0.1164 Iodobenzene 33.52 0.1656 Krypton 2.349 0.03978 Mercury 8.200 0.01696 Methane 2.283 0.04278 Methanol 9.649 0.06702 Methylamine 7.106 0.0588 Neon 0.2135 0.01709 Neopentane 17.17 0.1411 Nitric oxide 1.358 0.02789 Nitrogen 1.370 0.0387 Nitrogen dioxide 5.354 0.04424 Nitrogen trifluoride 3.58 0.0545 Nitrous oxide 3.832 0.04415 Octane 37.88 0.2374 1-Octanol 44.71 0.2442 Oxygen 1.382 0.03186 Ozone 3.570 0.0487 Pentane 19.26 0.146 1-Pentanol 25.88 0.1568 Phenol 22.93 0.1177 Phosphine 4.692 0.05156 Propane 8.779 0.08445 1-Propanol 16.26 0.1079 2-Propanol 15.82 0.1109 Propene 8.442 0.0824 Pyridine 19.77 0.1137 Pyrrole 18.82 0.1049 Radon 6.601 0.06239 Silane 4.377 0.05786 Silicon tetrafluoride 4.251 0.05571 Sulfur dioxide 6.803 0.05636 Sulfur hexafluoride 7.857 0.0879 Tetrachloromethane 20.01 0.1281 Tetrachlorosilane 20.96 0.1470 Tetrafluoroethylene 6.954 0.0809 Tetrafluoromethane 4.040 0.0633 Tetrafluorosilane 5.259 0.0724 Tetrahydrofuran 16.39 0.1082 Tin tetrachloride 27.27 0.1642 Thiophene 17.21 0.1058 Toluene 24.38 0.1463 1-1-1-Trichloroethane 20.15 0.1317 Trichloromethane 15.34 0.1019 Trifluoromethane 5.378 0.0640 Trimethylamine 13.37 0.1101 Water 5.536 0.03049 Xenon 4.250 0.05105 ==Units== 1 J·m3/mol2 = 1 m6·Pa/mol2 = 10 L2·bar/mol2 1 L2atm/mol2 = 0.101325 J·m3/mol2 = 0.101325 Pa·m6/mol2 1 dm3/mol = 1 L/mol = 1 m3/kmol (where kmol is kilomoles = 1000 moles) ==References== Category:Gas laws Constants (Data Page) J/(mol·K) Solid properties Std enthalpy change of formation ΔfH ~~o~~ solid −705.63 kJ/mol Standard molar entropy S ~~o~~ solid 109.29 J/(mol K) Heat capacity cp 91.12 J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid -674.80 kJ/mol Standard molar entropy S ~~o~~ liquid 172.91 J/(mol K) Heat capacity cp 125.5 J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas -584.59 kJ/mol Standard molar entropy S ~~o~~ gas 314.44 J/(mol K) Heat capacity cp 82.46 J/(mol K) == Spectral data == UV-Vis Spectrum Lambda-max nm Log Ε IR Spectrum NIST Major absorption bands cm−1 NMR Proton NMR ? K (? °C), ? The annual production in 1985 was around 13 million tons, almost all of which was converted into polyvinylchloride (PVC). ===Chloromethanes=== Most low molecular weight chlorinated hydrocarbons such as chloroform, dichloromethane, dichloroethene, and trichloroethane are useful solvents. Chlorine adds to the multiple bonds on alkenes and alkynes as well, giving di- or tetra-chloro compounds. ===Reaction with hydrogen chloride=== Alkenes react with hydrogen chloride (HCl) to give alkyl chlorides. Since higher order virial coefficients are generally much smaller than the second coefficient, the gas tends to behave as an ideal gas over a wider range of pressures when the temperature reaches the Boyle temperature (or when c = \frac{1}{V_m} or P are minimized). Supplementary data for aluminium chloride. == External MSDS == * Baker * Fisher * EM Science * Akzo Nobel (hexahydrate) * Science Stuff (hexahydrate) * External SDS == Thermodynamic properties == Phase behavior Triple point ? The Wurtz reaction reductively couples two alkyl halides to couple with sodium. ==Applications== ===Vinyl chloride=== The largest application of organochlorine chemistry is the production of vinyl chloride. Fourme, M. Renaud, C. R. Acad. Sci, Ser. C(Chim),1966, p. 69 C-Cl 1.75 Å Bond angle Cl-C-Cl 110.3° Dipole moment 1.08 D (gas) 1.04 DCRC Handbook of Chemistry and Physics. 89th ed./David R. Lide ed.-in- chief. Alternatively, the Appel reaction can be used: :250px ==Reactions== Alkyl chlorides are versatile building blocks in organic chemistry. – Close to that of Teflon Surface tension 28.5 dyn/cm at 10 °C 27.1 dyn/cm at 20 °C 26.67 dyn/cm at 25 °C 23.44 dyn/cm at 50 °C 21.7 dyn/cm at 60 °C 20.20 dyn/cm at 75 °C ViscosityLange's Handbook of Chemistry, 10th ed. pp. 1669–1674 0.786 mPa·s at –10 °C 0.699 mPa·s at 0 °C 0.563 mPa·s at 20 °C 0.542 mPa·s at 25 °C 0.464 mPa·s at 40 °C 0.389 mPa·s at 60 °C == Thermodynamic properties == Phase behavior Triple point 209.61 K (–63.54 °C), ?	1410	3.8	313.0	7.82	144	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \mathrm{~mol} \mathrm{CO}_2(\mathrm{~g})$, initially at $25^{\circ} \mathrm{C}$ and $10 \mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \mathrm{~m}}=28.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and calculate $\Delta T$.	Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975 allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known. == Equations == : \ln P_{\rm r} = f^{(0)} + \omega \cdot f^{(1)} : f^{(0)}=5.92714 - \frac{6.09648}{T_{\rm r}} - 1.28862 \cdot \ln T_{\rm r} + 0.169347 \cdot T_{\rm r}^6 : f^{(1)}=15.2518 - \frac{15.6875}{T_{\rm r}}-13.4721 \cdot \ln T_{\rm r} + 0.43577 \cdot T_{\rm r}^6 with :P_{\rm r}=\frac{P}{P_{\rm c}} (reduced pressure) and T_{\rm r}=\frac{T}{T_{\rm c}} (reduced temperature). == Typical errors == The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. In the second case, the gas will both heat and expand, causing the piston to do mechanical work on the atmosphere. Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT: : P^{1-\gamma} T^\gamma is constant : TV^{\gamma-1} is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. We assume the expansion occurs without exchange of heat (adiabatic expansion). To return to the target temperature (still with a free piston), the air must be heated, but is no longer under constant volume, since the piston is free to move as the gas is reheated. Consider the difference between adding heat to the gas with a locked piston and adding heat with a piston free to move, so that pressure remains constant. If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). The piston is now freed and moves outwards, stopping as the pressure inside the chamber reaches atmospheric pressure. Since the piston cannot move, the volume is constant. Auflage, McGraw-Hill, 1988 == Example calculation == For benzene with * Tc = 562.12 KBrunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006 * Pc = 4898 kPa * Tb = 353.15 KSilva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006 * ω = 0.2120Dortmund Data Bank the following calculation for T=Tb results: * Tr = 353.15 / 562.12 = 0.628247 * f(0) = -3.167428 * f(1) = -3.429560 * Pr = exp( f(0) \+ ω f(1) ) = 0.020354 * P = Pr * Pc = 99.69 kPa The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. However, CNG requires a much larger volume to store the energy equivalent of petrol and the use of very high pressures (3000 to 4000 psi, or 205 to 275 bar). Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures. The heat that is added to the gas goes only partly into heating the gas, while the rest is transformed into the mechanical work performed by the piston. For light-duty CNG cars to become a viable short-term climate strategy, methane leakage would need to be kept below 1.6% of total natural gas produced (approximately half the current amount for well to wheels – note difference from well to city)." Compressed natural gas (CNG) is a fuel gas mainly composed of methane (CH4), compressed to less than 1% of the volume it occupies at standard atmospheric pressure. * Being a gaseous fuel, CNG mixes easily and evenly in air. In a fire, the pressure in a gas cylinder rises in direct proportion to its temperature. Natural gas is being experimentally stored at lower pressure in a form known as an ANG (adsorbed natural gas) cylinder, where it is adsorbed at 35 bar (500 psi, the pressure of gas in natural gas pipelines) in various sponge-like materials, such as carbon and MOFs (metal-organic frameworks). ** The lifecycle greenhouse gas emissions for CNG compressed from California's pipeline natural gas is given a value of 67.70 grams of -equivalent per megajoule (gCO2e/MJ) by CARB (the California Air Resources Board), approximately 28 percent lower than the average petrol fuel in that market (95.86 gCO2e/MJ). The pressure inside is equal to atmospheric pressure.	-0.347	257	3.42	0.925	4096	A
Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. 3.17 Estimate the standard reaction Gibbs energy of $\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow$ $2 \mathrm{NH}_3(\mathrm{~g})$ at $1000 \mathrm{~K}$ from their values at $298 \mathrm{~K}$.	Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. The standard Gibbs free energy of formation (Gf°) of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 1 bar of pressure and the specified temperature, usually 298.15 K or 25 °C). The NIST Chemistry WebBook (see link below) is an online resource that contains standard enthalpy of formation for various compounds along with the standard absolute entropy for these compounds from which the standard Gibbs free energy of formation can be calculated. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . The table below lists the standard Gibbs function of formation for several elements and chemical compounds and is taken from Lange's Handbook of Chemistry. The USSA1976 acknowledges that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant. Value of R Unit SI units J⋅K−1⋅mol−1 m3⋅Pa⋅K−1⋅mol−1 kg⋅m2⋅s−2⋅K−1⋅mol−1 Other common units L⋅Pa⋅K−1⋅mol−1 L⋅kPa⋅K−1⋅mol−1 L⋅bar⋅K−1⋅mol−1 erg⋅K−1⋅mol−1 atm⋅ft3⋅lbmol−1⋅°R−1 psi⋅ft3⋅lbmol−1⋅°R−1 BTU⋅lbmol−1⋅°R−1 inH2O⋅ft3⋅lbmol−1⋅°R−1 torr⋅ft3⋅lbmol−1⋅°R−1 L⋅atm⋅K−1⋅mol−1 L⋅Torr⋅K−1⋅mol−1 cal⋅K−1⋅mol−1 m3⋅atm⋅K−1⋅mol−1 The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Note that all values are in kJ/mol. Far more extensive tables can be found in the CRC Handbook of Chemistry and Physics and the NIST JANAF tables.M. W. Chase, NIST – JANAF Thermochemical Tables, 4th Edition, Journal of Physical and Chemical Reference Data, Monograph 9, 1998. * The heat capacity of the gas from the boiling point to room temperature. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. ==References== ==External links== * Ideal gas calculator – Ideal gas calculator provides the correct information for the moles of gas involved. :ΔG˚ = -RTln(Keq) :ΔG˚ = (2.303)RT(pKeq) :ΔG˚ = -nFE˚1/2 Useful conversion factors: :-23.06 (kcal/mol)(e−)−1(V)−1 :1.37(pKeq) kcal/mol :1.37[-log(Keq)] kcal/mol == References == Category:Thermodynamic cycles In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. Mayer's relation relates the specific gas constant to the specific heat capacities for a calorically perfect gas and a thermally perfect gas. The temperature at standard pressure should be equal to the normal boiling point, but due to the considerable spread does not necessarily have to match values reported elsewhere. log refers to log base 10 (T/K) refers to temperature in Kelvin (K) (P/Pa) refers to pressure in Pascal (Pa) == References == ===CRC.a-m=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB): R = N_{\rm A} k. The value of R is then obtained from the relation :c_\mathrm{a}(0, T) = \sqrt{\frac{\gamma_0 R T}{A_\mathrm{r}(\mathrm{Ar}) M_\mathrm{u}}}, where: γ0 is the heat capacity ratio ( for monatomic gases such as argon); T is the temperature, TTPW = 273.16 K by the definition of the kelvin at that time; *Ar(Ar) is the relative atomic mass of argon and Mu = as defined at the time.	817.90	4.979	'-191.2'	+107	27	D
Could $131 \mathrm{g}$ of xenon gas in a vessel of volume $1.0 \mathrm{dm}^3$ exert a pressure of $20 \mathrm{atm}$ at $25^{\circ} \mathrm{C}$ if it behaved as a perfect gas? If not, what pressure would it exert?	If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it. Pressure vessels for gas storage may also be classified by volume. The ship was to carry compressed natural gas in vertical pressure bottles; however, this design failed because of the high cost of the pressure vessels. Boyle's law has been stated as: > The absolute pressure exerted by a given mass of an ideal gas is inversely > proportional to the volume it occupies if the temperature and amount of gas > remain unchanged within a closed system.Levine, Ira. Most gases behave like ideal gases at moderate pressures and temperatures. A gas cylinder is a pressure vessel for storage and containment of gases at above atmospheric pressure. As improvements in technology permitted higher pressures and lower temperatures, deviations from the ideal gas behavior became noticeable, and the relationship between pressure and volume can only be accurately described employing real gas theory.Levine, Ira. N. (1978), p. 11 notes that deviations occur with high pressures and temperatures. For gases that are liquid under storage, e.g., propane, the outlet pressure is dependent on the vapor pressure of the gas, and does not fall until the cylinder is nearly exhausted, although it will vary according to the temperature of the cylinder contents. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. Natural gas is being experimentally stored at lower pressure in a form known as an ANG (adsorbed natural gas) cylinder, where it is adsorbed at 35 bar (500 psi, the pressure of gas in natural gas pipelines) in various sponge-like materials, such as carbon and MOFs (metal-organic frameworks). However, CNG requires a much larger volume to store the energy equivalent of petrol and the use of very high pressures (3000 to 4000 psi, or 205 to 275 bar). In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. thumb\|upright=1.3\|An animation showing the relationship between pressure and volume when mass and temperature are held constant Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes the relationship between pressure and volume of a confined gas. Compressed natural gas (CNG) is a fuel gas mainly composed of methane (CH4), compressed to less than 1% of the volume it occupies at standard atmospheric pressure. That is, doubling the density of a quantity of air doubles its pressure. What the pressure should be according to the Hypothesis, that supposes the pressures and expansions to be in reciprocal relation." High-pressure gas cylinders are also called bottles. Boyle's Law states that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant. Conversely, reducing the volume of the gas increases the pressure. In a fire, the pressure in a gas cylinder rises in direct proportion to its temperature. VPT may refer to: * Valor por Tamaulipas * Vermont Public Television * Volume, temperature and pressure, the three parameters in the combined gas law	0.4207	48.6	24.0	5.1	5.0	C
Could $131 \mathrm{g}$ of xenon gas in a vessel of volume $1.0 \mathrm{dm}^3$ exert a pressure of $20 \mathrm{atm}$ at $25^{\circ} \mathrm{C}$ if it behaved as a perfect gas? If not, what pressure would it exert?	If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it. Pressure vessels for gas storage may also be classified by volume. * ISO 11439: Compressed natural gas (CNG) cylinders. A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. Because of that, the design and certification of pressure vessels is governed by design codes such as the ASME Boiler and Pressure Vessel Code in North America, the Pressure Equipment Directive of the EU (PED), Japanese Industrial Standard (JIS), CSA B51 in Canada, Australian Standards in Australia and other international standards like Lloyd's, Germanischer Lloyd, Det Norske Veritas, Société Générale de Surveillance (SGS S.A.), Lloyd’s Register Energy Nederland (formerly known as Stoomwezen) etc. Note that where the pressure-volume product is part of a safety standard, any incompressible liquid in the vessel can be excluded as it does not contribute to the potential energy stored in the vessel, so only the volume of the compressible part such as gas is used. ===List of standards=== * EN 13445: The current European Standard, harmonized with the Pressure Equipment Directive (Originally "97/23/EC", since 2014 "2014/68/EU"). Further the volume of the gas is (4πr3)/3. Boyle's law has been stated as: > The absolute pressure exerted by a given mass of an ideal gas is inversely > proportional to the volume it occupies if the temperature and amount of gas > remain unchanged within a closed system.Levine, Ira. A gas cylinder is a pressure vessel for storage and containment of gases at above atmospheric pressure. As improvements in technology permitted higher pressures and lower temperatures, deviations from the ideal gas behavior became noticeable, and the relationship between pressure and volume can only be accurately described employing real gas theory.Levine, Ira. N. (1978), p. 11 notes that deviations occur with high pressures and temperatures. Most gases behave like ideal gases at moderate pressures and temperatures. For gases that are liquid under storage, e.g., propane, the outlet pressure is dependent on the vapor pressure of the gas, and does not fall until the cylinder is nearly exhausted, although it will vary according to the temperature of the cylinder contents. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. The very small vessels used to make liquid butane fueled cigarette lighters are subjected to about 2 bar pressure, depending on ambient temperature. * EN 286 (Parts 1 to 4): European standard for simple pressure vessels (air tanks), harmonized with Council Directive 87/404/EEC. In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. thumb\|upright=1.3\|An animation showing the relationship between pressure and volume when mass and temperature are held constant Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes the relationship between pressure and volume of a confined gas. Other examples of pressure vessels are diving cylinders, recompression chambers, distillation towers, pressure reactors, autoclaves, and many other vessels in mining operations, oil refineries and petrochemical plants, nuclear reactor vessels, submarine and space ship habitats, atmospheric diving suits, pneumatic reservoirs, hydraulic reservoirs under pressure, rail vehicle airbrake reservoirs, road vehicle airbrake reservoirs, and storage vessels for high pressure permanent gases and liquified gases such as ammonia, chlorine, and LPG (propane, butane). That is, doubling the density of a quantity of air doubles its pressure. What the pressure should be according to the Hypothesis, that supposes the pressures and expansions to be in reciprocal relation." Boyle's Law states that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant. High-pressure gas cylinders are also called bottles.	4.85	24	4.56	226	4.738	B
The barometric formula relates the pressure of a gas of molar mass $M$ at an altitude $h$ to its pressure $p_0$ at sea level. Derive this relation by showing that the change in pressure $\mathrm{d} p$ for an infinitesimal change in altitude $\mathrm{d} h$ where the density is $\rho$ is $\mathrm{d} p=-\rho g \mathrm{~d} h$. Remember that $\rho$ depends on the pressure. Evaluate the external atmospheric pressure at a typical cruising altitude of an aircraft (11 km) when the pressure at ground level is 1.0 atm.	The other two values (pressure P and density ρ) are computed by simultaneously solving the equations resulting from: * the vertical pressure gradient resulting from hydrostatic balance, which relates the rate of change of pressure with geopotential altitude: :: \frac{dP}{dh} = - \rho g , and * the ideal gas law in molar form, which relates pressure , density, and temperature: :: \ P = \rho R_{\rm specific}T at each geopotential altitude, where g is the standard acceleration of gravity, and Rspecific is the specific gas constant for dry air (287.0528J⋅kg−1⋅K−1). The barometric formula is a formula used to model how the pressure (or density) of the air changes with altitude. == Pressure equations == thumb\|300px\|Pressure as a function of the height above the sea level There are two equations for computing pressure as a function of height. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C. where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/ft) in ISA h = height at which pressure is calculated (ft) h_b = height of reference level b (feet; e.g., hb = 36,089 ft) R^* = universal gas constant; using feet, kelvins, and (SI) moles: g_0 = gravitational acceleration: 32.17405 ft/s2 M = molar mass of Earth's air: 28.9644 lb/lb-mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. Equation 1: \rho = \rho_b \left[\frac{T_b - (h-h_b) L_b}{T_b}\right]^{\left(\frac{g_0 M}{R^* L_b}-1\right)} which is equivalent to the ratio of the relative pressure and temperature changes \rho = \rho_b \frac{P}{T} \frac{T_b}{P_b} Equation 2: \rho =\rho_b \exp\left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right] where {\rho} = mass density (kg/m3) T_b = standard temperature (K) L = standard temperature lapse rate (see table below) (K/m) in ISA h = height above sea level (geopotential meters) R^ = universal gas constant 8.3144598 N·m/(mol·K) g_0 = gravitational acceleration: 9.80665 m/s2 M = molar mass of Earth's air: 0.0289644 kg/mol or, converted to U.S. gravitational foot-pound-second units (no longer used in U.K.): {\rho} = mass density (slug/ft3) {T_b} = standard temperature (K) {L} = standard temperature lapse rate (K/ft) {h} = height above sea level (geopotential feet) {R^} = universal gas constant: 8.9494596×104 ft2/(s·K) {g_0} = gravitational acceleration: 32.17405 ft/s2 {M} = molar mass of Earth's air: 0.0289644 kg/mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. Pressure altitude is primarily used in aircraft-performance calculations and in high-altitude flight (i.e., above the transition altitude). == Inverse equation == Solving the equation for the pressure gives : p = 1013.25\left(1-\frac{h}{44307.694 m}\right)^{5.25530} hPa where are meter and hPa hecto-Pascal. Subscript b Height Above Sea Level (h) Mass Density (\rho) Standard Temperature (T') (K) Temperature Lapse Rate (L) (m) (ft) (kg/m3) (slug/ft3) (K/m) (K/ft) 0 0 0 1.2250 288.15 0.0065 0.0019812 1 11 000 36,089.24 0.36391 216.65 0.0 0.0 2 20 000 65,616.79 0.08803 216.65 -0.001 -0.0003048 3 32 000 104,986.87 0.01322 228.65 -0.0028 -0.00085344 4 47 000 154,199.48 0.00143 270.65 0.0 0.0 5 51 000 167,322.83 0.00086 270.65 0.0028 0.00085344 6 71 000 232,939.63 0.000064 214.65 0.002 0.0006096 ==Derivation== The barometric formula can be derived using the ideal gas law: P = \frac{\rho}{M} {R^} T Assuming that all pressure is hydrostatic: dP = - \rho g\,dz and dividing the dP by the P expression we get: \frac{dP}{P} = - \frac{M g\,dz}{R^T} Integrating this expression from the surface to the altitude z we get: P = P_0 e^{-\int_{0}^{z}{M g dz/R^T}} Assuming linear temperature change T = T_0 - L z and constant molar mass and gravitational acceleration, we get the first barometric formula: P = P_0 \cdot \left[\frac{T}{T_0}\right]^{\textstyle \frac{M g}{R^ L}} Instead, assuming constant temperature, integrating gives the second barometric formula: P = P_0 e^{-M g z/R^T} In this formulation, R is the gas constant, and the term RT/Mg gives the scale height (approximately equal to 8.4 km for the troposphere). The National Oceanic and Atmospheric Administration (NOAA) published the following formula for directly converting atmospheric pressure in millibars ( \mathrm{mb} ) to pressure altitude in feet ( \mathrm{ft} ): : h = 145366.45 \left[ 1 - \left( \frac{\text{Station pressure in millibars}}{1013.25} \right)^{0.190284} \right]. Atmospheric pressure decreases following the Barometric formula with altitude while the O2 fraction remains constant to about , so pO2 decreases with altitude as well. The first equation is applicable to the standard model of the troposphere in which the temperature is assumed to vary with altitude at a lapse rate of L_b: P = P_b \left[\frac{T_b - \left(h - h_b\right) L_b}{T_b}\right]^{\tfrac{g_0 M}{R^ L_b}} The second equation is applicable to the standard model of the stratosphere in which the temperature is assumed not to vary with altitude: P = P_b \exp \left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right] where: P_b = reference pressure T_b = reference temperature (K) L_b = temperature lapse rate (K/m) in ISA h = height at which pressure is calculated (m) h_b = height of reference level b (meters; e.g., hb = 11 000 m) R^* = universal gas constant: 8.3144598 J/(mol·K) g_0 = gravitational acceleration: 9.80665 m/s2 M = molar mass of Earth's air: 0.0289644 kg/mol Or converted to imperial units:Mechtly, E. A., 1973: The International System of Units, Physical Constants and Conversion Factors. The relationship between static pressure and pressure altitude is defined in terms of properties of the ISA. ==See also== * QNH * Flight level * Cabin altitude * Density altitude * Standard conditions for temperature and pressure * Barometric formula ==References== Category:Altitudes in aviation (The total air mass below a certain altitude is calculated by integrating over the density function.) Using the values T=273 K and M=29 g/mol as characteristic of the Earth's atmosphere, H = RT/Mg = (8.315273)/(299.8) = 7.99, or about 8 km, which coincidentally is approximate height of Mt. Everest. Pressure altitude is the altitude in the International Standard Atmosphere (ISA) with the same atmospheric pressure as that of the part of the atmosphere in question. Subscript b Height above sea level Static pressure Standard temperature (K) Temperature lapse rate Exponent g0 M / R L (m) (ft) (Pa) (inHg) (K/m) (K/ft) 0 0 0 101 325.00 29.92126 288.15 0.0065 0.0019812 5.2558 1 11 000 36,089 22 632.10 6.683245 216.65 0.0 0.0 -- 2 20 000 65,617 5474.89 1.616734 216.65 -0.001 -0.0003048 -34.1626 3 32 000 104,987 868.02 0.2563258 228.65 -0.0028 -0.00085344 -12.2009 4 47 000 154,199 110.91 0.0327506 270.65 0.0 0.0 -- 5 51 000 167,323 66.94 0.01976704 270.65 0.0028 0.00085344 12.2009 6 71 000 232,940 3.96 0.00116833 214.65 0.002 0.0006096 17.0813 ==Density equations== The expressions for calculating density are nearly identical to calculating pressure. The concentration of oxygen (O2) in sea-level air is 20.9%, so the partial pressure of O2 (pO2) is . A reference atmospheric model describes how the ideal gas properties (namely: pressure, temperature, density, and molecular weight) of an atmosphere change, primarily as a function of altitude, and sometimes also as a function of latitude, day of year, etc. For example, the U.S. Standard Atmosphere derives the values for air temperature, pressure, and mass density, as a function of altitude above sea level. For the isothermal-barotropic model, density and pressure turn out to be exponential functions of altitude. The increase in altitude necessary for P or ρ to drop to 1/e of its initial value is called the scale height: :H = \frac{R T}{M g_0} where R is the ideal gas constant, T is temperature, M is average molecular weight, and g0 is the gravitational acceleration at the planet's surface. Image:Liquid ocean atmosphere model.png ===Isothermal-barotropic approximation and scale height=== This atmospheric model assumes both molecular weight and temperature are constant over a wide range of altitude. For example, if the airfield elevation is 500 ~ \mathrm{ft} and the altimeter setting is 29.32 ~ \mathrm{inHg} , then : \begin{align} \text{PA} & = 500 + 1000 \times (29.92 - 29.32) \\\ & = 500 + 1000 \times 0.6 \\\ & = 500 + 600 \\\ & = 1100. \end{align} Alternatively, : \text{Pressure altitude (PA)} = \text{Elevation} + 30 \times (1013 - \text{QNH}). Other static atmospheric models may have other outputs, or depend on inputs besides altitude. ==Basic assumptions== The gas which comprises an atmosphere is usually assumed to be an ideal gas, which is to say: : \rho = \frac{M P}{R T} Where ρ is mass density, M is average molecular weight, P is pressure, T is temperature, and R is the ideal gas constant.	344	0	399.0	0.72	0.66666666666	D
A constant-volume perfect gas thermometer indicates a pressure of $6.69 \mathrm{kPa}$ at the triple point temperature of water (273.16 K). What pressure indicates a temperature of $100.00^{\circ} \mathrm{C}$?	By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use. The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water." The pressure melting point is nearly a constant 0 °C at pressures above the triple point at 611.7 Pa, where water can exist in only the solid or liquid phases, through atmospheric pressure (100 kPa) until about 10 MPa. In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly 273.15 + 0.01 = 273.16 degrees Kelvin. The kelvin, symbol K, is a unit of measurement for temperature. The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. In water, the critical point occurs at around Tc = , pc = and ρc = 356 kg/m3.The International Association for the Properties of Water and Steam "Guideline on the Use of Fundamental Physical Constants and Basic Constants of Water", 2001, p. 5 The existence of the liquid–gas critical point reveals a slight ambiguity in labelling the single phase regions. In the early decades of the 20th century, the Kelvin scale was often called the "absolute Celsius" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.For example, Encyclopaedia Britannica editions from the 1920s and 1950s, one example being the article "Planets". === Triple point standard === In 1873, William Thomson's older brother James coined the term triple point to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings. :: \gamma =\frac{ \left( c_p \right)_{air} * P }{ \lambda_v * MW_{ratio} } : \gamma = psychrometric constant [kPa °C−1], : P = atmospheric pressure [kPa], : \lambda_v = latent heat of water vaporization, 2.45 [MJ kg−1], : c_p = specific heat of air at constant pressure, [MJ kg−1 °C−1], : MW_{ratio} = ratio molecular weight of water vapor/dry air = 0.622. The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by * (1848 scale) = 100 () / () On this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature. * The boiling point of water is 100 degrees. * The boiling point of water is 100 degrees. At constant pressure the maximum number of independent variables is three – the temperature and two concentration values. The psychrometric constant \gamma relates the partial pressure of water in air to the air temperature. For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature. The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. Historically, the Kelvin scale was developed from the Celsius scale, such that 273.15 K was 0 °C (the approximate melting point of ice) and a change of one kelvin was exactly equal to a change of one degree Celsius. The boiling point of water is the temperature at which the saturated vapour pressure equals the ambient pressure. English translation (extract). that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0° and 100° C.	1410	1.2	9.14	420	1.4	C
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. An average human produces about $10 \mathrm{MJ}$ of heat each day through metabolic activity. Human bodies are actually open systems, and the main mechanism of heat loss is through the evaporation of water. What mass of water should be evaporated each day to maintain constant temperature?	The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). This will depend on the latent heat release as: T_e \approx T + \frac{L_v}{c_{pd}} r where: * L_v : latent heat of evaporation (2400 kJ/kg at 25°C to 2600 kJ/kg at −40°C) * c_{pd} : specific heat at constant pressure for air (≈ 1004 J/(kg·K)) Tables exist for exact values of the last two coefficients. == See also == * Wet-bulb temperature * Potential temperature * Atmospheric thermodynamics * Equivalent potential temperature ==Bibliography== * M Robitzsch, Aequivalenttemperatur und Aequivalentthemometer, Meteorologische Zeitschrift, 1928, pp. 313-315. The equation for evaporation given by Penman is: :E_{\mathrm{mass}}=\frac{m R_n + \rho_a c_p \left(\delta e \right) g_a }{\lambda_v \left(m + \gamma \right) } where: :m = Slope of the saturation vapor pressure curve (Pa K−1) :Rn = Net irradiance (W m−2) :ρa = density of air (kg m−3) :cp = heat capacity of air (J kg−1 K−1) :δe = vapor pressure deficit (Pa) :ga = momentum surface aerodynamic conductance (m s−1) :λv = latent heat of vaporization (J kg−1) :γ = psychrometric constant (Pa K−1) which (if the SI units in parentheses are used) will give the evaporation Emass in units of kg/(m2·s), kilograms of water evaporated every second for each square meter of area. Penman's equation requires daily mean temperature, wind speed, air pressure, and solar radiation to predict E. Simpler Hydrometeorological equations continue to be used where obtaining such data is impractical, to give comparable results within specific contexts, e.g. humid vs arid climates. ==Details== Numerous variations of the Penman equation are used to estimate evaporation from water, and land. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . In atmospheric science, equivalent temperature is the temperature of air in a parcel from which all the water vapor has been extracted by an adiabatic process. Another formula used is: citing :M=VO_2\left(\frac{RQ-0.7}{0.3}e_c+\frac{1-RQ}{0.3}e_f\right) where RQ is the respiratory quotient (ratio of volume CO2 produced to volume of O2 consumed), e_c is , the heat released per litre of oxygen by the oxidation of carbohydrate, and e_f is , the value for fat. The normal human body temperature is often stated as . However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other exactly defined physical constants. ==Specific gas constant== Rspecific for dry air Unit 287.052874 J⋅kg−1⋅K−1 53.3523 ft⋅lbf⋅lb−1⋅°R−1 1,716.46 ft⋅lbf⋅slug−1⋅°R−1 The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. Human body temperature varies. Normal human body temperature varies slightly from person to person and by the time of day. Temperature, wind speed, relative humidity impact the values of m, g, cp, ρ, and δe. ==Shuttleworth (1993)== In 1993, W.Jim Shuttleworth modified and adapted the Penman equation to use SI, which made calculating evaporation simpler.Shuttleworth, J., Putting the vap' into evaporation http://www.hydrol-earth-syst-sci.net/11/210/2007/hess-11-210-2007.pdf The resultant equation is: :E_{\mathrm{mass}}=\frac{m R_n + \gamma * 6.43\left(1+0.536 * U_2 \right)\delta e}{\lambda_v \left(m + \gamma \right) } where: :Emass = Evaporation rate (mm day−1) :m = Slope of the saturation vapor pressure curve (kPa K−1) :Rn = Net irradiance (MJ m−2 day−1) :γ = psychrometric constant = \frac{0.0016286 * P_{kPa}} {\lambda_v} (kPa K−1) :U2 = wind speed (m s−1) :δe = vapor pressure deficit (kPa) :λv = latent heat of vaporization (MJ kg−1) Note: this formula implicitly includes the division of the numerator by the density of water (1000 kg m−3) to obtain evaporation in units of mm d−1 ==Some useful relationships== :δe = (es \- ea) = (1 – relative humidity) es :es = saturated vapor pressure of air, as is found inside plant stoma. :ea = vapor pressure of free flowing air. :es, mmHg = exp(21.07-5336/Ta), approximation by Merva, 1975Merva, G.E. 1975. * J.V. Iribarne and W.L. Godson, Atmospheric Thermodynamics, published by D. Reidel Publishing Company, Dordrecht, Holland, 1973, 222 pages Category:Atmospheric thermodynamics Category:Atmospheric temperature In humans, the average internal temperature is widely accepted to be 37 °C (98.6 °F), a "normal" temperature established in the 1800s. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. Unfortunately the situation can become considerably more complex if the temperature is sufficiently high for molecules to dissociate or carry out other chemical reactions, in which case thermodynamic expressions arising from simple equations of state may not be adequate. === Thermodynamic expressions === Values based on approximations (particularly ) are in many cases not sufficiently accurate for practical engineering calculations, such as flow rates through pipes and valves at moderate to high pressures. Therefore, the heat capacity ratio in this example is 1.4. This equation assumes a daily time step so that net heat exchange with the ground is insignificant, and a unit area surrounded by similar open water or vegetation so that net heat & vapor exchange with the surrounding area cancels out. While some people think of these averages as representing normal or ideal measurements, a wide range of temperatures has been found in healthy people. An individual's body temperature typically changes by about between its highest and lowest points each day.	537	7	4.09	0.241	2.24	C
A constant-volume perfect gas thermometer indicates a pressure of $6.69 \mathrm{kPa}$ at the triple point temperature of water (273.16 K). What change of pressure indicates a change of $1.00 \mathrm{~K}$ at this temperature?	Historically, the Kelvin scale was developed from the Celsius scale, such that 273.15 K was 0 °C (the approximate melting point of ice) and a change of one kelvin was exactly equal to a change of one degree Celsius. The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by * (1848 scale) = 100 () / () On this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature. thumb\|400px\|Diagram showing pressure difference induced by a temperature difference. The kelvin, symbol K, is a unit of measurement for temperature. By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use. For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature. In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C. Vapour pressure of water (0–100 °C) T, °C T, °F P, kPa P, torr P, atm 0 32 0.6113 4.5851 0.0060 5 41 0.8726 6.5450 0.0086 10 50 1.2281 9.2115 0.0121 15 59 1.7056 12.7931 0.0168 20 68 2.3388 17.5424 0.0231 25 77 3.1690 23.7695 0.0313 30 86 4.2455 31.8439 0.0419 35 95 5.6267 42.2037 0.0555 40 104 7.3814 55.3651 0.0728 45 113 9.5898 71.9294 0.0946 50 122 12.3440 92.5876 0.1218 55 131 15.7520 118.1497 0.1555 60 140 19.9320 149.5023 0.1967 65 149 25.0220 187.6804 0.2469 70 158 31.1760 233.8392 0.3077 75 167 38.5630 289.2463 0.3806 80 176 47.3730 355.3267 0.4675 85 185 57.8150 433.6482 0.5706 90 194 70.1170 525.9208 0.6920 95 203 84.5290 634.0196 0.8342 100 212 101.3200 759.9625 1.0000 The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. Some of these are (in approximate order of increasing accuracy): Name Formula Description "Eq. 1" (August equation) P = \exp\left(20.386 - \frac{5132}{T}\right) is the vapour pressure in mmHg and is the temperature in kelvins. The (unattributed) constants are given as {\| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005): : (°C) (Lide Table) (Eq 1) (Antoine) (Magnus) (Tetens) (Buck) (Goff-Gratch) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%) A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). This value of "−273" was the negative reciprocal of 0.00366—the accepted coefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value. In the early decades of the 20th century, the Kelvin scale was often called the "absolute Celsius" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.For example, Encyclopaedia Britannica editions from the 1920s and 1950s, one example being the article "Planets". === Triple point standard === In 1873, William Thomson's older brother James coined the term triple point to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium. In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly 273.15 + 0.01 = 273.16 degrees Kelvin. The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water." This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings. :: \gamma =\frac{ \left( c_p \right)_{air} * P }{ \lambda_v * MW_{ratio} } : \gamma = psychrometric constant [kPa °C−1], : P = atmospheric pressure [kPa], : \lambda_v = latent heat of water vaporization, 2.45 [MJ kg−1], : c_p = specific heat of air at constant pressure, [MJ kg−1 °C−1], : MW_{ratio} = ratio molecular weight of water vapor/dry air = 0.622. The psychrometric constant \gamma relates the partial pressure of water in air to the air temperature. The Kelvin scale is an absolute scale, which is defined such that 0 K is absolute zero and a change of thermodynamic temperature by 1 kelvin corresponds to a change of thermal energy by . In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol . English translation (extract). that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0° and 100° C. In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was "now one of the major sources of the observed variability between different realizations of the water triple point", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water. === 2019 redefinition === In 2005, the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method. At constant pressure the maximum number of independent variables is three – the temperature and two concentration values.	-1270	0.0245	41.4	0.375	1.81	B
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When $229 \mathrm{~J}$ of energy is supplied as heat to $3.0 \mathrm{~mol} \mathrm{Ar}(\mathrm{g})$ at constant pressure, the temperature of the sample increases by $2.55 \mathrm{~K}$. Calculate the molar heat capacities at constant pressure of the gas.	Then the molar heat capacity (at constant volume) would be :cV,m = fR where R is the ideal gas constant. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.Lange's Handbook of Chemistry, 10th ed. p. 1524 All methods for the measurement of specific heat apply to molar heat capacity as well. ==Units== The SI unit of molar heat capacity heat is joule per kelvin per mole (J/(K⋅mol), J/(K mol), J K−1 mol−1, etc.). The following table shows the experimental molar heat capacities at constant pressure cP,m of the above polyatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000 °C, and the apparent number of degrees of freedom f* estimated by the formula f* = 2cP,m/R − 2: 25 °C 25 °C 500 °C 500 °C 5000 °C 5000 °C Gas cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* f Notes N≡N=O 38.6 7.3 51.8 10.5 62.0 12.9 13 "Nitrous oxide" NIST Chemistry WebBook, SRD 69, online. On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows: : C_{P,m} - C_{V,m} = \frac{C_{P} - C_{V}}{n} = \frac{n R}{n} = R This result would be consistent if the specific difference were derived directly from the general expression for c_p - c_v\, . == See also == Heat capacity ratio == References == David R. Gaskell (2008), Introduction to the thermodynamics of materials, Fifth Edition, Taylor & Francis. . The following is a table of some constant- pressure molar heat capacities cP,m of various diatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000 °C, and the apparent number of degrees of freedom f* estimated by the formula f* = 2cP,m/R − 2: 25 °C 25 °C 500 °C 500 °C 5000 °C 5000 °C Gas cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* H2 28.9 5.0 29.6 5.1 41.2 7.9 Not saturated."Hydrogen" NIST Chemistry WebBook, SRD 69, online. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. Like the specific heat, the measured molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). In modern terms the mass m of the sample divided by molar mass M gives the number of moles n. :m/M = n Therefore, using uppercase C for the full heat capacity (in joule per kelvin), we have: :C(M/m) = C/n = K = 3R or :C/n = 3R. Said another way, the atom-molar heat capacity of a solid substance is expected to be 3R = 24.94 J⋅K−1⋅mol−1, where "amol" denotes an amount of the solid that contains the Avogadro number of atoms. Like the heat capacity of an object, the molar heat capacity of a substance may vary, sometimes substantially, depending on the starting temperature T of the sample and the pressure P applied to it. The last value corresponds almost exactly to the predicted value for f = 7. right\|thumb\|upright=1.25\|Constant-volume specific heat capacity of diatomic gases (real gases) between about 200 K and 2000 K. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1. At high enough temperature, its molar heat capacity then should be cP,m = 7.5 R = 62.63 J⋅K−1⋅mol−1. Therefore, the word "molar", not "specific", should always be used for this quantity. ==Definition== The molar heat capacity of a substance, which may be denoted by cm, is the heat capacity C of a sample of the substance, divided by the amount (moles) n of the substance in the sample: :cm{} \;=\; \frac{C}{n} \;=\; \frac{1}{n} \lim_{\Delta T \rightarrow 0}\frac{Q}{\Delta T} where Q is the amount of heat needed to raise the temperature of the sample by ΔT. thumb\|upright=2.2\|Molar heat capacity of most elements at 25 °C is in the range between 2.8 R and 3.4 R: Plot as a function of atomic number with a y range from 22.5 to 30 J/mol K. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. In other words, that theory predicts that the molar heat capacity at constant volume cV,m of all monatomic gases will be the same; specifically, :cV,m = R where R is the ideal gas constant, about 8.31446 J⋅K−1⋅mol−1 (which is the product of the Boltzmann constant kB and the Avogadro constant). According to Mayer's relation, the molar heat capacity at constant pressure would be :cP,m = cV,m \+ R = fR + R = (f + 2)R Thus, each additional degree of freedom will contribute R to the molar heat capacity of the gas (both cV,m and cP,m). The same theory predicts that the molar heat capacity of a monatomic gas at constant pressure will be :cP,m = cV,m \+ R = R This prediction matches the experimental values, which, for helium through xenon, are 20.78, 20.79, 20.85, 20.95, and 21.01 J⋅K−1⋅mol−1, respectively;Shuen-Chen Hwang, Robert D. Lein, Daniel A. Morgan (2005). The molar heat capacity of the gas will then be determined only by the "active" degrees of freedom — that, for most molecules, can receive enough energy to overcome that quantum threshold.Quantum Physics and the Physics of large systems, Part 1A Physics, University of Cambridge, C.G. Smith, 2008. right\|thumb\|upright=1.25\|Constant- volume specific heat capacity of a diatomic gas (idealised). The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume ().	-20	+11	17.7	22	269	D
Express the van der Waals parameters $b=0.0226 \mathrm{dm}^3 \mathrm{~mol}^{-1}$ in SI base units.	* Analytical calculation of Van der Waals surfaces and volumes. Petitjean, On the Analytical Calculation of Van der Waals Surfaces and Volumes: Some Numerical Aspects, Journal of Computational Chemistry, Volume 15, Number 5, 1994, pp. 507–523. == External links == * VSAs for various molecules by Anton Antonov, The Wolfram Demonstrations Project, 2007. The van der Waals constant b volume can be used to calculate the van der Waals volume of an atom or molecule with experimental data derived from measurements on gases. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. These various methods give values for the van der Waals radius which are similar (1–2 Å, 100–200 pm) but not identical. The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances, and angles) are known. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. In Van der Waals' original derivation, given below, b' is four times the proper volume of the particle. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the Avogadro constant N. Useful tabulated values of Van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will be seen to present different values for the Van der Waals radius of the same atom. D-166. b = 23.7 cm/mol. Helium is a monatomic gas, and each mole of helium contains atoms (the Avogadro constant, N): V_{\rm w} = {b\over{N_{\rm A}}} Therefore, the van der Waals volume of a single atom V = 39.36 Å, which corresponds to r = 2.11 Å (≈ 200 picometers). The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. The first form of the Van der Waals equation of state given above can be recast in the following reduced form: :\left(p_R + \frac{3}{v_R^2}\right)(3v_R - 1) = (8 T_R) This equation is invariant for all fluids; that is, the same reduced form equation of state applies, no matter what a and b may be for the particular fluid. The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. Gas d (Å) b (cmmol) V (Å) r (Å) Hydrogen 0.74611 26.61 44.19 2.02 Nitrogen 1.0975 39.13 64.98 2.25 Oxygen 1.208 31.83 52.86 2.06 Chlorine 1.988 56.22 93.36 2.39 van der Waals radii r in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Tabulated values of van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will often have different values for the van der Waals radius of the same atom. The van der Waals volume of an atom or molecule may also be determined by experimental measurements on gases, notably from the van der Waals constant b, the polarizability α, or the molar refractivity A. Blaney and G. E. Ewing, Annual Review of Physical Chemistry, Vol. 27, pp. 553-586 (1976): Van der Waals Molecules.	−2	5	0.41887902047	0.000226	0.5	D
A diving bell has an air space of $3.0 \mathrm{m}^3$ when on the deck of a boat. What is the volume of the air space when the bell has been lowered to a depth of $50 \mathrm{m}$? Take the mean density of sea water to be $1.025 \mathrm{g} \mathrm{cm}^{-3}$ and assume that the temperature is the same as on the surface.	* Volume reduction of the air in an open bell due to increasing hydrostatic pressure as the bell is lowered is compensated. The bell is lowered into the water and to the working depth at a rate recommended by the decompression schedule, and which allows the divers to equalize comfortably. The bell is lowered through the water to working depth, so must be negatively buoyant. Each 10 metres (33 feet) of depth puts another atmosphere (1 bar, 14.7 psi, 101 kPa) of pressure on the hull, so at 300 metres (1,000 feet), the hull is withstanding thirty atmospheres (30 bar, 441 psi, 3,000 kPa) of water pressure. ===Test depth=== This is the maximum depth at which a submarine is permitted to operate under normal peacetime circumstances, and is tested during sea trials. Maximum Operating Depth (MOD) in metres sea water (msw) for pO2 1.2 to 1.6 MOD (msw) % oxygen 4 8 12 16 20 21 24 28 32 36 40 50 60 70 80 90 100 Maximum pO2 (bar) 1.6 390 190 123 90 70 66 57 47 40 34 30 22 17 13 10 8 6 1.5 365 178 115 84 65 61 53 44 37 32 28 20 15 11 9 7 5 1.4 340 165 107 78 60 57 48 40 34 29 25 18 13 10 8 6 4 1.3 315 153 98 71 55 52 44 36 31 26 23 16 12 9 6 4 3 1.2 290 140 90 65 50 47 40 33 28 23 20 14 10 7 5 3 2 These depths are rounded to the nearest metre. ==See also== * == Notes == == References == == Sources == * * * * Category:Dive planning Category:Underwater diving safety Category:Breathing gases Wet bells with an air space will have the air space topped up as the bell descends and the air is compressed by increasing hydrostatic pressure. The physics of the diving bell applies also to an underwater habitat equipped with a moon pool, which is like a diving bell enlarged to the size of a room or two, and with the water–air interface at the bottom confined to a section rather than forming the entire bottom of the structure. ===Wet bell=== thumb\|upright\|Open diving bell on a stern mounted launch and recovery system A wet bell is a platform for lowering and lifting divers to and from the underwater workplace, which has an air filled space, open at the bottom, where the divers can stand or sit with their heads out of the water. It transports this air to its diving bell to replenish the air supply in the bell. The pressure produced by depth in water, is converted to pressure in feet sea water (fsw) or metres sea water (msw) by multiplying with the appropriate conversion factor, 33 fsw per atm, or 10 msw per bar. Air is trapped inside the bell by pressure of the water at the interface. Of this total pressure which can be tolerated by the diver, 1 atmosphere is due to surface pressure of the Earth's air, and the rest is due to the depth in water. The bell is ballasted so as to remain upright in the water and to be negatively buoyant, so that it will sink even when full of air. If the divers are breathing from the bell airspace at the time, it may need to be vented with additional air to maintain a low carbon dioxide level. Adding pressurized gas ensures that the gas space within the bell remains at constant volume as the bell descends in the water. A diving bell is a rigid chamber used to transport divers from the surface to depth and back in open water, usually for the purpose of performing underwater work. The diving bell would be connected via the mating flange of an airlock to the deck decompression chamber or saturation system for transfer under pressure of the occupants. == Air-lock diving bells == thumb\|Barge with air-lock diving bell for working on moorings Service vessel with diving bell which can be lowered to 10 m and accessed via airlock and a 2 m diameter access tube\|thumb\|right The air lock diving-bell plant was a purpose-built barge for the laying, examination and repair of moorings for battleships at Gibraltar harbour. So the 1 atmosphere or bar contributed by the air is subtracted to give the pressure due to the depth of water. In underwater diving activities such as saturation diving, technical diving and nitrox diving, the maximum operating depth (MOD) of a breathing gas is the depth below which the partial pressure of oxygen (pO2) of the gas mix exceeds an acceptable limit. For example, if a gas contains 36% oxygen and the maximum pO2 is 1.4 bar, the MOD (msw) is 10 msw/bar x [(1.4 bar / 0.36) − 1] = 28.9 msw. == Tables == Maximum Operating Depth (MOD) in feet sea water (fsw) for pO2 1.2 to 1.6 MOD (fsw) % oxygen 4 8 12 16 20 21 24 28 32 36 40 50 60 70 80 90 100 Maximum pO2 (bar) 1.6 1287 627 407 297 231 218 187 156 132 114 99 73 55 42 33 26 20 1.5 1205 586 380 276 215 203 173 144 122 105 91 66 50 38 29 22 17 1.4 1122 545 352 256 198 187 160 132 111 95 83 59 44 33 25 18 13 1.3 1040 503 325 235 182 171 146 120 101 86 74 53 39 28 21 15 10 1.2 957 462 297 215 165 156 132 108 91 77 66 46 33 24 17 11 7 These depths are rounded to the nearest foot. The internal pressure in the bell is usually kept at atmospheric pressure to minimise run time by eliminating the need for decompression, so the seal between the bell skirt and the submarine deck is critical to the safety of the operation. The 6 m × 4 m × 2.5 m bell is accessible through a 2 m diameter tube and an airlock. In 1689, Denis Papin suggested that the pressure and fresh air inside a diving bell could be maintained by a force pump or bellows.	92	35.91	0.05882352941	0.5	8.87	D
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression $\Delta G / \text{J}=-85.40+36.5(T / \text{K})$. Calculate the value of $\Delta S$ for the process.	The Gibbs energy of any system is and an infinitesimal change in G, at constant temperature and pressure, yields :dG=dU+pdV-TdS. The Gibbs free energy is expressed as : G(p,T) = U + pV - TS = H - TS where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy. Moreover, we also have \begin{align} K_\text{eq} &= e^{-\frac{\Delta_\text{r} G^\circ}{RT}}, \\\ \Delta_\text{r} G^\circ &= -RT\left(\ln K_\text{eq}\right) = -2.303\,RT\left(\log_{10} K_\text{eq}\right), \end{align} which relates the equilibrium constant with Gibbs free energy. The equation is:Physical chemistry, P. W. Atkins, Oxford University Press, 1978, where H is the enthalpy, T the absolute temperature and G the Gibbs free energy of the system, all at constant pressure p. Integrating with respect to T (again p is constant) it becomes: : \frac{\Delta G^\ominus(T_2)}{T_2} - \frac{\Delta G^\ominus(T_1)}{T_1} = \Delta H^\ominus \left(\frac{1}{T_2} - \frac{1}{T_1}\right) This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature T2 with knowledge of just the standard Gibbs free energy change of formation and the standard enthalpy change of formation for the individual components. This implies that at equilibrium Q_\text{r} = K_\text{eq} and \Delta_\text{r} G = 0. ==Standard Gibbs energy change of formation== Table of selected substancesCRC Handbook of Chemistry and Physics, 2009, pp. 5-4–5-42, 90th ed., Lide. The equation reads:Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, :\left( \frac{\partial ( \Delta G^\ominus/T ) } {\partial T} \right)_p = - \frac {\Delta H^\ominus} {T^2} with ΔG as the change in Gibbs energy due to reaction, and ΔH as the enthalpy of reaction (often, but not necessarily, assumed to be independent of temperature). The unit system used (K or R for T) is irrelevant because of the usage of the reduced values Tr and Pr. ==See also== Vapour pressure of water Antoine equation Tetens equation Arden Buck equation Goff–Gratch equation == References == Category:Thermodynamic models The Gibbs free energy change , measured in joules in SI) is the maximum amount of non-volume expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975 allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known. == Equations == : \ln P_{\rm r} = f^{(0)} + \omega \cdot f^{(1)} : f^{(0)}=5.92714 - \frac{6.09648}{T_{\rm r}} - 1.28862 \cdot \ln T_{\rm r} + 0.169347 \cdot T_{\rm r}^6 : f^{(1)}=15.2518 - \frac{15.6875}{T_{\rm r}}-13.4721 \cdot \ln T_{\rm r} + 0.43577 \cdot T_{\rm r}^6 with :P_{\rm r}=\frac{P}{P_{\rm c}} (reduced pressure) and T_{\rm r}=\frac{T}{T_{\rm c}} (reduced temperature). == Typical errors == The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. Auflage, McGraw-Hill, 1988 == Example calculation == For benzene with Tc = 562.12 KBrunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006 * Pc = 4898 kPa * Tb = 353.15 KSilva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006 * ω = 0.2120Dortmund Data Bank the following calculation for T=Tb results: * Tr = 353.15 / 562.12 = 0.628247 * f(0) = -3.167428 * f(1) = -3.429560 * Pr = exp( f(0) \+ ω f(1) ) = 0.020354 * P = Pr * Pc = 99.69 kPa The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The gas constant occurs in the ideal gas law: PV = nRT = m R_{\rm specific} T where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. Substance (state) ΔfG° ΔfG° Substance (state) (kJ/mol) (kcal/mol) NO(g) 87.6 20.9 NO2(g) 51.3 12.3 N2O(g) 103.7 24.78 H2O(g) −228.6 −54.64 H2O(l) −237.1 −56.67 CO2(g) −394.4 −94.26 CO(g) −137.2 −32.79 CH4(g) −50.5 −12.1 C2H6(g) −32.0 −7.65 C3H8(g) −23.4 −5.59 C6H6(g) 129.7 29.76 C6H6(l) 124.5 31.00 The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, in their standard states (the most stable form of the element at 25 °C and 100 kPa). The equation states that the change in the G/T ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor H/T2. ==Chemical reactions and work== The typical applications of this equation are to chemical reactions. The gas constant is expressed in the same unit as are molar entropy and molar heat. ==Dimensions== From the ideal gas law PV = nRT we get: :R = \frac{PV}{nT} where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . Also, using the reaction isotherm equation,Chemistry, Matter, and the Universe, R.E. Dickerson, I. Geis, W.A. Benjamin Inc. (USA), 1976, that is :\frac{\Delta G^\ominus}{T} = -R \ln K which relates the Gibbs energy to a chemical equilibrium constant, the van 't Hoff equation can be derived.Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, Since the change in a system's Gibbs energy is equal to the maximum amount of non-expansion work that the system can do in a process, the Gibbs-Helmholtz equation may be used to estimate how much non-expansion work can be done by a chemical process as a function of temperature. As a necessary condition for the reaction to occur at constant temperature and pressure, ΔG must be smaller than the non- pressure-volume (non-pV, e.g. electrical) work, which is often equal to zero (then ΔG must be negative). One can think of ∆G as the amount of "free" or "useful" energy available to do non-pV work at constant temperature and pressure. Each quantity in the equations above can be divided by the amount of substance, measured in moles, to form molar Gibbs free energy. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas law and the standard sea-level conditions (SSL) (air density ρ0 = 1.225 kg/m3, temperature T0 = 288.15 K and pressure p0 = ), we have that Rair = P0/(ρ0T0) = . However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other exactly defined physical constants. ==Specific gas constant== Rspecific for dry air Unit 287.052874 J⋅kg−1⋅K−1 53.3523 ft⋅lbf⋅lb−1⋅°R−1 1,716.46 ft⋅lbf⋅slug−1⋅°R−1 The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture.	1000	+107	0.70710678	-36.5	+116.0	D
Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. At $298 \mathrm{~K}$ the standard enthalpy of combustion of sucrose is $-5797 \mathrm{~kJ}$ $\mathrm{mol}^{-1}$ and the standard Gibbs energy of the reaction is $-6333 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Estimate the additional non-expansion work that may be obtained by raising the temperature to blood temperature, $37^{\circ} \mathrm{C}$.	The Sugden Award is an annual award for contributions to combustion research. Part V - Evaluation of Models for the chemical source term" Combustion and Flame, 127 2023 (2001). * 2000. This gives the same result as the Weir formula at RQ = 1 (burning only carbohydrates), and almost the same value at RQ = 0.7 (burning only fat). ⊅Σ′ ==History== Antoine Lavoisier noted in 1780 that heat production, in some cases, can be predicted from oxygen consumption, using multiple regression. T.C. Chew, K. N.C. Bray, R. E. Britter, "Spatially Resolved Flamelet Statistics for Reaction Rate Modelling" Combustion and Flame 80 65-82 (1990). * 1989. Thermokinetics deals with the study of thermal decomposition kinetics. ==See also== Thermogravimetry Differential thermal analysis Differential scanning calorimetry ==References== * Category:Chemical kinetics Another formula used is: citing :M=VO_2\left(\frac{RQ-0.7}{0.3}e_c+\frac{1-RQ}{0.3}e_f\right) where RQ is the respiratory quotient (ratio of volume CO2 produced to volume of O2 consumed), e_c is , the heat released per litre of oxygen by the oxidation of carbohydrate, and e_f is , the value for fat. The prize is awarded by the British Section of The Combustion Institute for the published paper with at least one British Section member as author, which makes the most significant contribution to combustion research. Combustion Theory and Modelling is a bimonthly peer-reviewed scientific journal covering research on combustion. K.M. Leung and R.P. Lindstedt, "Detailed modelling of C1-C3 alkane diffusion flames" Combustion and Flame 102 129-160 (1995). * 1994. Progress in Energy and Combustion Science is a bimonthly peer-reviewed review journal published by Elsevier. A Bordwell thermodynamic cycle use experimentally determined and reasonable estimates of Gibbs free energy (ΔG˚) values to determine unknown and experimentally inaccessible values. == Overview == Analogous to Hess's Law which deal with the summation of enthalpy (ΔH) values, Bordwell thermodynamic cycles deal with the summation of Gibbs free energy (ΔG) values. Indirect calorimetry calculates heat that living organisms produce by measuring either their production of carbon dioxide and nitrogen waste (frequently ammonia in aquatic organisms, or urea in terrestrial ones), or from their consumption of oxygen. The theoretical bases of indirect calorimetry: a review." :ΔG˚ = -RTln(Keq) :ΔG˚ = (2.303)RT(pKeq) :ΔG˚ = -nFE˚1/2 Useful conversion factors: :-23.06 (kcal/mol)(e−)−1(V)−1 :1.37(pKeq) kcal/mol :1.37[-log(Keq)] kcal/mol == References == Category:Thermodynamic cycles F.C. Lockwood, M. Costa and P. Costen, "Detailed Measurements in a heavy fuel oil-fired furnace" Combustion Science and Technology 77 1-26 (1991). * 1990. Metabolism. 1988 Mar;37(3):287-301. ==Scientific background== Indirect calorimetry measures O2 consumption and CO2 production. thumb\|Indirect calorimetry metabolic cart measuring oxygen uptake (O2) and carbon dioxide production (CO2) of a spontaneously breathing subject (dilution method with canopy hood). Indirect calorimetry estimates the type and rate of substrate utilization and energy metabolism in vivo starting from gas exchange measurements (oxygen consumption and carbon dioxide production during rest and steady-state exercise). Ambient and diluted fractions of O2 and CO2 are measured for a known ventilation rate, and O2 consumption and CO2 production are determined and converted into Resting Energy Expenditure.Academy of Nutrition and Dietetics "Measuring RMR with Indirect Calorimetry (IC)." R.S.M. Chrystie, I.S. Burns, C.F. Kaminski "Temperature response of an acoustically- forced turbulent lean premixed flame: A quantitative experimental determination", Combustion Science and Technology, vol. 185, pp. 180–199, (2013). * 2012. J.F.Griffiths and B.J.Whitaker, "Thermokinetic Interactions Leading to Knock during Homogeneous Charge Compression Ignition", Combustion and Flame 131 386-399 (2002). * 2001. Balthasar and M. Kraft, "A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames" Combustion and Flame 133 289 (2003). * 2002.	-100	0.0029	4.0	-21	0.000216	D
The composition of the atmosphere is approximately 80 per cent nitrogen and 20 per cent oxygen by mass. At what height above the surface of the Earth would the atmosphere become 90 per cent nitrogen and 10 per cent oxygen by mass? Assume that the temperature of the atmosphere is constant at $25^{\circ} \mathrm{C}$. What is the pressure of the atmosphere at that height?	Total atmospheric mass is 5.1480×1018 kg (1.135×1019 lb), about 2.5% less than would be inferred from the average sea level pressure and Earth's area of 51007.2 megahectares, this portion being displaced by Earth's mountainous terrain. Hp is 8.4km, but for different gasses (measuring their partial pressure), it is again different and depends upon molar mass, giving 8.7 for nitrogen, 7.6 for oxygen and 5.6 for carbon dioxide. ====Total content==== Further note that since g, Earth's gravitational acceleration, is approximately constant with altitude in the atmosphere, the pressure at height h is proportional to the integral of the density in the column above h, and therefore to the mass in the atmosphere above height h. For an isothermal atmosphere, (1-\frac{1}{e}) or about 63% of the total mass of the atmosphere exists between the planet's surface and one scale height. In summary, the mass of Earth's atmosphere is distributed approximately as follows:Lutgens, Frederick K. and Edward J. Tarbuck (1995) The Atmosphere, Prentice Hall, 6th ed., pp. 14–17, * 50% is below . * 90% is below . * 99.99997% is below , the Kármán line. The concentration of oxygen (O2) in sea-level air is 20.9%, so the partial pressure of O2 (pO2) is . Using the values T=273 K and M=29 g/mol as characteristic of the Earth's atmosphere, H = RT/Mg = (8.315273)/(299.8) = 7.99, or about 8 km, which coincidentally is approximate height of Mt. Everest. The partial pressure of dry air p_\text{d} is found considering partial pressure, resulting in: p_\text{d} = p - p_\text{v} where p simply denotes the observed absolute pressure. ==Variation with altitude== thumb\|upright=2.0\|Standard atmosphere: , , ===Troposphere=== To calculate the density of air as a function of altitude, one requires additional parameters. For the troposphere, the lowest part (~10 km) of the atmosphere, they are listed below, along with their values according to the International Standard Atmosphere, using for calculation the universal gas constant instead of the air specific constant: p_0, sea level standard atmospheric pressure, 101325Pa T_0, sea level standard temperature, 288.15K g, earth-surface gravitational acceleration, 9.80665m/s2 L, temperature lapse rate, 0.0065K/m R, ideal (universal) gas constant, 8.31446J/(mol·K) M, molar mass of dry air, 0.0289652kg/mol Temperature at altitude h meters above sea level is approximated by the following formula (only valid inside the troposphere, no more than ~18km above Earth's surface (and lower away from Equator)): T = T_0 - L h The pressure at altitude h is given by: p = p_0 \left(1 - \frac{L h}{T_0}\right)^\frac{g M}{R L} Density can then be calculated according to a molar form of the ideal gas law: \rho = \frac{p M}{R T} = \frac{p M}{R T_0 \left(1 - \frac{Lh}{T_0}\right)} = \frac{p_0 M}{R T_0} \left(1 - \frac{L h}{T_0} \right)^{\frac{g M}{R L} - 1} where: M, molar mass R, ideal gas constant T, absolute temperature p, absolute pressure Note that the density close to the ground is \rho_0 = \frac{p_0 M}{R T_0} It can be easily verified that the hydrostatic equation holds: \frac{dp}{dh} = -g\rho . ====Exponential approximation==== As the temperature varies with height inside the troposphere by less than 25%, \frac{Lh}{T_0} < 0.25 and one may approximate: \rho = \rho_0 e^{\left(\frac{g M}{R L} - 1\right) \ln \left(1 - \frac{L h}{T_0}\right)} \approx \rho_0 e^{-\left(\frac{g M}{R L} - 1\right)\frac{L h}{T_0}} = \rho_0 e^{-\left(\frac{g M h}{R T_0} - \frac{L h}{T_0}\right)} Thus: \rho \approx \rho_0 e^{-h/H_n} Which is identical to the isothermal solution, except that Hn, the height scale of the exponential fall for density (as well as for number density n), is not equal to RT0/gM as one would expect for an isothermal atmosphere, but rather: \frac{1}{H_n} = \frac{g M}{R T_0} - \frac{L}{T_0} Which gives Hn = 10.4km. Air composition, temperature, and atmospheric pressure vary with altitude. The average temperature of the atmosphere at Earth's surface is or , depending on the reference. ==Physical properties== ===Pressure and thickness=== The average atmospheric pressure at sea level is defined by the International Standard Atmosphere as . Atmospheric pressure is the total weight of the air above unit area at the point where the pressure is measured. As of 2023, by mole fraction (i.e., by number of molecules), dry air contains 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases. Pressure altitude is the altitude in the International Standard Atmosphere (ISA) with the same atmospheric pressure as that of the part of the atmosphere in question. R_\text{specific}, the specific gas constant for dry air, which using the values presented above would be approximately in J⋅kg−1⋅K−1. According to the American National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480 kg with an annual range due to water vapor of 1.2 or 1.5 kg, depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. Therefore the mass fraction of the troposphere out of all the atmosphere is given using the approximated formula for p: 1 - \frac{p(h = 11\text{ km})}{p_0} = 1 - \left(\frac{T(11\text{ km})}{T_0} \right)^\frac{g M}{R L} \approx 76\% For nitrogen, it is 75%, while for oxygen this is 79%, and for carbon dioxide, 88%. ===Tropopause=== Higher than the troposphere, at the tropopause, the temperature is approximately constant with altitude (up to ~20km) and is 220K. The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. Air pressure actually decreases exponentially with altitude, dropping by half every or by a factor of 1/e (0.368) every , (this is called the scale height) -- for altitudes out to around . The atmospheric pressure at the top of the stratosphere is roughly 1/1000 the pressure at sea level. For example, the U.S. Standard Atmosphere derives the values for air temperature, pressure, and mass density, as a function of altitude above sea level. Both the pressure and density obey this law, so, denoting the height of the border between the troposphere and the tropopause as U: \begin{align} p &= p(U) e^{-\frac{h - U}{H_\text{TP}}} = p_0 \left(1 - \frac{L U}{T_0}\right)^\frac{g M}{R L} e^{-\frac{h - U}{H_\text{TP}}} \\\ \rho &= \rho(U) e^{-\frac{h - U}{H_\text{TP}}} = \rho_0 \left(1 - \frac{L U}{T_0}\right)^{\frac{g M}{R L} - 1} e^{-\frac{h - U}{H_\text{TP}}} \end{align} ==Composition== ==See also== Air Atmospheric drag Lighter than air Density Atmosphere of Earth International Standard Atmosphere U.S. Standard Atmosphere NRLMSISE-00 ==Notes== ==References== ==External links== Conversions of density units ρ by Sengpielaudio Air density and density altitude calculations and by Richard Shelquist Air density calculations by Sengpielaudio (section under Speed of sound in humid air) Air density calculator by Engineering design encyclopedia Atmospheric pressure calculator by wolfdynamics Air iTools - Air density calculator for mobile by JSyA Revised formula for the density of moist air (CIPM-2007) by NIST Category:Atmospheric thermodynamics A The average mass of the atmosphere is about 5 quadrillion (5) tonnes or 1/1,200,000 the mass of Earth.	0.0029	14	1.16	1.2	2	A
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate $\Delta S_\text{tot}$ when two copper blocks, each of mass $10.0 \mathrm{~kg}$, one at $100^{\circ} \mathrm{C}$ and the other at $0^{\circ} \mathrm{C}$, are placed in contact in an isolated container. The specific heat capacity of copper is $0.385 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~g}^{-1}$ and may be assumed constant over the temperature range involved.	Copper has a thermal conductivity of 231 Btu/(hr-ft-F). However, the thermal conductivity of stainless steel is 1/30th times than that of copper. Copper heat exchangers for improving indoor ait quality: Cooling season at Ft. Jackson. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). As the solution circulates through the copper header, the temperature rises. Therefore, the heat capacity ratio in this example is 1.4. Copper has many desirable properties for thermally efficient and durable heat exchangers. This article focuses on beneficial properties and common applications of copper in heat exchangers. First and foremost, copper is an excellent conductor of heat. Thermal conductivity of some common metals Metal Thermal conductivity (Btu/(hr-ft-F)) (W/(m•K)) Silver 247.87 429 Copper 231 399 Gold 183 316 Aluminium 136 235 Yellow brass 69.33 120 Cast iron 46.33 80.1 Stainless steel 8.1 14.0 Further information about the thermal conductivity of selected metals is available. ===Corrosion resistance=== Corrosion resistance is essential in heat transfer applications where fluids are involved, such as in hot water tanks, radiators, etc. Copper heat exchangers are the preferred material in these units because of their high thermal conductivity and ease of fabrication. Hence the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992. The behavior of the heat capacity near the peak is described by the formula C\approx A_\pm t^{-\alpha}+B_\pm where t=\|1-T/T_c\| is the reduced temperature, T_c is the Lambda point temperature, A_\pm,B_\pm are constants (different above and below the transition temperature), and is the critical exponent: \alpha=-0.0127(3). The formula is: :\alpha = \frac{ k }{ \rho c_{p} } where * is thermal conductivity (W/(m·K)) * is specific heat capacity (J/(kg·K)) * is density (kg/m3) Together, can be considered the volumetric heat capacity (J/(m3·K)). thumb\|250px\|The plot of the specific heat capacity versus temperature. The copper heat pipe transfers thermal energy from within the solar tube into a copper header. This means that copper's high thermal conductivity allows heat to pass through it quickly. Non-copper heat exchangers are also available. Copper has a 60% better thermal conductivity rating than aluminum and has almost 30 times more thermal conductivity than stainless steel. Part 1: Feasibility of usage in a temperate zone; Part 2: Demonstration of usage in a cold zone; Final report to the International Copper Association Ltd. New copper heat exchanger technologies for specific applications are also introduced. ==History== Heat exchangers using copper and its alloys have evolved along with heat transfer technologies over the past several hundred years. During the same time period, antimicrobial copper was able to limit bacterial loads associated with the copper heat exchanger fins by 99.99% and fungal loads by 99.74%.Michels, H. (2011).	11000	0.59	169.0	+93.4	+3.03	D
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. A sample consisting of $2.0 \mathrm{~mol} \mathrm{CO}_2$ occupies a fixed volume of $15.0 \mathrm{dm}^3$ at $300 \mathrm{~K}$. When it is supplied with $2.35 \mathrm{~kJ}$ of energy as heat its temperature increases to $341 \mathrm{~K}$. Assume that $\mathrm{CO}_2$ is described by the van der Waals equation of state, and calculate $\Delta U$.	Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). In this case specific volume changes are small and it can be written in a simplified form: :(p+A)(V-B)=CT, \, where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters. == See also == * Gas laws * Ideal gas * Inversion temperature * Iteration * Maxwell construction * Real gas * Theorem of corresponding states * Van der Waals constants (data page) * Redlich–Kwong equation of state ==References== ==Further reading== * * . The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PVm=RT. Above the critical temperature, TC, the Van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region. We get : p = \frac{NkT}{V-Nb'} - \frac{N^2 a'}{V^2} \Rightarrow \left(p + \frac{N^2 a'}{V^2} \right)(V-Nb') = NkT \Rightarrow \left(p + \frac{n^2 a}{V^2} \right)(V-nb) = nRT. ==Maxwell equal area rule== Below the critical temperature, the Van der Waals equation seems to predict qualitatively incorrect relationships. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. Since: :p=-\left(\frac{\partial A}{\partial V}\right)_{T,N} where A is the Helmholtz free energy, it follows that the equal area rule can be expressed as: :p_V=\frac{A(V_L,T,N)-A(V_G,T,N)}{V_G-V_L}is Since the gas and liquid volumes are functions of pV and T only, this equation is then solved numerically to obtain pV as a function of temperature (and number of particles N), which may then be used to determine the gas and liquid volumes. thumb\|800px\|Locus of coexistence for two phases of Van der Waals fluid A pseudo-3D plot of the locus of liquid and vapor volumes versus temperature and pressure is shown in the accompanying figure. The ideal gas law states that the volume V occupied by n moles of any gas has a pressure P at temperature T given by the following relationship, where R is the gas constant: :PV=nRT To account for the volume occupied by real gas molecules, the Van der Waals equation replaces V/n in the ideal gas law with (V_m-b), where Vm is the molar volume of the gas and b is the volume occupied by the molecules of one mole: :P(V_m - b)=R T thumb\|Van der Waals equation on a wall in Leiden The second modification made to the ideal gas law accounts for interaction between molecules of the gas. Therefore, they will respond to changes in roughly the same way, even though their measurable physical characteristics may differ significantly. ===Cubic equation=== The Van der Waals equation is a cubic equation of state; in the reduced formulation the cubic equation is: :{v_R^3}-\frac{1}{3}\left({1+\frac{8T_R}{p_R}}\right){v_R^2} +\frac{3}{p_R}v_R- \frac{1}{p_R}= 0 At the critical temperature, where T_R=p_R=1 we get as expected :{v_R^3}-3v_R^2 +3v_R- 1=\left(v_R -1\right)^3 = 0 \quad \Longleftrightarrow \quad v_R=1 For TR < 1, there are 3 values for vR. Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and b (volume occupied by molecules) values, then a and b for the mixture can be calculated as :m = total number of moles of gas present, :for each i, m_i = number of moles of gas i present, and x_i = \frac{m_i}{m} :a = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{a_i a_j}) :b = \sum_{i=1}^{i=n} \sum_{j=1}^{i=n} ( x_i x_j \sqrt{b_i b_j}) and the rule of adding partial pressures becomes invalid if the numerical result of the equation \left(p + ({n^2 a}/{V^2})\right)\left(V-nb\right) = nRT is significantly different from the ideal gas equation pV = nRT . ===Reduced form=== The Van der Waals equation can also be expressed in terms of reduced properties: :\left(P_r + \frac{3}{V_r^2}\right)\left(V_r-\frac{1}{3}\right) = \frac{8}{3}T_r The equation in reduced form is exactly the same for every gas, this is consistent with the Theorem of corresponding states. In the derivation of ideal gas laws on the basis of kinetic theory of gases some assumption have been made. ===Compressibility factor=== The compressibility factor for the Van der Waals equation is: : Z = \frac{P V_m}{RT} = \frac{V_m}{V_m-b} - \frac{a}{V_m RT} Or in reduced form by substitution of P_r=P/P_c, T_r=T/T_c, V_r=V_m/V_c: : Z = \frac{V_r}{V_r-\frac{1}{3}} - \frac{9}{8 V_r T_r} At the critical point: : Z_c = \frac{P_c V_c}{RT_c} = \frac{3}{8} = 0.375 ==Validity== The Van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.. The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). Therefore, the heat capacity ratio in this example is 1.4. However, near the phase transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the Van der Waals equation fails to accurately model observed experimental behavior. == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. == Specific heat capacity == J/(mol·K) J/(g·K) 1 H hydrogen (H2, gas) use 28.836 14.304 CRC 28.836 14.304 WEL 28.82 LNG 28.84 2 He helium (gas) use 20.786 5.193 CRC 20.786 5.193 WEL 20.786 LNG 20.786 3 Li lithium use 24.860 3.582 CRC 24.860 3.582 WEL 24.8 LNG 24.8 4 Be beryllium use 16.443 1.825 CRC 16.443 1.825 WEL 16.4 LNG 16.38 5 B boron (rhombic) use 11.087 1.026 CRC 11.087 1.026 WEL 11.1 LNG 11.1 6 C carbon (graphite) use 8.517 0.709 CRC 8.517 0.709 WEL 8.53 LNG 8.517 6 C carbon (diamond, nonstd state) use 6.115 0.509 WEL 6.115 LNG 6.116 7 N nitrogen (N2, gas) use 29.124 1.040 CRC 29.124 1.040 WEL 29.12 LNG 29.124 8 O oxygen (O2, gas) use 29.378 0.918 CRC 29.378 0.918 WEL 29.4 LNG 29.4 9 F fluorine (F2, gas) use 31.304 0.824 CRC 31.304 0.824 WEL 31.3 LNG 31.30 10 Ne neon (gas) use 20.786 1.030 CRC 20.786 1.030 WEL 20.786 LNG 20.786 11 Na sodium use 28.230 1.228 CRC 28.230 1.228 WEL 28.2 LNG 28.15 12 Mg magnesium use 24.869 1.023 CRC 24.869 1.023 WEL 24.9 LNG 24.87 13 Al aluminium use 24.200 0.897 CRC 24.200 0.897 WEL 24.4 LNG 24.4 14 Si silicon use 19.789 0.705 CRC 19.789 0.705 WEL 20.0 LNG 20.00 15 P phosphorus (white) use 23.824 0.769 CRC 23.824 0.769 WEL 23.84 LNG 23.83 15 P phosphorus (red, nonstd state) use 21.19 0.684 WEL 21.2 LNG 21.19 16 S sulfur (rhombic) use 22.75 0.710 CRC 22.75 0.710 WEL 22.6 LNG 22.60 16 S sulfur (monoclinic, nonstd state) use 23.23 0.724 LNG 23.23 17 Cl chlorine (Cl2 gas) use 33.949 0.479 CRC 33.949 0.479 WEL 33.91 LNG 33.95 18 Ar argon (gas) use 20.786 0.520 CRC 20.786 0.520 WEL 20.786 LNG 20.79 19 K potassium use 29.600 0.757 CRC 29.600 0.757 WEL 29.6 LNG 29.60 20 Ca calcium use 25.929 0.647 CRC 25.929 0.647 WEL 25.3 LNG 25.9 21 Sc scandium use 25.52 0.568 CRC 25.52 0.568 WEL 25.5 LNG 25.52 22 Ti titanium use 25.060 0.523 CRC 25.060 0.523 WEL 25.0 LNG 25.0 23 V vanadium use 24.89 0.489 CRC 24.89 0.489 WEL 24.9 LNG 24.90 24 Cr chromium use 23.35 0.449 CRC 23.35 0.449 WEL 23.3 LNG 23.43 25 Mn manganese use 26.32 0.479 CRC 26.32 0.479 WEL 26.3 LNG 26.30 26 Fe iron (alpha) use 25.10 0.449 CRC 25.10 0.449 WEL 25.1 LNG 25.09 27 Co cobalt use 24.81 0.421 CRC 24.81 0.421 WEL 24.8 LNG 24.8 28 Ni nickel use 26.07 0.444 CRC 26.07 0.444 WEL 26.1 LNG 26.1 29 Cu copper use 24.440 0.385 CRC 24.440 0.385 WEL 24.43 LNG 24.44 30 Zn zinc use 25.390 0.388 CRC 25.390 0.388 WEL 25.4 LNG 25.40 31 Ga gallium use 25.86 0.371 CRC 25.86 0.371 WEL 25.9 LNG 26.06 32 Ge germanium use 23.222 0.320 CRC 23.222 0.320 WEL 23.35 LNG 23.3 33 As arsenic (alpha, gray) use 24.64 0.329 CRC 24.64 0.329 WEL 24.6 LNG 24.64 34 Se selenium (hexagonal) use 25.363 0.321 CRC 25.363 0.321 WEL 25.36 LNG 24.98 35 Br bromine use (Br2) 75.69 0.474 CRC 36.057 0.226 WEL (liquid) 75.69 WEL (Br2, gas, nonstd state) 36.0 LNG (Br2, liquid) 75.67 36 Kr krypton (gas) use 20.786 0.248 CRC 20.786 0.248 WEL 20.786 LNG 20.786 37 Rb rubidium use 31.060 0.363 CRC 31.060 0.363 WEL 31.1 LNG 31.06 38 Sr strontium use 26.4 0.301 CRC 26.4 0.301 WEL 26 LNG 26.79 39 Y yttrium use 26.53 0.298 CRC 26.53 0.298 WEL 26.5 LNG 26.51 40 Zr zirconium use 25.36 0.278 CRC 25.36 0.278 WEL 25.4 LNG 25.40 41 Nb niobium use 24.60 0.265 CRC 24.60 0.265 WEL 24.6 LNG 24.67 42 Mo molybdenum use 24.06 0.251 CRC 24.06 0.251 WEL 24.1 LNG 24.13 43 Tc technetium use 24.27 LNG 24.27 44 Ru ruthenium use 24.06 0.238 CRC 24.06 0.238 WEL 24.1 LNG 24.1 45 Rh rhodium use 24.98 0.243 CRC 24.98 0.243 WEL 25.0 LNG 24.98 46 Pd palladium use 25.98 0.244 CRC 25.98 0.246 [sic] WEL 26.0 LNG 25.94 47 Ag silver use 25.350 0.235 CRC 25.350 0.235 WEL 25.4 LNG 25.4 48 Cd cadmium use 26.020 0.232 CRC 26.020 0.232 WEL 26.0 LNG 25.9 49 In indium use 26.74 0.233 CRC 26.74 0.233 WEL 26.7 LNG 26.7 50 Sn tin (white) use 27.112 0.228 CRC 27.112 0.228 WEL 27.0 LNG 26.99 50 Sn tin (gray, nonstd state) use 25.77 0.217 WEL 25.8 LNG 25.77 51 Sb antimony use 25.23 0.207 CRC 25.23 0.207 WEL 25.2 LNG 25.2 52 Te tellurium use 25.73 0.202 CRC 25.73 0.202 WEL 25.7 LNG 25.70 53 I iodine use (I2) 54.44 0.214 CRC 36.888 0.145 WEL (solid) 54.44 WEL (I2, gas, nonstd state) 36.9 LNG (I2, solid) 54.44 LNG (I2, gas, nonstd state) 36.86 54 Xe xenon (gas) use 20.786 0.158 CRC 20.786 0.158 WEL 20.786 LNG 20.786 55 Cs caesium use 32.210 0.242 CRC 32.210 0.242 WEL 32.2 LNG 32.20 56 Ba barium use 28.07 0.204 CRC 28.07 0.204 WEL 28.1 LNG 28.10 57 La lanthanum use 27.11 0.195 CRC 27.11 0.195 WEL 27.1 LNG 27.11 58 Ce cerium (gamma, fcc) use 26.94 0.192 CRC 26.94 0.192 WEL 26.9 LNG 26.9 59 Pr praseodymium use 27.20 0.193 CRC 27.20 0.193 WEL 27.2 LNG 27.20 60 Nd neodymium use 27.45 0.190 CRC 27.45 0.190 WEL 27.4 LNG 27.5 62 Sm samarium use 29.54 0.197 CRC 29.54 0.197 WEL 29.5 LNG 29.54 63 Eu europium use 27.66 0.182 CRC 27.66 0.182 WEL 27.7 LNG 27.66 64 Gd gadolinium use 37.03 0.236 CRC 37.03 0.236 WEL 37.0 LNG 37.03 65 Tb terbium use 28.91 0.182 CRC 28.91 0.182 WEL 28.9 LNG 28.91 66 Dy dysprosium use 27.7 0.170 CRC 27.7 0.170 WEL 27.2 LNG 27.7 67 Ho holmium use 27.15 0.165 CRC 27.15 0.165 WEL 27.2 LNG 27.15 68 Er erbium use 28.12 0.168 CRC 28.12 0.168 WEL 28.1 LNG 28.12 69 Tm thulium use 27.03 0.160 CRC 27.03 0.160 WEL 27.0 LNG 27.03 70 Yb ytterbium use 26.74 0.155 CRC 26.74 0.155 WEL 26.7 LNG 26.74 71 Lu lutetium use 26.86 0.154 CRC 26.86 0.154 WEL 26.9 LNG 26.86 72 Hf hafnium (hexagonal) use 25.73 0.144 CRC 25.73 0.144 WEL 25.7 LNG 25.69 73 Ta tantalum use 25.36 0.140 CRC 25.36 0.140 WEL 25.4 LNG 25.40 74 W tungsten use 24.27 0.132 CRC 24.27 0.132 WEL 24.3 LNG 24.3 75 Re rhenium use 25.48 0.137 CRC 25.48 0.137 WEL 25.5 LNG 25.5 76 Os osmium use 24.7 0.130 CRC 24.7 0.130 WEL 25 LNG 24.7 77 Ir iridium use 25.10 0.131 CRC 25.10 0.131 WEL 25.1 LNG 25.06 78 Pt platinum use 25.86 0.133 CRC 25.86 0.133 WEL 25.9 79 Au gold use 25.418 0.129 CRC 25.418 0.129 WEL 25.42 LNG 25.36 80 Hg mercury (liquid) use 27.983 0.140 CRC 27.983 0.140 WEL 27.98 LNG 28.00 81 Tl thallium use 26.32 0.129 CRC 26.32 0.129 WEL 26.3 LNG 26.32 82 Pb lead use 26.650 0.129 CRC 26.650 0.129 WEL 26.4 LNG 26.84 83 Bi bismuth use 25.52 0.122 CRC 25.52 0.122 WEL 25.5 LNG 25.5 84 Po polonium use 26.4 LNG 26.4 86 Rn radon (gas) use 20.786 0.094 CRC 20.786 0.094 WEL 20.79 LNG 20.79 87 Fr francium use 31.80 LNG 31.80 89 Ac actinium use 27.2 0.120 CRC 27.2 0.120 WEL 27.2 LNG 27.2 90 Th thorium use 26.230 0.113 CRC 26.230 0.113 WEL 27.3 LNG 27.32 92 U uranium use 27.665 0.116 CRC 27.665 0.116 WEL 27.7 LNG 27.66 93 Np neptunium use 29.46 LNG 29.46 94 Pu plutonium use 35.5 LNG 35.5 95 Am americium use 62.7 LNG 62.7 == Notes == All values refer to 25 °C and to the thermodynamically stable standard state at that temperature unless noted. The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. An isotherm of the Van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal. == Other parameters, forms and applications == ===Other thermodynamic parameters=== We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for the finite size of the molecules.	1.92	-57.2	2.35	30	1.2	C
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The standard enthalpy of formation of ethylbenzene is $-12.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Calculate its standard enthalpy of combustion.	For example, the standard enthalpy of combustion of ethane gas refers to the reaction C2H6 (g) + (7/2) O2 (g) → 2 CO2 (g) + 3 H2O (l). However the standard enthalpy of combustion is readily measurable using bomb calorimetry. * Standard enthalpy of combustion is the enthalpy change when one mole of an organic compound reacts with molecular oxygen (O2) to form carbon dioxide and liquid water. Since enthalpy is a state function, its value is the same for any path between given initial and final states, so that the measured ΔH is the same as if the temperature stayed constant during the combustion.Engel and Reid p.65 For reactions which are incomplete, the equilibrium constant can be determined as a function of temperature. The standard enthalpy of formation is then determined using Hess's law. Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol . == Hess's law == For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. The enthalpy of formation of one mole of ethane gas refers to the reaction 2 C (graphite) + 3 H2 (g) → C2H6 (g). The standard enthalpy of formation, which has been determined for a vast number of substances, is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). * Standard enthalpy of formation is the enthalpy change when one mole of any compound is formed from its constituent elements in their standard states. Accordingly, the calculation of standard enthalpy of reaction is the most established way of quantifying the conversion of chemical potential energy into thermal energy. ==Enthalpy of reaction for standard conditions defined and measured== The standard enthalpy of a reaction is defined so as to depend simply upon the standard conditions that are specified for it, not simply on the conditions under which the reactions actually occur. Petrucci, Harwood and Herring, pages 241–243 Finally the reaction enthalpy may be estimated using bond energies for the bonds which are broken and formed in the reaction of interest. It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method. == Use in calculation for other reactions == The standard enthalpy change of any reaction can be calculated from the standard enthalpies of formation of reactants and products using Hess's law. Most values of standard thermochemical data are tabulated at either (25°C, 1 bar) or (25°C, 1 atm). For example, the standard enthalpy of formation of carbon dioxide is the enthalpy of the following reaction under the above conditions: :C(s, graphite) + O2(g) -> CO2(g) All elements are written in their standard states, and one mole of product is formed. This method is only approximate, however, because a reported bond energy is only an average value for different molecules with bonds between the same elements.Petrucci, Harwood and Herring, pages 422–423 ==References== Category:Enthalpy Category:Thermochemistry Category:Thermodynamics pl:Standardowe molowe ciepło tworzenia The standard enthalpy of reaction (denoted \Delta_{\text {rxn}} H^\ominus or \Delta H_{\text {reaction}}^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). Progress in Energy and Combustion Science is a bimonthly peer-reviewed review journal published by Elsevier. The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products Elements in their standard states make no contribution to the enthalpy calculations for the reaction, since the enthalpy of an element in its standard state is zero.	0.63	-4564.7	'-2.0'	7.58	-50	B
A scientist proposed the following equation of state: $$ p=\frac{R T}{V_{\mathrm{m}}}-\frac{B}{V_{\mathrm{m}}^2}+\frac{C}{V_{\mathrm{m}}^3} $$ Show that the equation leads to critical behaviour. Find the critical constants of the gas in terms of $B$ and $C$ and an expression for the critical compression factor.	When the equation expressed in reduced form, an identical equation is obtained for all gases: : P_\text{r} = \frac{3 T_\text{r}}{V_\text{r} - b'} - \frac{1}{b' \sqrt{T_\text{r}} V_\text{r} \left(V_\text{r}+b'\right)} where b' is: : b' = 2^{1/3}-1 \approx 0.25992 In addition, the compressibility factor at the critical point is the same for every substance: : Z_\text{c}=\frac{p_\text{c} V_\text{c}}{R T_\text{c}}=1/3 \approx 0.33333 This is an improvement over the van der Waals equation prediction of the critical compressibility factor, which is Z_\text{c} = 3/8 = 0.375 . It predicts a value of 3/8 = 0.375 that is found to be an overestimate when compared to real gases. ==Compressibility factor at the critical point== The compressibility factor at the critical point, which is defined as Z_c=\frac{P_c v_c \mu}{R T_c}, where the subscript c indicates physical quantities measured at the critical point, is predicted to be a constant independent of substance by many equations of state. Here T_c and P_c are known as the critical temperature and critical pressure of a gas. As for the compressibility of gases, the principle of corresponding states indicates that any pure gas at the same reduced temperature, T_r, and reduced pressure, P_r, should have the same compressibility factor. Because interactions between large numbers of molecules are rare, the virial equation is usually truncated after the third term. page73 When this truncation is assumed, the compressibility factor is linked to the intermolecular-force potential φ by: :Z = 1 + 2\pi \frac{N_\text{A}}{V_\text{m}} \int_0^\infty \left(1 - \exp \left(\frac{\varphi}{kT}\right)\right) r^2 dr The Real gas article features more theoretical methods to compute compressibility factors. ==Physical mechanism of temperature and pressure dependence== Deviations of the compressibility factor, Z, from unity are due to attractive and repulsive intermolecular forces. By substituting the variables in the reduced form and the compressibility factor at critical point : \\{p_\text{r}=p/P_\text{c}, T_\text{r}=T/T_\text{c}, V_\text{r}=V_\text{m}/V_\text{c}, Z_\text{c}=\frac{P_\text{c} V_\text{c}}{R T_\text{c}}\\} we obtain : p_\text{r} P_\text{c} = \frac{R\,T_\text{r} T_\text{c}}{V_\text{r} V_\text{c}-b} - \frac{a \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} V_\text{c}\left(V_\text{r} V_\text{c+}b\right)} = \frac{R\,T_\text{r} T_\text{c}}{V_\text{r} V_\text{c}-\frac{\Omega_b\,R T_\text{c}}{P_\text{c}}} - \frac{\frac{\Omega_a\,R^2 T_\text{c}^2}{P_\text{c}} \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} V_\text{c}\left(V_\text{r} V_\text{c}+\frac{\Omega_b\,R T_\text{c}}{P_\text{c}}\right)} = : = \frac{R\,T_\text{r} T_\text{c}}{V_\text{c}\left(V_\text{r}-\frac{\Omega_b\,R T_\text{c}}{P_\text{c} V_\text{c}}\right)} - \frac{\frac{\Omega_a\,R^2 T_\text{c}^2}{P_\text{c}} \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} V_\text{c}^2\left(V_\text{r}+\frac{\Omega_b\,R T_\text{c}}{P_\text{c} V_\text{c}}\right)} = \frac{R\,T_\text{r} T_\text{c}}{V_\text{c}\left(V_\text{r}-\frac{\Omega_b}{Z_\text{c}}\right)} - \frac{\frac{\Omega_a\,R^2 T_\text{c}^2}{P_\text{c}} \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} V_\text{c}^2\left(V_\text{r}+\frac{\Omega_b}{Z_\text{c}}\right)} thus leading to : p_\text{r} = \frac{R\,T_\text{r} T_\text{c}}{P_\text{c} V_\text{c}\left(V_\text{r}-\frac{\Omega_b}{Z_\text{c}}\right)} - \frac{\frac{\Omega_a\,R^2 T_\text{c}^2}{P_\text{c}^2} \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} V_\text{c}^2\left(V_\text{r}+\frac{\Omega_b}{Z_\text{c}}\right)} = \frac{T_\text{r}}{Z_\text{c}\left(V_\text{r}-\frac{\Omega_b}{Z_\text{c}}\right)} - \frac{\frac{\Omega_a}{Z_\text{c}^2} \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} \left(V_\text{r}+\frac{\Omega_b}{Z_\text{c}}\right)} Thus, the Soave–Redlich–Kwong equation in reduced form only depends on ω and Z_\text{c} of the substance, contrary to both the VdW and RK equation which are consistent with the theorem of corresponding states and the reduced form is one for all substances: : p_\text{r} = \frac{T_\text{r}}{Z_\text{c}\left(V_\text{r}-\frac{\Omega_b}{Z_\text{c}}\right)} - \frac{\frac{\Omega_a}{Z_\text{c}^2} \alpha\left(\omega, T_\text{r}\right)}{V_\text{r} \left(V_\text{r}+\frac{\Omega_b}{Z_\text{c}}\right)} We can also write it in the polynomial form, with: : A = \frac{a \alpha P}{R^2 T^2} : B = \frac{bP}{RT} In terms of the compressibility factor, we have: : 0 = Z^3-Z^2+Z\left(A-B-B^2\right) - AB. The substance-specific constants a and b can be calculated from the critical properties p_\text{c} and V_\text{c} (noting that V_\text{c} is the molar volume at the critical point and p_\text{c} is the critical pressure) as: : a = 3 p_\text{c} V_\text{c}^2 : b = \frac{V_\text{c}}{3}. The table below for a selection of gases uses the following conventions: * T_c: critical temperature [K] * P_c: critical pressure [Pa] * v_c: critical specific volume [m3⋅kg−1] * R: gas constant (8.314 J⋅K−1⋅mol−1) * \mu: Molar mass [kg⋅mol−1] Substance P_c [Pa] T_c [K] v_c [m3/kg] Z_c H2O 647.3 0.23 4He 5.2 0.31 He 5.2 0.30 H2 33.2 0.30 Ne 44.5 0.29 N2 126.2 0.29 Ar 150.7 0.29 Xe 289.7 0.29 O2 154.8 0.291 CO2 304.2 0.275 SO2 430.0 0.275 CH4 190.7 0.285 C3H8 370.0 0.267 ==See also== Van der Waals equation Equation of state Compressibility factors Johannes Diderik van der Waals equation Noro- Frenkel law of corresponding states ==References== ==External links== Properties of Natural Gases. The unique relationship between the compressibility factor and the reduced temperature, T_r, and the reduced pressure, P_r, was first recognized by Johannes Diderik van der Waals in 1873 and is known as the two-parameter principle of corresponding states. The equation is given below, as are relationships between its parameters and the critical constants: : \begin{align} p &= \frac{R\,T}{V_\text{m} - b} - \frac{a}{\sqrt{T}\,V_\text{m}\left(V_\text{m} + b\right)} \\\\[3pt] a &= \frac{\Omega_a\,R^2 T_\text{c}^\frac{5}{2}}{p_\text{c}} \approx 0.42748\frac{R^2\,T_\text{c}^\frac{5}{2}}{P_\text{c}} \\\\[3pt] b &= \frac{\Omega_b\,R T_\text{c}}{P_\text{c}} \approx 0.08664\frac{R\,T_\text{c}}{p_\text{c}} \\\\[3pt] \Omega_a &= \left[9\left(2^{1/3}-1\right)\right]^{-1} \approx 0.42748 \\\\[3pt] \Omega_b &= \frac{2^{1/3}-1}{3} \approx 0.08664 \end{align} Another, equivalent form of the Redlich–Kwong equation is the expression of the model's compressibility factor: : Z=\frac{p V_\text{m}}{RT} = \frac{V_\text{m}}{V_\text{m} - b} - \frac{a}{R T^{3/2} \left(V_\text{m} + b\right)} The Redlich–Kwong equation is adequate for calculation of gas phase properties when the reduced pressure (defined in the previous section) is less than about one-half of the ratio of the temperature to the reduced temperature, : P_\text{r} < \frac{T}{2T_\text{c}}. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document) In general, deviation from ideal behaviour becomes more significant the closer a gas is to a phase change, the lower the temperature or the larger the pressure. Above the Boyle temperature, the compressibility factor is always greater than unity and increases slowly but steadily as pressure increases. ==Experimental values== It is extremely difficult to generalize at what pressures or temperatures the deviation from the ideal gas becomes important. Expressions for (a,b) written as functions of (T_\text{c},p_\text{c}) may also be obtained and are often used to parameterize the equation because the critical temperature and pressure are readily accessible to experiment. Cubic equations of state are a specific class of thermodynamic models for modeling the pressure of a gas as a function of temperature and density and which can be rewritten as a cubic function of the molar volume. Experimental values for the compressibility factor confirm this. The quantum gases hydrogen, helium, and neon do not conform to the corresponding-states behavior and the reduced pressure and temperature for those three gases should be redefined in the following manner to improve the accuracy of predicting their compressibility factors when using the generalized graphs: : T_r = \frac{T}{T_c + 8} and P_r = \frac{P}{P_c + 8} where the temperatures are in kelvins and the pressures are in atmospheres. ==Reading a generalized compressibility chart== In order to read a compressibility chart, the reduced pressure and temperature must be known. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document) *Theorem of corresponding states on SklogWiki. The compressibility factor is defined in thermodynamics and engineering frequently as: :Z = \frac{p}{\rho R_\text{specific} T}, where p is the pressure, \rho is the density of the gas and R_\text{specific} = \frac{R}{M} is the specific gas constant, page 327 M being the molar mass, and the T is the absolute temperature (kelvin or Rankine scale). Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound- specific empirical constants as input. # The model should provide reasonable accuracy near the critical point, particularly for calculations of the compressibility factor and liquid density. # Gases deviate from ideal-gas behavior the most in the vicinity of the critical point. page 139 ==Theoretical models== The virial equation is especially useful to describe the causes of non-ideality at a molecular level (very few gases are mono-atomic) as it is derived directly from statistical mechanics: :Z = 1 + \frac{B}{V_\mathrm{m}} + \frac{C}{V_\mathrm{m}^2} + \frac{D}{V_\mathrm{m}^3} + \dots Where the coefficients in the numerator are known as virial coefficients and are functions of temperature. Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts that plot Z as a function of pressure at constant temperature.	0.333333	4.86	'-114.4'	0.5	+0.60	A
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The standard enthalpy of decomposition of the yellow complex $\mathrm{H}_3 \mathrm{NSO}_2$ into $\mathrm{NH}_3$ and $\mathrm{SO}_2$ is $+40 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Calculate the standard enthalpy of formation of $\mathrm{H}_3 \mathrm{NSO}_2$.	The standard enthalpy of formation is then determined using Hess's law. Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol . == Hess's law == For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. Coefficients from this source: : ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. This is true for all enthalpies of formation. This calculation has a tacit assumption of ideal solution between reactants and products where the enthalpy of mixing is zero. For example, the standard enthalpy of formation of carbon dioxide is the enthalpy of the following reaction under the above conditions: :C(s, graphite) + O2(g) -> CO2(g) All elements are written in their standard states, and one mole of product is formed. == Heat of vaporization == kJ/mol 1 H hydrogen (H2) use (H2) 0.904 CRC (H2) 0.90 LNG 0.904 2 He helium use 0.0829 CRC 0.08 LNG 0.0829 WEL 0.083 3 Li lithium use 136 LNG 147.1 WEL 147 Zhang et al. 136 4 Be beryllium use 292 LNG 297 WEL 297 Zhang et al. 292 5 B boron use 508 CRC 480 LNG 480 WEL 507 Zhang et al. 508 6 C carbon use WEL (sublimation) 715 7 N nitrogen (N2) use (N2) 5.57 CRC (N2) 5.57 LNG (N2) 5.577 WEL (per mole N atoms) 2.79 Zhang et al. 5.58 8 O oxygen (O2) use (O2) 6.82 CRC (O2) 6.82 LNG (O2) 6.820 WEL (per mole O atoms) 3.41 Zhang et al. 6.82 9 F fluorine (F2) use (F2) 6.62 CRC (F2) 6.62 LNG (F2) 6.62 WEL (per mole F atoms) 3.27 Zhang et al. 6.32 10 Ne neon use 1.71 CRC 1.71 LNG 1.71 WEL 1.75 Zhang et al. 1.9 11 Na sodium use 97.42 LNG 97.42 WEL 97.7 Zhang et al. 97.4 12 Mg magnesium use 128 LNG 128 WEL 128 Zhang et al. 132 13 Al aluminium use 284 CRC 294 LNG 294.0 WEL 293 Zhang et al. 284 14 Si silicon use 359 LNG 359 WEL 359 Zhang et al. 383 15 P phosphorus use 12.4 CRC 12.4 LNG 12.4 WEL 12.4 Zhang et al. 51.9 (white) 16 S sulfur use (mono) 45 CRC 45 LNG (mono) 45 WEL 9.8 Zhang et al. 45 17 Cl chlorine (Cl2) use (Cl2) 20.41 CRC (Cl2) 20.41 LNG (Cl2) 20.41 WEL (per mole Cl atoms) 10.2 Zhang et al. 20.4 18 Ar argon use 6.53 CRC 6.43 LNG 6.43 WEL 6.5 Zhang et al. 6.53 19 K potassium use 76.90 LNG 76.90 WEL 76.9 Zhang et al. 79.1 20 Ca calcium use 154.7 LNG 154.7 WEL 155 Zhang et al. 153 21 Sc scandium use 332.7 LNG 332.7 WEL 318 Zhang et al. 310 22 Ti titanium use 425 LNG 425 WEL 425 Zhang et al. 427 23 V vanadium use 444 LNG 459 WEL 453 Zhang et al. 451 24 Cr chromium use 339.5 LNG 339.5 WEL 339 Zhang et al. 347 25 Mn manganese use 221 LNG 221 WEL 220 Zhang et al. 225 26 Fe iron use 340 LNG 340 WEL 347 Zhang et al. 354 27 Co cobalt use 377 LNG 377 WEL 375 Zhang et al. 390 28 Ni nickel use 379 LNG 377.5 WEL 378 Zhang et al. 379 29 Cu copper use 300.4 LNG 300.4 WEL 300 Zhang et al. 305 30 Zn zinc use 115 LNG 123.6 WEL 119 Zhang et al. 115 31 Ga gallium use 256 CRC 254 LNG 254 WEL 256 Zhang et al. 256 32 Ge germanium use 334 CRC 334 LNG 334 WEL 334 Zhang et al. 330 33 As arsenic use 32.4 WEL 32.4 (sublimation) Zhang et al. 32.4 34 Se selenium use 95.48 CRC 95.48 LNG 95.48 WEL 26 Zhang et al. 95.5 35 Br bromine (Br2) use (Br2) 29.96 CRC (Br2) 29.96 LNG (Br2) 29.96 WEL (per mole Br atoms) 14.8 Zhang et al. 30 36 Kr krypton use 9.08 CRC 9.08 LNG 9.08 WEL 9.02 Zhang et al. 9.03 37 Rb rubidium use 75.77 LNG 75.77 WEL 72 Zhang et al. 69 38 Sr strontium use 141 LNG 136.9 WEL 137 Zhang et al. 141 39 Y yttrium use 390 LNG 365 WEL 380 Zhang et al. 363 40 Zr zirconium use 573 LNG 573 WEL 580 Zhang et al. 591 41 Nb niobium use 689.9 LNG 689.9 WEL 690 Zhang et al. 682 42 Mo molybdenum use 617 LNG 617 WEL 600 Zhang et al. 617 43 Tc technetium use 585.2 LNG 585.2 WEL 550 44 Ru ruthenium use 619 LNG 591.6 WEL 580 Zhang et al. 619 45 Rh rhodium use 494 LNG 494 WEL 495 Zhang et al. 493 46 Pd palladium use 358 LNG 362 WEL 380 Zhang et al. 358 47 Ag silver use 254 LNG 258 WEL 255 Zhang et al. 254 48 Cd cadmium use 99.87 CRC 99.87 LNG 99.9 WEL 100 Zhang et al. 100 49 In indium use 231.8 LNG 231.8 WEL 230 Zhang et al. 225 50 Sn tin use (white) 296.1 LNG (white) 296.1 WEL 290 Zhang et al. 296 51 Sb antimony use 193.43 LNG 193.43 WEL 68 Zhang et al. 193 52 Te tellurium use 114.1 CRC 114.1 LNG 114.1 WEL 48 Zhang et al. 114 53 I iodine (I2) use (I2) 41.57 CRC (I2) 41.57 LNG (I2) 41.6 WEL (per mole I atoms) 20.9 Zhang et al. 41.6 54 Xe xenon use 12.64 CRC 12.57 LNG 12.64 WEL 12.64 Zhang et al. 12.6 55 Cs caesium use 63.9 LNG 63.9 WEL 65 Zhang et al. 66.1 56 Ba barium use 140.3 CRC 140 LNG 140.3 WEL 140 Zhang et al. 142 57 La lanthanum use 400 LNG 402.1 WEL 400 Zhang et al. 400 58 Ce cerium use 398 LNG 398 WEL 350 Zhang et al. 398 59 Pr praseodymium use 331 LNG 331 WEL 330 Zhang et al. 331 60 Nd neodymium use 289 LNG 289 WEL 285 Zhang et al. 289 61 Pm promethium use 289 LNG 289 WEL 290 62 Sm samarium use 192 LNG 165 WEL 175 Zhang et al. 192 63 Eu europium use 176 LNG 176 WEL 175 Zhang et al. 176 64 Gd gadolinium use 301.3 LNG 301.3 WEL 305 Zhang et al. 301 65 Tb terbium use 391 LNG 293 WEL 295 Zhang et al. 391 66 Dy dysprosium use 280 LNG 280 WEL 280 Zhang et al. 280 67 Ho holmium use 251 LNG 71 WEL 265 Zhang et al. 251 68 Er erbium use 280 LNG 280 WEL 285 Zhang et al. 280 69 Tm thulium use 191 LNG 247 WEL 250 Zhang et al. 191 70 Yb ytterbium use 129 LNG 159 WEL 160 Zhang et al. 129 71 Lu lutetium use 414 LNG 414 WEL 415 Zhang et al. 414 72 Hf hafnium use 648 LNG 571 WEL 630 Zhang et al. 648 73 Ta tantalum use 732.8 LNG 732.8 WEL 735 Zhang et al. 753 74 W tungsten use 806.7 LNG 806.7 WEL 800 Zhang et al. 774 75 Re rhenium use 704 LNG 704 WEL 705 Zhang et al. 707 76 Os osmium use 678 LNG 738 WEL 630 Zhang et al. 678 77 Ir iridium use 564 LNG 231.8 WEL 560 Zhang et al. 564 78 Pt platinum use 510 LNG 469 WEL 490 Zhang et al. 510 79 Au gold use 342 CRC 324 LNG 324 WEL 330 Zhang et al. 342 80 Hg mercury use 59.11 CRC 59.11 LNG 59.1 WEL 59.2 Zhang et al. 58.2 81 Tl thallium use 165 LNG 165 WEL 165 Zhang et al. 162 82 Pb lead use 179.5 CRC 179.5 LNG 179.5 WEL 178 Zhang et al. 177 83 Bi bismuth use 179 CRC 151 LNG 151 WEL 160 Zhang et al. 179 84 Po polonium use 102.91 LNG 102.91 WEL about 100 85 At astatine use 54.39 (At2) GME 54.39 (At2) WEL about 40 86 Rn radon use 18.10 LNG 18.10 WEL 17 87 Fr francium use ca. 65 WEL about 65 88 Ra radium use 113 LNG 113 WEL about 125 89 Ac actinium use 400 WEL 400 90 Th thorium use 514 LNG 514 WEL 530 91 Pa protactinium use 481 LNG 481 WEL 470 92 U uranium use 417.1 LNG 417.1 WEL 420 93 Np neptunium use 336 LNG 336 WEL 335 94 Pu plutonium use 333.5 LNG 333.5 WEL 325 == Notes == * Values refer to the enthalpy change in the conversion of liquid to gas at the boiling point (normal, 101.325 kPa). == References == ===Zhang et al.=== ===CRC=== As quoted from various sources in an online version of: * David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 84th Edition. It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method. == Use in calculation for other reactions == The standard enthalpy change of any reaction can be calculated from the standard enthalpies of formation of reactants and products using Hess's law. The Sabatier reaction or Sabatier process produces methane and water from a reaction of hydrogen with carbon dioxide at elevated temperatures (optimally 300–400 °C) and pressures (perhaps 3 MPa ) in the presence of a nickel catalyst. However O2 is an element in its standard state, so that \Delta_{\text{f}} H^{\ominus }(\text{O}_2) = 0, and the heat of reaction is simplified to :\Delta_{\text{r}} H^{\ominus } = [\Delta_{\text{f}} H^{\ominus }(\text{CO}_2) + 2\Delta_{\text{f}} H^{\ominus } (\text{H}_2{}\text{O})] - \Delta_{\text{f}} H^{\ominus }(\text{CH}_4), which is the equation in the previous section for the enthalpy of combustion \Delta_{\text{comb}}H^{\ominus }. == Key concepts for enthalpy calculations == When a reaction is reversed, the magnitude of ΔH stays the same, but the sign changes. All elements in their reference states (oxygen gas, solid carbon in the form of graphite, etc.) have a standard enthalpy of formation of zero, as there is no change involved in their formation. However the standard enthalpy of combustion is readily measurable using bomb calorimetry. thumb\|The Mollier enthalpy–entropy diagram for water and steam. J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products Elements in their standard states make no contribution to the enthalpy calculations for the reaction, since the enthalpy of an element in its standard state is zero. Boca Raton, Florida, 2003; Section 6, Fluid Properties; Enthalpy of Vaporization ===GME=== Kugler HK & Keller C (eds) 1985, Gmelin handbook of inorganic and organometallic chemistry, 8th ed.,	4	0.0024	0.0	-383	7.00	D
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A sample of carbon dioxide of mass $2.45 \mathrm{~g}$ at $27.0^{\circ} \mathrm{C}$ is allowed to expand reversibly and adiabatically from $500 \mathrm{~cm}^3$ to $3.00 \mathrm{dm}^3$. What is the work done by the gas?	Such work done by compression is thermodynamic work as here defined. When work, for example pressure–volume work, is done on its surroundings by a closed system that cannot pass heat in or out because it is confined by an adiabatic wall, the work is said to be adiabatic for the system as well as for the surroundings. Carbon dioxide reforming (also known as dry reforming) is a method of producing synthesis gas (mixtures of hydrogen and carbon monoxide) from the reaction of carbon dioxide with hydrocarbons such as methane with the aid of noble metal catalysts (typically Ni or Ni alloys). For a quasi-static adiabatic process, the change in internal energy is equal to minus the integral amount of work done by the system, so the work also depends only on the initial and final states of the process and is one and the same for every intermediate path. The work is due to change of system volume by expansion or contraction of the system. Changes in the potential energy of a body as a whole with respect to forces in its surroundings, and in the kinetic energy of the body moving as a whole with respect to its surroundings, are by definition excluded from the body's cardinal energy (examples are internal energy and enthalpy). ===Nearly reversible transfer of energy by work in the surroundings=== In the surroundings of a thermodynamic system, external to it, all the various mechanical and non-mechanical macroscopic forms of work can be converted into each other with no limitation in principle due to the laws of thermodynamics, so that the energy conversion efficiency can approach 100% in some cases; such conversion is required to be frictionless, and consequently adiabatic.F.C.Andrews Thermodynamics: Principles and Applications (Wiley- Interscience 1971), , p.17-18. To get an actual and precise physical measurement of a quantity of thermodynamic work, it is necessary to take account of the irreversibility by restoring the system to its initial condition by running a cycle, for example a Carnot cycle, that includes the target work as a step. Adiabatic work is done without matter transfer and without heat transfer. Pressure gain combustion is a combustion process whereby gas expansion by heat release is constrained, causing a rise in stagnation pressure and allowing work extraction by expansion to the initial pressure. Synthesis gas is conventionally produced via the steam reforming reaction or coal gasification. In a process of transfer of energy from or to a thermodynamic system, the change of internal energy of the system is defined in theory by the amount of adiabatic work that would have been necessary to reach the final from the initial state, such adiabatic work being measurable only through the externally measurable mechanical or deformation variables of the system, that provide full information about the forces exerted by the surroundings on the system during the process. Work in compressed air, compressed air work or hyperbaric work is occupational activity in an enclosed atmosphere at a controlled ambient pressure significantly higher than the adjacent normal atmospheric pressure. Work done on a thermodynamic system, by devices or systems in the surroundings, is performed by actions such as compression, and includes shaft work, stirring, and rubbing. Thermodynamic work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. Then for a given amount of work transferred, the exchange of volumes involves different pressures, inversely with the piston areas, for mechanical equilibrium. The quantity of thermodynamic work is defined as work done by the system on its surroundings. # The gasification process occurs as the char reacts with steam and carbon dioxide to produce carbon monoxide and hydrogen, via the reactions C + H2O → H2 \+ CO and C + CO2 → 2CO. Gasification is a process that converts biomass- or fossil fuel-based carbonaceous materials into gases, including as the largest fractions: nitrogen (N2), carbon monoxide (CO), hydrogen (H2), and carbon dioxide (). In particular, in principle, all macroscopic forms of work can be converted into the mechanical work of lifting a weight, which was the original form of thermodynamic work considered by Carnot and Joule (see History section above). Such work is adiabatic for the surroundings, even though it is associated with friction within the system. Several kinds of thermodynamic work are especially important. The dry reforming reaction may be represented by: :CH4 + CO2 <=>[975^oC] 2CO + 2H2 Thus, two greenhouse gases are consumed and useful chemical building blocks, hydrogen and carbon monoxide, are produced.	21	-32	0.36	3.2	-194	E
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the work needed for a $65 \mathrm{~kg}$ person to climb through $4.0 \mathrm{~m}$ on the surface of the Earth.	Other definitions which roughly produce the same numbers have been devised, such as: : \text{1 MET}\ = 1 \, \frac{\text{kcal}}{\text{kg}\times\text{h}}\ = 4.184 \, \frac{\text{kJ}}{\text{kg}\times\text{h}} = 1.162 \, \frac{\text{W}}{\text{kg}} where * kcal = kilocalorie * kg = kilogram * h = hour * kJ = kilojoule * W = watt ===Based on watts produced and body surface area=== Still another definition is based on the body surface area, BSA, and energy itself, where the BSA is expressed in m2: : \text{1 MET}\ = 58.2 \, \frac{\text{J}}{\text{s}\times\text{BSA}}\ = 58.2 \, \frac{\text{W}}{\text{m}^2} = 18.4 \, \frac{\text{Btu}}{\text{h}\times\text{ft}^2} which is equal to the rate of energy produced per unit surface area of an average person seated at rest. Work in compressed air, compressed air work or hyperbaric work is occupational activity in an enclosed atmosphere at a controlled ambient pressure significantly higher than the adjacent normal atmospheric pressure. Health and fitness studies often bracket cohort activity levels in MET⋅hours/week. ==Quantitative definitions== ===Based on oxygen utilization and body mass=== The original definition of metabolic equivalent of task is the oxygen used by a person in milliliters per minute per kilogram body mass divided by 3.5. The metabolic equivalent of task (MET) is the objective measure of the ratio of the rate at which a person expends energy, relative to the mass of that person, while performing some specific physical activity compared to a reference, currently set by convention at an absolute 3.5 mL of oxygen per kg per minute, which is the energy expended when sitting quietly by a reference individual, chosen to be roughly representative of the general population, and thereby suited to epidemiological surveys. A 4 MET activity expends 4 times the energy used by the body at rest. By convention, 1 MET is considered equivalent to the consumption of 3.5 ml O2·kg−1·min−1 (or 3.5 ml of oxygen per kilogram of body mass per minute) and is roughly equivalent to the expenditure of 1 kcal per kilogram of body weight per hour. In the winter of 1980-1981 Tasker was part of an eight-man team (with Alan Rouse, John Porter, Brian Hall, Adrian Burgess, Alan Burgess, Pete Thexton and Paul Nunn) attempting to make a difficult winter assault on the West Face of Mount Everest; this was unsuccessful but was recounted in Tasker's first book Everest the Cruel Way. A person could also achieve 120 MET-minutes by doing an 8 MET activity for 15 minutes. RMR measurements by calorimetry in medical surveys have shown that the conventional 1-MET value overestimates the actual resting O2 consumption and energy expenditures by about 20% to 30% on the average; body composition (ratio of body fat to lean body mass) accounted for most of the variance. ==Standardized definition for research== The Compendium of Physical Activities was developed for use in epidemiologic studies to standardize the assignment of MET intensities in physical activity questionnaires. If a person does a 4 MET activity for 30 minutes, he or she has done 4 x 30 = 120 MET-minutes (or 2.0 MET-hours) of physical activity. One MET is defined as 1 kcal/kg/hour and is roughly equivalent to the energy cost of sitting quietly. Since the RMR of a person depends mainly on lean body mass (and not total weight) and other physiological factors such as health status and age, actual RMR (and thus 1-MET energy equivalents) may vary significantly from the kcal/(kg·h) rule of thumb. Joe Tasker (12 May 1948 – 17 May 1982) was a British climber, active during the late 1970s and early 1980s. For example, 1 MET is the rate of energy expenditure while at rest. A small team consisting of Tasker, Boardman, and Doug Scott made an ascent of Kangchenjunga (at 8,598 m the third highest mountain in the world) by a new route from the North-West in 1979 (with Georges Bettembourg also on the team but not making the summit); this was also the first ascent of the mountain without the use of supplementary oxygen. Tasker had delivered his manuscript for his second book, Savage Arena, which recounted his climbing life from the 1960s-1980, on the eve of his departure for the British Everest expedition in 1982. thumb\|upright=1.75\|An illustration of Dalton's law using the gases of air at sea level. The BSA of an average person is 1.8 m2 (19 ft2). At a vertex where both climbers are at peaks or both climbers are at valleys, the degree is four: both climbers may choose independently of each other which direction to go. At the vertex (0,0), the degree is one: the only possible direction for both climbers to go is onto the mountain. Although the RMR of any person may deviate from the reference value, MET can be thought of as an index of the intensity of activities: for example, an activity with a MET value of 2, such as walking at a slow pace (e.g., 3 km/h) would require twice the energy that an average person consumes at rest (e.g., sitting quietly). ==Use== MET: The ratio of the work metabolic rate to the resting metabolic rate. A MET is the ratio of the rate of energy expended during an activity to the rate of energy expended at rest.	2.0	2600	0.082	12	+87.8	B
What pressure would $131 \mathrm{g}$ of xenon gas in a vessel of volume $1.0 \mathrm{dm}^3$ exert at $25^{\circ} \mathrm{C}$ if it behaved as a van der Waals gas?	* ISO 11439: Compressed natural gas (CNG) cylinders. Further the volume of the gas is (4πr3)/3. Pressure vessels for gas storage may also be classified by volume. * IS 2825–1969 (RE1977)_code_unfired_Pressure_vessels. * EN 286 (Parts 1 to 4): European standard for simple pressure vessels (air tanks), harmonized with Council Directive 87/404/EEC. VPT may refer to: * Valor por Tamaulipas * Vermont Public Television * Volume, temperature and pressure, the three parameters in the combined gas law Because of that, the design and certification of pressure vessels is governed by design codes such as the ASME Boiler and Pressure Vessel Code in North America, the Pressure Equipment Directive of the EU (PED), Japanese Industrial Standard (JIS), CSA B51 in Canada, Australian Standards in Australia and other international standards like Lloyd's, Germanischer Lloyd, Det Norske Veritas, Société Générale de Surveillance (SGS S.A.), Lloyd’s Register Energy Nederland (formerly known as Stoomwezen) etc. Note that where the pressure-volume product is part of a safety standard, any incompressible liquid in the vessel can be excluded as it does not contribute to the potential energy stored in the vessel, so only the volume of the compressible part such as gas is used. ===List of standards=== * EN 13445: The current European Standard, harmonized with the Pressure Equipment Directive (Originally "97/23/EC", since 2014 "2014/68/EU"). The very small vessels used to make liquid butane fueled cigarette lighters are subjected to about 2 bar pressure, depending on ambient temperature. If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. The exact formula varies with the tank shape but depends on the density, ρ, and maximum allowable stress σ of the material in addition to the pressure P and volume V of the vessel. New York:McGraw-Hill, , pg 108 thumb\|300px\|Stress in the cylinder body of a pressure vessel. EN 13445 - Unfired Pressure Vessels is a standard that provides rules for the design, fabrication, and inspection of pressure vessels EN 13445 consists of 8 parts: * EN 13445-1 : Unfired pressure vessels - Part 1: General * EN 13445-2 : Unfired pressure vessels - Part 2: Materials * EN 13445-3 : Unfired pressure vessels - Part 3: Design * EN 13445-4 : Unfired pressure vessels - Part 4: Fabrication * EN 13445-5 : Unfired pressure vessels - Part 5: Inspection and testing * EN 13445-6 : Unfired pressure vessels - Part 6: Requirements for the design and fabrication of pressure vessels and pressure parts constructed from spheroidal graphite cast iron * EN 13445-8 : Unfired pressure vessels - Part 8: Additional requirements for pressure vessels of aluminium and aluminium alloys * EN 13445-10:2015 : Unfired pressure vessels - Part 10: Additional requirements for pressure vessels of nickel and nickel alloys. A gas cylinder is a pressure vessel for storage and containment of gases at above atmospheric pressure. From about 1975 until now, the standard pressure is . Hydraulic (filled with water) testing pressure is usually 50% higher than the working pressure. ==== Vessel thread ==== Until 1990, high pressure cylinders were produced with conical (tapered) threads. PV Publishing, Inc. Oklahoma City, OK ==Further reading== * Megyesy, Eugene F. (2008, 14th ed.) Pressure Vessel Handbook. ISBN 978-0-626-23561-1 == See also == * * * * * * * * * * * * * - a small, inexpensive, disposable metal gas cylinder for providing pneumatic power * * * * – a device for measuring leaf water potentials * * * or Knock-out drum * * * ==Notes== ==References== * A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed. * E.P. Popov, Engineering Mechanics of Solids, 1st ed. * Megyesy, Eugene F. "Pressure Vessel Handbook, 14th Edition." High-pressure gas cylinders are also called bottles. For a stored gas, PV is proportional to the mass of gas at a given temperature, thus :M = {3 \over 2} nRT {\rho \over \sigma}. (see gas law) The other factors are constant for a given vessel shape and material. * ASME Boiler and Pressure Vessel Code Section VIII: Rules for Construction of Pressure Vessels.	22	0.0182	1.25	3.07	260	A
A constant-volume perfect gas thermometer indicates a pressure of $6.69 \mathrm{kPa}$ at the triple point temperature of water (273.16 K). What change of pressure indicates a change of $1.00 \mathrm{~K}$ at the latter temperature?	:V \propto T\, or :\frac{V}{T}=k V is the volume, T is the thermodynamic temperature, k is the constant for the system. k is not a fixed constant across all systems and therefore needs to be found experimentally for a given system through testing with known temperature values. ==Pressure Thermometer and Absolute Zero== thumb\|left\|180px\|Plots of pressure vs temperature for three different gas samples extrapolate to absolute zero. thumb\|400px\|Diagram showing pressure difference induced by a temperature difference. Historically, the Kelvin scale was developed from the Celsius scale, such that 273.15 K was 0 °C (the approximate melting point of ice) and a change of one kelvin was exactly equal to a change of one degree Celsius. The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by * (1848 scale) = 100 () / () On this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature. The pressure melting point is nearly a constant 0 °C at pressures above the triple point at 611.7 Pa, where water can exist in only the solid or liquid phases, through atmospheric pressure (100 kPa) until about 10 MPa. The kelvin, symbol K, is a unit of measurement for temperature. By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use. For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature. In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings. :: \gamma =\frac{ \left( c_p \right)_{air} * P }{ \lambda_v * MW_{ratio} } : \gamma = psychrometric constant [kPa °C−1], : P = atmospheric pressure [kPa], : \lambda_v = latent heat of water vaporization, 2.45 [MJ kg−1], : c_p = specific heat of air at constant pressure, [MJ kg−1 °C−1], : MW_{ratio} = ratio molecular weight of water vapor/dry air = 0.622. The psychrometric constant \gamma relates the partial pressure of water in air to the air temperature. In the early decades of the 20th century, the Kelvin scale was often called the "absolute Celsius" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.For example, Encyclopaedia Britannica editions from the 1920s and 1950s, one example being the article "Planets". === Triple point standard === In 1873, William Thomson's older brother James coined the term triple point to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium. The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water." In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol . English translation (extract). that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0° and 100° C. In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was "now one of the major sources of the observed variability between different realizations of the water triple point", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water. === 2019 redefinition === In 2005, the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method. Thus an increment of 1 °C equals of the temperature difference between the melting and boiling points. To the extent that the gas is ideal, the pressure depends linearly on temperature, and the extrapolation to zero pressure occurs at absolute zero. The Kelvin scale is an absolute scale, which is defined such that 0 K is absolute zero and a change of thermodynamic temperature by 1 kelvin corresponds to a change of thermal energy by . In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly 273.15 + 0.01 = 273.16 degrees Kelvin. This value of "−273" was the negative reciprocal of 0.00366—the accepted coefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value. The pressure melting point of ice is the temperature at which ice melts at a given pressure.	48	16	2.0	0.0182	0.0245	E
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the work needed for a $65 \mathrm{~kg}$ person to climb through $4.0 \mathrm{~m}$ on the surface of the Moon $\left(g=1.60 \mathrm{~m} \mathrm{~s}^{-2}\right)$.	The acceleration due to gravity on the surface of the Moon is approximately 1.625 m/s2, about 16.6% that on Earth's surface or 0.166 . The mass of the Moon is M = 7.3458 × 1022 kg and the mean density is 3346 kg/m3. Work in compressed air, compressed air work or hyperbaric work is occupational activity in an enclosed atmosphere at a controlled ambient pressure significantly higher than the adjacent normal atmospheric pressure. thumb\|Apollo astronauts work on the Moon to collect samples and explore. The lunar GM = 4902.8001 km3/s2 from GRAIL analyses. Consequently, it is conventional to express the lunar mass M multiplied by the gravitational constant G. The atmosphere of the Moon is a very scant presence of gases surrounding the Moon. Another important source is the bombardment of the lunar surface by micrometeorites, the solar wind, and sunlight, in a process known as sputtering. == Escape velocity and atmospheric hold == Gases can: * be re-implanted into the regolith as a result of the Moon's gravity; * escape the Moon entirely if the particle is moving at or above the lunar escape velocity of , or ; * be lost to space either by solar radiation pressure or, if the gases are ionized, by being swept away in the solar wind's magnetic field. == Composition == What little atmosphere the Moon has consists of some unusual gases, including sodium and potassium, which are not found in the atmospheres of Earth, Mars, or Venus. Because weight is directly dependent upon gravitational acceleration, things on the Moon will weigh only 16.6% (= 1/6) of what they weigh on the Earth. ==Gravitational field== The gravitational field of the Moon has been measured by tracking the radio signals emitted by orbiting spacecraft. The ancient lunar atmosphere was eventually stripped away by solar winds and dissipated into space. == See also == * Atmosphere of Mercury * Exosphere * Lunar Atmosphere and Dust Environment Explorer (LADEE) * Orders of magnitude (pressure) * Sodium tail of the Moon == References == Category:Lunar science Moon Moon The lunar GM is 1/81.30057 of the Earth's GM. == Theory == For the lunar gravity field, it is conventional to use an equatorial radius of R = 1738.0 km. thumb\|upright=1.5\|At the Swamp Works, a sculpture made of lunar soil simulant representing construction on the Moon by robots working together with humans. The average daytime abundances of the elements known to be present in the lunar atmosphere, in atoms per cubic centimeter, are as follows: Argon: 20,000–100,000 Helium: 5,000–30,000 Neon: up to 20,000 Sodium: 70 Potassium: 17 Hydrogen: fewer than 17 This yields approximately 80,000 total atoms per cubic centimeter, marginally higher than the quantity posited to exist in the atmosphere of Mercury. It returned approximately of Lunar surface material. The building is where Apollo astronauts practiced working with the Lunar Module for lunar landings and extravehicular activities. thumb\|Students traverse a simulated crater in a moonbuggy they designed and built themselves. The NASA Human Exploration Rover Challenge, prior to 2014 referred to as the Great Moonbuggy Race, is an annual competition for high school and college students to design, build, and race human-powered, collapsible vehicles over simulated lunar/Martian terrain. The obstacles are constructed of discarded tires, plywood, some 20 tons of gravel and five tons of sand, all to simulate lunar craters, basins, and rilles. * The moonbuggy (pre-2014) must fit into a cube and be no more than 4 ft wide. Roger Joseph Boscovich was the first modern astronomer to argue for the lack of atmosphere around the Moon in his De lunae atmosphaera (1753). == Sources == One source of the lunar atmosphere is outgassing: the release of gases such as radon and helium resulting from radioactive decay within the crust and mantle. The C31 coefficient is large. ==Simulating lunar gravity== In January 2022 China was reported by the South China Morning Post to have built a small (60 centimeters in diameter) research facility to simulate low lunar gravity with the help of magnets. National Academies Press, Washington, DC (1997). ==Sample- return missions== ===First missions=== thumb\|Lunar sample 60016 on display at Space Center Houston Lunar Samples Vault, at NASA's Johnson Space Center The Apollo program returned over of lunar rocks and regolith (including lunar 'soil') to the Lunar Receiving Laboratory in Houston.Orloff 2004, "Extravehicular Activity" Today, 75% of the samples are stored at the Lunar Sample Laboratory Facility built in 1979.	1.22	0.245	420.0	4	0.264	C
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When $120 \mathrm{mg}$ of naphthalene, $\mathrm{C}_{10} \mathrm{H}_8(\mathrm{~s})$, was burned in a bomb calorimeter the temperature rose by $3.05 \mathrm{~K}$. By how much will the temperature rise when $10 \mathrm{mg}$ of phenol, $\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}(\mathrm{s})$, is burned in the calorimeter under the same conditions?	The high heat values are conventionally measured with a bomb calorimeter. The temperature may depend on pressure, because at lower pressure there will be more dissociation of the combustion products, implying a lower adiabatic temperature. ≈6332 Aluminium Oxygen 3732 6750 Lithium Oxygen 2438 4420 Phosphorus (white) Oxygen 2969 5376 Zirconium Oxygen 4005 7241 ==Thermodynamics== thumb\|right\|300px\|First law of thermodynamics for a closed reacting system From the first law of thermodynamics for a closed reacting system we have :{}_RQ_P - {}_RW_P = U_P - U_R where, {}_RQ_P and {}_RW_P are the heat and work transferred from the system to the surroundings during the process, respectively, and U_R and U_P are the internal energy of the reactants and products, respectively. That is, the heat of combustion, ΔH°comb, is the heat of reaction of the following process: : (std.) + (c + - ) (g) → c (g) + (l) + (g) Chlorine and sulfur are not quite standardized; they are usually assumed to convert to hydrogen chloride gas and or gas, respectively, or to dilute aqueous hydrochloric and sulfuric acids, respectively, when the combustion is conducted in a bomb calorimeter containing some quantity of water. == Ways of determination == ===Gross and net=== Zwolinski and Wilhoit defined, in 1972, "gross" and "net" values for heats of combustion. * However, for true energy calculations in some specific cases, the higher heating value is correct. They may also be calculated as the difference between the heat of formation ΔH of the products and reactants (though this approach is somewhat artificial since most heats of formation are typically calculated from measured heats of combustion). Since the heat of combustion of these elements is known, the heating value can be calculated using Dulong's Formula: LHV [kJ/g]= 33.87mC \+ 122.3(mH \- mO ÷ 8) + 9.4mS where mC, mH, mO, mN, and mS are the contents of carbon, hydrogen, oxygen, nitrogen, and sulfur on any (wet, dry or ash free) basis, respectively. === Higher heating value === The higher heating value (HHV; gross energy, upper heating value, gross calorific value GCV, or higher calorific value; HCV) indicates the upper limit of the available thermal energy produced by a complete combustion of fuel. Among the variables affecting burn rate are pressure and temperature. The calorific value is the total energy released as heat when a substance undergoes complete combustion with oxygen under standard conditions. As a result, these substances will burn at a constant pressure, which allows the gas to expand during the process. == Common flame temperatures == Assuming initial atmospheric conditions (1bar and 20 °C), the following tableSee under "Tables" in the external references below. lists the flame temperature for various fuels under constant pressure conditions. Thermokinetics deals with the study of thermal decomposition kinetics. ==See also== Thermogravimetry Differential thermal analysis Differential scanning calorimetry ==References== * Category:Chemical kinetics This value is important for fuels like wood or coal, which will usually contain some amount of water prior to burning. == Measuring heating values == The higher heating value is experimentally determined in a bomb calorimeter. Incomplete reaction at higher temperature further curtails the effect of a larger heat of combustion. There are a number of programs available that can calculate the adiabatic flame temperature taking into account dissociation through equilibrium constants (Stanjan, NASA CEA, AFTP). The temperatures mentioned here are for a stoichiometric fuel-oxidizer mixture (i.e. equivalence ratio φ = 1). It may be expressed with the quantities: * energy/mole of fuel * energy/mass of fuel * energy/volume of the fuel There are two kinds of enthalpy of combustion, called high(er) and low(er) heat(ing) value, depending on how much the products are allowed to cool and whether compounds like are allowed to condense. This table is in Standard cubic metres (1atm, 15°C), to convert to values per Normal cubic metre (1atm, 0°C), multiply above table by 1.0549. == See also == * Adiabatic flame temperature * Cost of electricity by source * Electrical efficiency * Energy content of fuel * Energy conversion efficiency * Energy density * Energy value of coal * Exothermic reaction * Figure of merit * Fire * Food energy * Internal energy * ISO 15971 * Mechanical efficiency * Thermal efficiency * Wobbe index: heat density == References == ==Further reading== * == External links == * NIST Chemistry WebBook * Category:Engineering thermodynamics Category:Combustion Category:Fuels Category:Thermodynamic properties Category:Nuclear physics Category:Thermochemistry == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li lithium use (T/K) 797 885 995 1144 1337 1610 CRC.f,k (T/°C) 524.3 612.3 722.1 871.2 1064.3 1337.1 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.673 - 8310 / (T/K) CR2 (T/K) liquid, m.p. to 1000 K: log (P/Pa) = 10.061 - 8023 / (T/K) 797.4 885.4 995.3 KAL (T/K) 1040 1145 1200 1275 1345 1415 1530 1630 SMI.a (T/K) liquid, 325..725 °C: log (P/Pa) = 9.625 - 7480 / (T/K) 777 867 981 4 Be beryllium use (T/K) 1462 1608 1791 2023 2327 2742 CRC.b (T/°C) 1189 (s) 1335 1518 1750 2054 2469 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.048 - 17020 / (T/K) - 0.4440 log (T/K) 1461.8 CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.792 - 15731 / (T/K) 1606.5 1789.2 SMI.c,g (T/K) solid, 942..1284 °C: log (P/Pa) = 12.115 - 18220 / (T/K) 1504 SMI.c,g (T/K) liquid, 1284..1582 °C: log (P/Pa) = 11.075 - 16590 / (T/K) 1647 1828 5 B boron use (T/K) 2348 2562 2822 3141 3545 4072 CRC.b (T/°C) 2075 2289 2549 2868 3272 3799 SMI.c (T/K) solid, 1052..1648 °C: log (P/Pa) = 13.255 - 21370 / (T/K) 1612 1744 1899 6 C carbon (graphite) use (T/K) 2839 3048 3289 3572 3908 CRC.h (T/°C) 2566 (s) 2775 (s) 3016 (s) 3299 (s) 3635 (s) 7 N nitrogen use (T/K) 37 41 46 53 62 77 CRC.a,d (T/°C) -236 (s) -232 (s) -226.8 (s) -220.2 (s) -211.1 (s) -195.9 KAL (T/K) 48.1 (s) 53.0 (s) 55.4 (s) 59.0 (s) 62.1 (s) 65.8 71.8 77.4 8 O oxygen use (T/K) 61 73 90 CRC.a,i (T/°C) -211.9 -200.5 -183.1 KAL (T/K) 55.4 61.3 64.3 68.8 72.7 77.1 83.9 90.2 9 F fluorine use (T/K) 38 44 50 58 69 85 CRC.a,d (T/°C) -235 (s) -229.5 (s) -222.9 (s) -214.8 -204.3 -188.3 KAL (T/K) 53 58 61 65.3 68.9 73.0 79.3 85.0 10 Ne neon use (T/K) 12 13 15 18 21 27 CRC.b (T/°C) -261 (s) -260 (s) -258 (s) -255 (s) -252 (s) -246.1 KAL (T/K) 16.3 (s) 18.1 (s) 19.0 (s) 20.4 (s) 21.6 (s) 22.9 (s) 24.9 27.1 11 Na sodium use (T/K) 554 617 697 802 946 1153 CRC.f,k (T/°C) 280.6 344.2 424.3 529 673 880.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.304 - 5603 / (T/K) CR2 (T/K) liquid, m.p. to 700 K: log (P/Pa) = 9.710 - 5377 / (T/K) 553.8 617.3 697.4 KAL (T/K) 729 807 846 904 954 1010 1095 1175 SMI.a (T/K) liquid, 158..437 °C: log (P/Pa) = 9.835 - 5480 / (T/K) 557 620 699 12 Mg magnesium use (T/K) 701 773 861 971 1132 1361 CRC.b (T/°C) 428 (s) 500 (s) 588 (s) 698 859 1088 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.495 - 7813 / (T/K) - 0.8253 log (T/K) 700.9 772.7 861.2 892.0 KAL (T/K) 891 979 1025 1085 1140 1205 1295 1375 SMI.a (T/K) solid, 287..605 °C: log (P/Pa) = 10.945 - 7741 / (T/K) 707 778 865 13 Al aluminium use (T/K) 1482 1632 1817 2054 2364 2790 CRC.b (T/°C) 1209 1359 1544 1781 2091 2517 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.465 - 17342 / (T/K) - 0.7927 log (T/K) CR2 (T/K) liquid, m.p. to 1800 K: log (P/Pa) = 10.917 - 16211 / (T/K) 1484.9 1634.7 1818.0 KAL (T/K) 1885 2060 2140 2260 2360 2430 2640 2790 SMI.c,l (T/K) liquid, 843..1465 °C: log (P/Pa) = 11.115 - 15630 / (T/K) 1406 1545 14 Si silicon use (T/K) 1908 2102 2339 2636 3021 3537 CRC.b (T/°C) 1635 1829 2066 2363 2748 3264 KAL (T/K) 2380 2590 2690 2840 2970 3100 3310 3490 SMI.c (T/K) solid, 1024..1410 °C: log (P/Pa) = 12.325 - 19720 / (T/K) 1600 SMI.c (T/K) liquid, 1410..1670 °C: log (P/Pa) = 11.675 - 18550 / (T/K) 1738 1917 15 P phosphorus (white) use (T/K) 279 307 342 388 453 549 CRC.c,e (T/°C) 6 (s) 34 (s) 69 115 180 276 KAL (T/K) 365 398 414 439 460 484 520.5 553.6 15 P phosphorus (red) use (T/K) 455 489 529 576 635 704 CRC.b,c (T/°C) 182 (s) 216 (s) 256 (s) 303 (s) 362 (s) 431 (s) 16 S sulfur use (T/K) 375 408 449 508 591 717 CRC.c (T/°C) 102 (s) 135 176 235 318 444 KAL (T/K) 462 505.7 528.0 561.3 590.1 622.5 672.4 717.8 17 Cl chlorine use (T/K) 128 139 153 170 197 239 CRC.a (T/°C) -145 (s) -133.7 (s) -120.2 (s) -103.6 (s) -76.1 -34.2 KAL (T/K) 158 (s) 170 (s) 176.3 187.4 197.0 207.8 224.3 239.2 18 Ar argon use (T/K) 47 53 61 71 87 CRC.a,d,l (T/°C) -226.4 (s) -220.3 (s) -212.4 (s) -201.7 (s) -186.0 KAL (T/K) 55.0 (s) 60.7 (s) 63.6 (s) 67.8 (s) 71.4 (s) 75.4 (s) 81.4 (s) 87.3 19 K potassium use (T/K) 473 530 601 697 832 1029 CRC.f,k (T/°C) 200.2 256.5 328 424 559 756.2 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.967 - 4646 / (T/K) CR2 (T/K) liquid, m.p. to 600 K: log (P/Pa) = 9.408 - 4453 / (T/K) 473.3 529.6 601.1 KAL (T/K) 633 704 740 794 841 894 975 1050 SMI.a (T/K) liquid, 91..338 °C: log (P/Pa) = 9.485 - 4503 / (T/K) 475 531 602 20 Ca calcium use (T/K) 864 956 1071 1227 1443 1755 CRC.b (T/°C) 591 (s) 683 (s) 798 (s) 954 1170 1482 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 15.133 - 9517 / (T/K) - 1.4030 log (T/K) 864.2 956.4 1071.5 1112.0 KAL (T/K) 1105 1220 1280 1365 1440 1525 1650 1765 SMI.a (T/K) 408..817 °C: log (P/Pa) = 10.425 - 9055 / (T/K) 869 961 1075 21 Sc scandium use (T/K) 1645 1804 (2006) (2266) (2613) (3101) CRC.c (T/°C) 1372 (s) 1531 (s) 1733 (i) 1993 (i) 2340 (i) 2828 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 11.656 - 19721 / (T/K) + 0.2885 log (T/K) - 0.3663 (T/K) 10−3 CR2 liquid, m.p. to 2000 K: log (P/Pa) = 10.801 - 17681 / (T/K) SMI.c (T/K) 1058..1804 °C: log (P/Pa) = 11.065 - 18570 / (T/K) 1678 1845 2049 22 Ti titanium use (T/K) 1982 2171 (2403) 2692 3064 3558 CRC.b (T/°C) 1709 1898 2130 (e) 2419 2791 3285 CR2 solid, 298 K to m.p.: log (P/Pa) = 16.931 - 24991 / (T/K) - 1.3376 log (T/K) CR2 (T/K) liquid, m.p. to 2400 K: log (P/Pa) = 11.364 - 22747 / (T/K) 2001.7 2194.8 SMI.c (T/K) solid, 1134..1727 °C: log (P/Pa) = 10.375 - 18640 / (T/K) 1797 1988 SMI.c (T/K) liquid, 1727..1965 °C: log (P/Pa) = 11.105 - 20110 / (T/K) 2209 23 V vanadium use (T/K) 2101 2289 2523 2814 3187 3679 CRC.b (T/°C) 1828 (s) 2016 2250 2541 2914 3406 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.750 - 27132 / (T/K) - 0.5501 log (T/K) 2099.6 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.935 - 25011 / (T/K) 2287.2 2517.5 SMI.c (T/K) 1465..2207 °C: log (P/Pa) = 12.445 - 26620 / (T/K) 2139 2326 24 Cr chromium use (T/K) 1656 1807 1991 2223 2530 2942 CRC.b (T/°C) 1383 (s) 1534 (s) 1718 (s) 1950 2257 2669 CR2 solid, 298 K to 2000 K: log (P/Pa) = 11.806 - 20733 / (T/K) + 0.4391 log (T/K) - 0.4094 (T/K)−3 KAL (T/K) 2020 2180 2260 2370 2470 2580 2730 2870 SMI.c,l (T/K) solid, 907..1504 °C: log (P/Pa) = 12.005 - 17560 / (T/K) 1463 1596 1755 25 Mn manganese use (T/K) 1228 1347 1493 1691 1955 2333 CRC.b (T/°C) 955 (s) 1074 (s) 1220 (s) 1418 1682 2060 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.811 - 15097 / (T/K) - 1.7896 log (T/K) 1229.2 1346.6 1490.0 KAL (T/K) 1560 1710 1780 1890 1980 2080 2240 2390 SMI.c (T/K) 717..1251 °C: log (P/Pa) = 11.375 - 14100 / (T/K) 1240 1359 1504 26 Fe iron use (T/K) 1728 1890 2091 2346 2679 3132 CRC.b (T/°C) 1455 (s) 1617 1818 2073 2406 2859 CR2 solid, 298 K to m.p.: log (P/Pa) = 12.106 - 21723 / (T/K) + 0.4536 log (T/K) - 0.5846 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 11.353 - 19574 / (T/K) 1890.7 2092.8 KAL (T/K) 2110 2290 2380 2500 2610 2720 2890 3030 SMI.c,f (T/K) solid, 1094..1535 °C: log (P/Pa) = 11.755 - 20000 / (T/K) 1701 SMI.c,f (T/K) liquid, 1535..1783 °C: log (P/Pa) = 12.535 - 21400 / (T/K) 1855 2031 27 Co cobalt use (T/K) 1790 1960 2165 2423 2755 3198 CRC.b (T/°C) 1517 1687 1892 2150 2482 2925 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.982 - 22576 / (T/K) - 1.0280 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.494 - 20578 / (T/K) 1790.3 1960.9 2167.5 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21960 / (T/K) 1900 2081 2298 28 Ni nickel use (T/K) 1783 1950 2154 2410 2741 3184 CRC.b (T/°C) 1510 1677 1881 2137 2468 2911 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.563 - 22606 / (T/K) - 0.8717 log (T/K) CR2 (T/K) liquid, m.p. to 2150 K: log (P/Pa) = 11.672 - 20765 / (T/K) 1779.0 1945.7 2146.9 KAL (T/K) 2230 2410 2500 2630 2740 2860 3030 3180 SMI.c,q solid, 1157..1455 °C: log (P/Pa) = 12.405 - 21840 / (T/K) SMI.c,q (T/K) liquid, 1455..1884 °C: log (P/Pa) = 11.675 - 20600 / (T/K) 1764 1930 2129 29 Cu copper use (T/K) 1509 1661 1850 2089 2404 2836 CRC.b (T/°C) 1236 1388 1577 1816 2131 2563 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.129 - 17748 / (T/K) - 0.7317 log (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.855 - 16415 / (T/K) 1512.2 1665.7 1853.8 KAL (T/K) 1940 2110 2200 2320 2420 2540 2710 2860 SMI.c,f solid, 946..1083 °C: log (P/Pa) = 11.935 - 18060 / (T/K) SMI.c,f (T/K) liquid, 1083..1628 °C: log (P/Pa) = 10.845 - 16580 / (T/K) 1529 1684 1875 30 Zn zinc use (T/K) 610 670 750 852 990 (1185) CRC.b (T/°C) 337 (s) 397 (s) 477 579 717 912 (e) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 11.108 - 6776 / (T/K) 610.0 670.4 CR2 (T/K) liquid, m.p. to 750 K: log (P/Pa) = 10.384 - 6286 / (T/K) 749.8 KAL (T/K) 780 854 891 945 991 1040 1120 1185 SMI.a (T/K) solid, 211..405 °C: log (P/Pa) = 11.065 - 6744 / (T/K) 609 670 31 Ga gallium use (T/K) 1310 1448 1620 1838 2125 2518 CRC.b (T/°C) 1037 1175 1347 1565 1852 2245 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.663 - 14208 / (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 11.760 - 13984 / (T/K) - 0.3413 log (T/K) 1307.4 1444.4 1613.8 KAL (T/K) 1665 1820 1900 2000 2100 2200 2350 2480 SMI.c (T/K) liquid, 771..1443 °C: log (P/Pa) = 9.915 - 13360 / (T/K) 1347 1499 1688 32 Ge germanium use (T/K) 1644 1814 2023 2287 2633 3104 CRC.b (T/°C) 1371 1541 1750 2014 2360 2831 SMI.c (T/K) 897..1635 °C: log (P/Pa) = 10.065 - 15150 / (T/K) 1505 1671 1878 33 As arsenic use (T/K) 553 596 646 706 781 874 CRC.c (T/°C) 280 (s) 323 (s) 373 (s) 433 (s) 508 (s) 601 (s) KAL (T/K) 656 (s) 701 (s) 723 (s) 754 (s) 780 (s) 808 (s) 849 (s) 883 (s) 34 Se selenium use (T/K) 500 552 617 704 813 958 CRC.c (T/°C) 227 279 344 431 540 685 KAL (T/K) 636 695 724 767 803 844 904 958 35 Br bromine use (T/K) 185 201 220 244 276 332 CRC.a (T/°C) -87.7 (s) -71.8 (s) -52.7 (s) -29.3 (s) 2.5 58.4 KAL (T/K) 227 (s) 244.1 (s) 252.1 (s) 263.6 (s) 275.7 290.0 312.0 332.0 36 Kr krypton use (T/K) 59 65 74 84 99 120 CRC.d (T/°C) -214.0 (s) -208.0 (s) -199.4 (s) -188.9 (s) -174.6 (s) -153.6 KAL (T/K) 77 (s) 84.3 (s) 88.1 (s) 93.8 (s) 98.6 (s) 103.9 (s) 112.0 (s) 119.7 37 Rb rubidium use (T/K) 434 486 552 641 769 958 CRC.f,k (T/°C) 160.4 212.5 278.9 368 496.1 685.3 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.863 - 4215 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.318 - 4040 / (T/K) 433.6 485.7 552.1 KAL (T/K) 583 649 684 735 779 829 907 978 SMI.d (T/K) liquid, 59.4..283 °C: log (P/Pa) = 9.545 - 4132 / (T/K) 433 484 548 38 Sr strontium use (T/K) 796 882 990 1139 1345 1646 CRC.b (T/°C) 523 (s) 609 (s) 717 (s) 866 1072 1373 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.232 - 8572 / (T/K) - 1.1926 log (T/K) 795.7 882.0 989.9 1028.0 KAL (T/K) 1040 (s) 1150 1205 1285 1355 1430 1550 1660 SMI.c (T/K) solid, 361..750 °C: log (P/Pa) = 10.255 - 8324 / (T/K) 812 899 1008 39 Y yttrium use (T/K) 1883 2075 (2320) (2627) (3036) (3607) CRC.c (T/°C) 1610.1 1802.3 2047 (i) 2354 (i) 2763 (i) 3334 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.741 - 22306 / (T/K) - 0.8705 log (T/K) CR2 (T/K) liquid, m.p. to 2300 K: log (P/Pa) = 10.801 - 20341 / (T/K) 1883.3 2075.4 SMI.c (T/K) 1249..2056 °C: log (P/Pa) = 11.555 - 21970 / (T/K) 1901 2081 2299 40 Zr zirconium use (T/K) 2639 2891 3197 3575 4053 4678 CRC.b (T/°C) 2366 2618 2924 3302 3780 4405 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.014 - 31512 / (T/K) - 0.7890 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.812 - 30295 / (T/K) SMI.c (T/K) solid, 1527..2127 °C: log (P/Pa) = 11.505 - 25870 / (T/K) 2249 SMI.c (T/K) liquid, 2127..2459 °C: log (P/Pa) = 12.165 - 27430 / (T/K) 2457 2698 41 Nb niobium use (T/K) 2942 3207 3524 3910 4393 5013 CRC.b (T/°C) 2669 2934 3251 3637 4120 4740 CR2 solid, 298 K to 2500 K: log (P/Pa) = 13.828 - 37818 / (T/K) - 0.2575 log (T/K) SMI.n 2194..2539 °C: log (P/Pa) = 13.495 - 40400 / (T/K) 42 Mo molybdenum use (T/K) 2742 2994 3312 3707 4212 4879 CRC.b (T/°C) 2469 (s) 2721 3039 3434 3939 4606 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.535 - 34626 / (T/K) - 1.1331 log (T/K) KAL (T/K) 3420 3720 3860 4060 4220 4410 4680 4900 SMI.r (T/K) solid, 1923..2533 °C: log (P/Pa) = 10.925 - 30310 / (T/K) 2774 43 Tc technetium use (T/K) (2727) (2998) (3324) (3726) (4234) (4894) CRC.b (T/°C) 2454 (e) 2725 (e) 3051 (e) 3453 (e) 3961 (e) 4621 (e) 44 Ru ruthenium use (T/K) 2588 2811 3087 3424 3845 4388 CRC.b (T/°C) 2315 (s) 2538 2814 3151 3572 4115 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.761 - 34154 / (T/K) - 0.4723 log (T/K) 2597.6 SMI.c (T/K) 1913..2946 °C: log (P/Pa) = 12.625 - 33800 / (T/K) 2677 2908 3181 45 Rh rhodium use (T/K) 2288 2496 2749 3063 3405 3997 CRC.b (T/°C) 2015 2223 2476 2790 3132 3724 CR2 solid, 298 K to m.p.: log (P/Pa) = 15.174 - 29010 / (T/K) - 0.7068 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.808 - 26792 / (T/K) 2269.0 2478.9 SMI.c (T/K) 1681..2607 °C: log (P/Pa) = 12.675 - 30400 / (T/K) 2398 2604 2848 46 Pd palladium use (T/K) 1721 1897 2117 2395 2753 3234 CRC.b (T/°C) 1448 (s) 1624 1844 2122 2480 2961 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.508 - 19813 / (T/K) - 0.9258 log (T/K) 1721.0 CR2 (T/K) liquid, m.p. to 2100 K: log (P/Pa) = 10.432 - 17899 / (T/K) 1897.7 SMI.c (T/K) 1156..2000 °C: log (P/Pa) = 10.585 - 19230 / (T/K) 1817 2006 2240 47 Ag silver use (T/K) 1283 1413 1575 1782 2055 2433 CRC.b (T/°C) 1010 1140 1302 1509 1782 2160 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.133 - 14999 / (T/K) - 0.7845 log (T/K) CR2 (T/K) liquid, m.p. to 1600 K: log (P/Pa) = 10.758 - 13827 / (T/K) 1285.3 1417.0 1578.8 KAL (T/K) 1640 1790 1865 1970 2060 2160 2310 2440 SMI.a solid, 767..961 °C: log (P/Pa) = 11.405 - 14850 / (T/K) SMI.a (T/K) liquid, 961..1353 °C: log (P/Pa) = 10.785 - 14090 / (T/K) 1306 1440 1604 48 Cd cadmium use (T/K) 530 583 654 745 867 1040 CRC.b (T/°C) 257 (s) 310 (s) 381 472 594 767 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 10.945 - 5799 / (T/K) 529.8 583.1 CR2 (T/K) liquid, m.p. to 650 K: log (P/Pa) = 10.248 - 5392 / (T/K) 653.7 KAL (T/K) 683 748 781 829 870 915 983 1045 SMI.a (T/K) solid, 148..321 °C: log (P/Pa) = 10.905 - 5798 / (T/K) 532 585 49 In indium use (T/K) 1196 1325 1485 1690 1962 2340 CRC.b (T/°C) 923 1052 1212 1417 1689 2067 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.997 - 12548 / (T/K) CR2 (T/K) liquid, m.p. to 1500 K: log (P/Pa) = 10.380 - 12276 / (T/K) 1182.7 1308.7 1464.9 SMI.c,m (T/K) liquid, 667..1260 °C: log (P/Pa) = 10.055 - 12150 / (T/K) 1208 1342 1508 50 Sn tin use (T/K) 1497 1657 1855 2107 2438 2893 CRC.b (T/°C) 1224 1384 1582 1834 2165 2620 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.042 - 15710 / (T/K) CR2 (T/K) liquid, m.p. to 1850 K: log (P/Pa) = 10.268 - 15332 / (T/K) 1493.2 1654.3 1854.4 KAL (T/K) 1930 2120 2210 2350 2470 2600 2800 2990 SMI.c (T/K) liquid, 823..1609 °C: log (P/Pa) = 9.095 - 13110 / (T/K) 1441 1620 1848 51 Sb antimony use (T/K) 807 876 1011 1219 1491 1858 CRC.b,c (T/°C) 534 (s) 603 (s) 738 946 1218 1585 KAL (T/K) 1065 1220 1295 1405 1495 1595 1740 1890 SMI.c (T/K) 466..904 °C: log (P/Pa) = 10.545 - 9913 / (T/K) 940 1039 1160 52 Te tellurium use (T/K) (775) (888) 1042 1266 CRC.d (T/°C) 502 (e) 615 (e) 768.8 992.4 KAL (T/K) 806 888 929 990 1040 1100 1190 1270 53 I iodine (rhombic) use (T/K) 260 282 309 342 381 457 CRC.a,b (T/°C) -12.8 (s) 9.3 (s) 35.9 (s) 68.7 (s) 108 (s) 184.0 KAL (T/K) 318 (s) 341.8 (s) 353.1 (s) 369.3 (s) 382.7 (s) 400.8 430.6 457.5 54 Xe xenon use (T/K) 83 92 103 117 137 165 CRC.d,m (T/°C) -190 (s) -181 (s) -170 (s) -155.8 (s) -136.6 (s) -108.4 KAL (T/K) 107 (s) 117.3 (s) 122.5 (s) 130.1 (s) 136.6 (s) 143.8 (s) 154.7 (s) 165.0 55 Cs caesium use (T/K) 418 469 534 623 750 940 CRC.f,k (T/°C) 144.5 195.6 260.9 350.0 477.1 667.0 CR2 solid, 298 K to m.p.: log (P/Pa) = 9.717 - 3999 / (T/K) CR2 (T/K) liquid, m.p. to 550 K: log (P/Pa) = 9.171 - 3830 / (T/K) 417.6 468.7 534.1 KAL (T/K) 559 624 657 708 752 802 883 959 SMI.e (T/K) liquid, 45..277 °C: log (P/Pa) = 8.985 - 3774 / (T/K) 420 473 540 56 Ba barium use (T/K) 911 1038 1185 1388 1686 2170 CRC.e (T/°C) 638 (s) 765 912 1115 1413 1897 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 17.411 - 9690 / (T/K) - 2.2890 log (T/K) 911.0 CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.013 - 8163 / (T/K) 1018.7 1164.0 KAL (T/K) 1165 1290 1360 1455 1540 1635 1780 1910 SMI.c (T/K) 418..858 °C: log (P/Pa) = 10.005 - 8908 / (T/K) 890 989 1113 57 La lanthanum use (T/K) (2005) (2208) (2458) (2772) (3178) (3726) CRC.c (T/°C) 1732 (i) 1935 (i) 2185 (i) 2499 (i) 2905 (i) 3453 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 12.469 - 22551 / (T/K) - 0.3142 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.917 - 21855 / (T/K) 2001.9 2203.8 2450.9 SMI.c (T/K) liquid, 1023..1754 °C: log (P/Pa) = 11.005 - 18000 / (T/K) 1636 1799 1999 58 Ce cerium use (T/K) 1992 2194 2442 2754 3159 3705 CRC.g (T/°C) 1719 1921 2169 2481 2886 3432 CR2 solid, 298 K to m.p.: log (P/Pa) = 11.145 - 21752 / (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 10.617 - 21200 / (T/K) 1996.8 2204.4 2460.3 SMI.c (T/K) liquid, 1004..1599 °C: log (P/Pa) = 12.865 - 20100 / (T/K) 1562 1694 1850 59 Pr praseodymium use (T/K) 1771 1973 (2227) (2571) (3054) (3779) CRC.c (T/°C) 1497.7 1699.4 1954 (i) 2298 (i) 2781 (i) 3506 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.865 - 18720 / (T/K) - 0.9512 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 9.778 - 17315 / (T/K) 1770.8 1972.5 60 Nd neodymium use (T/K) 1595 1774 1998 (2296) (2715) (3336) CRC.c (T/°C) 1322.3 1501.2 1725.3 2023 (i) 2442 (i) 3063 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.002 - 17264 / (T/K) - 0.9519 log (T/K) CR2 (T/K) liquid, m.p. to 2000 K: log (P/Pa) = 9.918 - 15824 / (T/K) 1595.5 1774.4 1998.5 62 Sm samarium use (T/K) 1001 1106 1240 (1421) (1675) (2061) CRC.c (T/°C) 728 (s) 833 (s) 967 (s) 1148 (i) 1402 (i) 1788 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.994 - 11034 / (T/K) - 1.3287 log (T/K) 1002.5 1109.2 1242.2 1289.0 63 Eu europium use (T/K) 863 957 1072 1234 1452 1796 CRC.g (T/°C) 590 (s) 684 (s) 799 (s) 961 1179 1523 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.246 - 9459 / (T/K) - 1.1661 log (T/K) 874.6 968.8 1086.5 64 Gd gadolinium use (T/K) (1836) (2028) (2267) (2573) (2976) (3535) CRC.c (T/°C) 1563 (i) 1755 (i) 1994 (i) 2300 (i) 2703 (i) 3262 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 13.350 - 20861 / (T/K) - 0.5775 log (T/K) CR2 (T/K) liquid, m.p. to 2250 K: log (P/Pa) = 10.563 - 19389 / (T/K) 1835.6 2027.5 2264.3 65 Tb terbium use (T/K) 1789 1979 (2201) (2505) (2913) (3491) CRC.c (T/°C) 1516.1 1706.1 1928 (i) 2232 (i) 2640 (i) 3218 (i) CR2 solid, 298 K to m.p.: log (P/Pa) = 14.516 - 20457 / (T/K) - 0.9247 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.417 - 18639 / (T/K) 1789.3 1979.3 2214.4 66 Dy dysprosium use (T/K) 1378 1523 (1704) (1954) (2304) (2831) CRC.c (T/°C) 1105 (s) 1250 (s) 1431 (i) 1681 (i) 2031 (i) 2558 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.585 - 15336 / (T/K) - 1.1114 log (T/K) 1382.3 1526.5 67 Ho holmium use (T/K) 1432 1584 (1775) (2040) (2410) (2964) CRC.c (T/°C) 1159 (s) 1311 (s) 1502 (i) 1767 (i) 2137 (i) 2691 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.791 - 15899 / (T/K) - 1.1753 log (T/K) 1434.8 1585.2 68 Er erbium use (T/K) 1504 1663 (1885) (2163) (2552) (3132) CRC.c (T/°C) 1231 (s) 1390 (s) 1612 (i) 1890 (i) 2279 (i) 2859 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 14.922 - 16642 / (T/K) - 1.2154 log (T/K) 1504.7 1663.0 CR2 (T/K) liquid, m.p. to 1900 K: log (P/Pa) = 9.674 - 14380 / (T/K) 1873.9 69 Tm thulium use (T/K) 1117 1235 1381 1570 (1821) (2217) CRC.c (T/°C) 844 (s) 962 (s) 1108 (s) 1297 (s) 1548 (i) 1944 (i) CR2 (T/K) solid, 298 K to 1400 K: log (P/Pa) = 13.888 - 12270 / (T/K) - 0.9564 log (T/K) 1118.3 1235.5 1381.0 70 Yb ytterbium use (T/K) 736 813 910 1047 (1266) (1465) CRC.c (T/°C) 463 (s) 540 (s) 637 (s) 774 (s) 993 (i) 1192 (i) CR2 (T/K) solid, 298 K to 900 K: log (P/Pa) = 14.117 - 8111 / (T/K) - 1.0849 log (T/K) 737.0 814.4 71 Lu lutetium use (T/K) 1906 2103 2346 (2653) (3072) (3663) CRC.c (T/°C) 1633 (s) 1829.8 2072.8 2380 (i) 2799 (i) 3390 (i) CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 13.799 - 22423 / (T/K) - 0.6200 log (T/K) 1905.9 CR2 (T/K) liquid, m.p. to 2350 K: log (P/Pa) = 10.654 - 20302 / (T/K) 2103.0 2346.0 72 Hf hafnium use (T/K) 2689 2954 3277 3679 4194 4876 CRC.e (T/°C) 2416 2681 3004 3406 3921 4603 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.451 - 32482 / (T/K) - 0.6735 log (T/K) 73 Ta tantalum use (T/K) 3297 3597 3957 4395 4939 5634 CRC.b (T/°C) 3024 3324 3684 4122 4666 5361 CR2 solid, 248 K to 2500 K: log (P/Pa) = 21.813 - 41346 / (T/K) - 3.2152 log (T/K) + 0.7437 (T/K) 10−3 SMI.o,p solid, 2407..2820 °C: log (P/Pa) = 12.125 - 40210 / (T/K) 74 W tungsten use (T/K) 3477 3773 4137 4579 5127 5823 CRC.b (T/°C) 3204 (s) 3500 3864 4306 4854 5550 CR2 solid, 298 K to 2350 K: log (P/Pa) = 7.951 - 44094 / (T/K) + 1.3677 log (T/K) CR2 solid, 2200 K to 2500 K: log (P/Pa) = -49.521 - 57687 / (T/K) - 12.2231 log (T/K) KAL (T/K) 4300 4630 4790 5020 5200 5400 5690 5940 SMI.s (T/K) solid, 2554..3309 °C: log (P/Pa) = 11.365 - 40260 / (T/K) 3542 75 Re rhenium use (T/K) 3303 3614 4009 4500 5127 5954 CRC.b (T/°C) 3030 (s) 3341 3736 4227 4854 5681 CR2 solid, 298 K to 2500 K: log (P/Pa) = 16.549 - 40726 / (T/K) - 1.1629 log (T/K) 76 Os osmium use (T/K) 3160 3423 3751 4148 4638 5256 CRC.b (T/°C) 2887 (s) 3150 3478 3875 4365 4983 CR2 solid, 298 K to 2500 K: log (P/Pa) = 14.425 - 41198 / (T/K) - 0.3896 log (T/K) SMI.c (T/K) 2101..3221 °C: log (P/Pa) = 12.715 - 37000 / (T/K) 2910 3158 3453 77 Ir iridium use (T/K) 2713 2957 3252 3614 4069 4659 CRC.b (T/°C) 2440 (s) 2684 2979 3341 3796 4386 CR2 solid, 298 K to 2500 K: log (P/Pa) = 15.512 - 35099 / (T/K) - 0.7500 log (T/K) SMI.c (T/K) 1993..3118 °C: log (P/Pa) = 12.185 - 34110 / (T/K) 2799 3050 3349 78 Pt platinum use (T/K) 2330 (2550) 2815 3143 3556 4094 CRC.b (T/°C) 2057 2277 (e) 2542 2870 3283 3821 CR2 solid, 298 K to m.p.: log (P/Pa) = 4.888 - 29387 / (T/K) + 1.1039 log (T/K) - 0.4527 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 11.392 - 26856 / (T/K) 2357.4 KAL (T/K) 2910 3150 3260 3420 3560 3700 3910 4090 SMI.c (T/K) 1606..2582 °C: log (P/Pa) = 11.758 - 27500 / (T/K) 2339 2556 2818 79 Au gold use (T/K) 1646 1814 2021 2281 2620 3078 CRC.b (T/°C) 1373 1541 1748 2008 2347 2805 CR2 solid, 298 K to m.p.: log (P/Pa) = 14.158 - 19343 / (T/K) - 0.7479 log (T/K) CR2 (T/K) liquid, m.p. to 2050 K: log (P/Pa) = 10.838 - 18024 / (T/K) 1663.0 1832.1 2039.4 KAL (T/K) 2100 2290 2390 2520 2640 2770 2960 3120 SMI.a (T/K) 1083..1867 °C: log (P/Pa) = 10.775 - 18520 / (T/K) 1719 1895 2111 80 Hg mercury use (T/K) 315 350 393 449 523 629 CRC.j,k (T/°C) 42.0 76.6 120.0 175.6 250.3 355.9 CR2 (T/K) liquid, 298 K to 400 K: log (P/Pa) = 10.122 - 3190 / (T/K) 315.2 349.7 392.8 KAL (T/K) 408 448.8 468.8 498.4 523.4 551.2 592.9 629.8 81 Tl thallium use (T/K) 882 977 1097 1252 1461 1758 CRC.b (T/°C) 609 704 824 979 1188 1485 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.977 - 9447 / (T/K) CR2 (T/K) liquid, m.p. to 1100 K: log (P/Pa) = 10.265 - 9037 / (T/K) 880.4 975.4 1093.4 KAL (T/K) 1125 1235 1290 1370 1440 1515 1630 1730 SMI.a (T/K) liquid, 405..821 °C: log (P/Pa) = 10.275 - 8920 / (T/K) 868 962 1078 82 Pb lead use (T/K) 978 1088 1229 1412 1660 2027 CRC.b (T/°C) 705 815 956 1139 1387 1754 CR2 solid, 298 K to m.p.: log (P/Pa) = 10.649 - 10143 / (T/K) CR2 (T/K) liquid, m.p. to 1200 K: log (P/Pa) = 9.917 - 9701 / (T/K) 978.2 1087.9 KAL (T/K) 1285 1420 1485 1585 1670 1760 1905 2030 SMI.a (T/K) liquid, 483..975 °C: log (P/Pa) = 9.815 - 9600 / (T/K) 978 1089 1228 83 Bi bismuth use (T/K) 941 1041 1165 1325 1538 1835 CRC.b (T/°C) 668 768 892 1052 1265 1562 KAL (T/K) 1225 1350 1410 1505 1580 1670 1800 1920 SMI.c (T/K) liquid, 474..934 °C: log (P/Pa) = 10.265 - 9824 / (T/K) 957 1060 1189 84 Po polonium use (T/K) (846) 1003 1236 CRC.d (T/°C) 573 (e) 730.2 963.3 85 At astatine use (T/K) 361 392 429 475 531 607 CRC.b (T/°C) 88 (s) 119 (s) 156 (s) 202 (s) 258 (s) 334 86 Rn radon use (T/K) 110 121 134 152 176 211 CRC.d (T/°C) -163 (s) -152 (s) -139 (s) -121.4 (s) -97.6 (s) -62.3 KAL (T/K) 139 (s) 152 (s) 158 (s) 168 (s) 176 (s) 184 (s) 198 (s) 211 87 Fr francium use (T/K) (404) (454) (519) (608) (738) (946) CRC.b (T/°C) 131 (e) 181 (e) 246 (e) 335 (e) 465 (e) 673 (e) 88 Ra radium use (T/K) 819 906 1037 1209 1446 1799 CRC.b (T/°C) 546 (s) 633 (s) 764 936 1173 1526 90 Th thorium use (T/K) 2633 2907 3248 3683 4259 5055 CRC.b (T/°C) 2360 2634 2975 3410 3986 4782 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.674 - 31483 / (T/K) - 0.5288 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = -13.447 - 24569 / (T/K) + 6.6473 log (T/K) SMI.c (T/K) 1686..2715 °C: log (P/Pa) = 11.645 - 28440 / (T/K) 2442 2672 2949 91 Pa protactinium CR2 solid, 298 K to m.p.: log (P/Pa) = 15.558 - 34869 / (T/K) - 1.0075 log (T/K) CR2 liquid, m.p. to 2500 K: log (P/Pa) = 11.183 - 32874 / (T/K) 92 U uranium use (T/K) 2325 2564 2859 3234 3727 4402 CRC.b (T/°C) 2052 2291 2586 2961 3454 4129 CR2 solid, 298 K to m.p.: log (P/Pa) = 5.776 - 27729 / (T/K) + 2.6982 log (T/K) - 1.5471 (T/K) 10−3 CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 25.741 - 28776 / (T/K) - 4.0962 log (T/K) 2422.6 SMI.c (T/K) liquid, 1461..2338 °C: log (P/Pa) = 12.005 - 25800 / (T/K) 2149 2344 2579 93 Np neptunium use (T/K) 2194 2437 CR2 solid, 298 K to m.p.: log (P/Pa) = 24.649 - 24886 / (T/K) - 3.9991 log (T/K) CR2 (T/K) liquid, m.p. to 2500 K: log (P/Pa) = 15.082 - 23378 / (T/K) - 1.3250 log (T/K) 2194.1 2436.6 94 Pu plutonium use (T/K) 1756 1953 2198 2511 2926 3499 CRC.b (T/°C) 1483 1680 1925 2238 2653 3226 CR2 solid, 500 K to m.p.: log (P/Pa) = 23.864 - 18460 / (T/K) - 4.4720 log (T/K) CR2 solid, 298 K to 600 K: log (P/Pa) = 31.166 - 19162 / (T/K) - 6.6675 log (T/K) CR2 (T/K) liquid, m.p. to 2450 K: log (P/Pa) = 8.672 - 16658 / (T/K) 1920.9 2171.3 95 Am americium use (T/K) 1239 1356 CR2 (T/K) solid, 298 K to m.p.: log (P/Pa) = 16.317 - 15059 / (T/K) - 1.3449 log (T/K) 1238.7 1356.1 96 Cm curium use (T/K) 1788 1982 CR2 solid, 298 K to m.p.: log (P/Pa) = 13.375 - 20364 / (T/K) - 0.5770 log (T/K) CR2 (T/K) liquid, m.p. to 2200 K: log (P/Pa) = 10.229 - 18292 / (T/K) 1788.2 1982.0 == Notes == Values are given in terms of temperature necessary to reach the specified pressure. This is because some of the energy released during combustion goes, as work, into changing the volume of the control system. thumb\|right\|300px\|Constant volume flame temperature of a number of fuels, with air If we make the assumption that combustion goes to completion (i.e. forming only and ), we can calculate the adiabatic flame temperature by hand either at stoichiometric conditions or lean of stoichiometry (excess air). Coefficients from this source: : ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. thumb\|upright\|Ethanol burning with its spectrum depicted In the study of combustion, the adiabatic flame temperature is the temperature reached by a flame under ideal conditions. The definition in which the combustion products are all returned to the reference temperature is more easily calculated from the higher heating value than when using other definitions and will in fact give a slightly different answer. === Gross heating value === Gross heating value accounts for water in the exhaust leaving as vapor, as does LHV, but gross heating value also includes liquid water in the fuel prior to combustion. This result can be explained through Le Chatelier's principle. ==See also== Flame speed ==References== == External links == === General information === * Computation of adiabatic flame temperature * Adiabatic flame temperature === Tables === * adiabatic flame temperature of hydrogen, methane, propane and octane with oxygen or air as oxidizers * * Temperature of a blue flame and common materials === Calculators === * Online adiabatic flame temperature calculator using Cantera * Adiabatic flame temperature program * Gaseq, program for performing chemical equilibrium calculations.	1.6	205	46.7	5.9	0.38	B
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the final pressure of a sample of carbon dioxide that expands reversibly and adiabatically from $57.4 \mathrm{kPa}$ and $1.0 \mathrm{dm}^3$ to a final volume of $2.0 \mathrm{dm}^3$. Take $\gamma=1.4$.	The solubility turned out to be very low: from 0.02 to 0.10 %. thumb\|Carbon dioxide pressure-temperature phase diagram == Uses == thumb\|219x219px\|Fire extinguisher Uses of liquid carbon dioxide include the preservation of food, in fire extinguishers, and in commercial food processes. Liquid carbon dioxide is a type of liquid which is formed from highly compressed and cooled gaseous carbon dioxide. "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975 allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known. == Equations == : \ln P_{\rm r} = f^{(0)} + \omega \cdot f^{(1)} : f^{(0)}=5.92714 - \frac{6.09648}{T_{\rm r}} - 1.28862 \cdot \ln T_{\rm r} + 0.169347 \cdot T_{\rm r}^6 : f^{(1)}=15.2518 - \frac{15.6875}{T_{\rm r}}-13.4721 \cdot \ln T_{\rm r} + 0.43577 \cdot T_{\rm r}^6 with :P_{\rm r}=\frac{P}{P_{\rm c}} (reduced pressure) and T_{\rm r}=\frac{T}{T_{\rm c}} (reduced temperature). == Typical errors == The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. Compressed natural gas (CNG) is a fuel gas mainly composed of methane (CH4), compressed to less than 1% of the volume it occupies at standard atmospheric pressure. Accumulation of carbon dioxide is predominantly a result of hypoperfusion and not hypoxia. At this temperature, the pressure is measured in a range from 15 to 60 atmospheres. The solubility of water in liquid carbon dioxide is measured in a range of temperatures, ranging from to . thumb\|Jets of liquid carbon dioxide Liquid carbon dioxide is the liquid state of carbon dioxide (), which cannot occur under atmospheric pressure. Normocapnia or normocarbia is a state of normal arterial carbon dioxide pressure, usually about 40 mmHg. == See also == * * * == References == The Free Dictionary - Normocapnia Category:Diving medicine Category:Pulmonology Auflage, McGraw-Hill, 1988 == Example calculation == For benzene with Tc = 562.12 KBrunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006 * Pc = 4898 kPa * Tb = 353.15 KSilva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006 * ω = 0.2120Dortmund Data Bank the following calculation for T=Tb results: * Tr = 353.15 / 562.12 = 0.628247 * f(0) = -3.167428 * f(1) = -3.429560 * Pr = exp( f(0) \+ ω f(1) ) = 0.020354 * P = Pr * Pc = 99.69 kPa The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. According to the model, each exhalatory segment of capnogram waveform follows the analytical expression: p_D(t) = p_A (1 - e ^{-\alpha}e^{\alpha e^{-t/\tau}}) where * p_D(t)represents the partial pressure of carbon dioxide measured by the capnogram as a function of time t since the beginning of exhalation. * p_Arepresents the alveolar partial pressure of carbon dioxide. * \alpharepresents the inverse of the dead space fraction (i.e. the ratio of tidal volume to dead space volume). * \taurepresents the pulmonary time constant (i.e. the product of pulmonary resistance and compliance) In particular, this model explains the rounded "shark-fin" shape of the capnogram observed in patients with obstructive lung disease. == See also == * Integrated pulmonary index * Medical equipment * Medical test * Respiratory monitoring * Colorimetric capnography == Citations == == External links == * CapnoBase.org: Respiratory signal database that contains clinical and simulated capnogram recordings Category:Anesthesia Category:Breath tests Category:Diagnostic emergency medicine Category:Diagnostic intensive care medicine Category:Diagnostic pulmonology However, CNG requires a much larger volume to store the energy equivalent of petrol and the use of very high pressures (3000 to 4000 psi, or 205 to 275 bar). In healthy individuals, the difference between arterial blood and expired gas partial pressures is very small (normal difference 4-5 mmHg). Low-temperature carbon dioxide is commercially used in its solid form, commonly known as "dry ice". Gastric tonometry describes the measurement of the carbon dioxide level inside the stomach in order to assess the degree of blood flow to the stomach and bowel. For pressures above 1 bar, that means, above the normal boiling point, the typical errors are below 2%. Because the introduction of a nasogastric tube is almost routine in critically ill patients, the measurement of gastric carbon dioxide can be an easy method to monitor tissue perfusion. Capnography is the monitoring of the concentration or partial pressure of carbon dioxide () in the respiratory gases. For light-duty CNG cars to become a viable short-term climate strategy, methane leakage would need to be kept below 1.6% of total natural gas produced (approximately half the current amount for well to wheels – note difference from well to city)." ** The lifecycle greenhouse gas emissions for CNG compressed from California's pipeline natural gas is given a value of 67.70 grams of -equivalent per megajoule (gCO2e/MJ) by CARB (the California Air Resources Board), approximately 28 percent lower than the average petrol fuel in that market (95.86 gCO2e/MJ). Natural gas is being experimentally stored at lower pressure in a form known as an ANG (adsorbed natural gas) cylinder, where it is adsorbed at 35 bar (500 psi, the pressure of gas in natural gas pipelines) in various sponge-like materials, such as carbon and MOFs (metal-organic frameworks). In this process known as high pressure ANG, a high pressure CNG tank is filled by absorbers such as activated carbon (which is an adsorbent with high surface area) and stores natural gas by both CNG and ANG mechanisms.	0.22222222	1.1	4.86	22	49	D
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When $229 \mathrm{~J}$ of energy is supplied as heat to $3.0 \mathrm{~mol} \mathrm{Ar}(\mathrm{g})$ at constant pressure, the temperature of the sample increases by $2.55 \mathrm{~K}$. Calculate the molar heat capacities at constant volume.	Then the molar heat capacity (at constant volume) would be :cV,m = fR where R is the ideal gas constant. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.Lange's Handbook of Chemistry, 10th ed. p. 1524 All methods for the measurement of specific heat apply to molar heat capacity as well. ==Units== The SI unit of molar heat capacity heat is joule per kelvin per mole (J/(K⋅mol), J/(K mol), J K−1 mol−1, etc.). On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows: : C_{P,m} - C_{V,m} = \frac{C_{P} - C_{V}}{n} = \frac{n R}{n} = R This result would be consistent if the specific difference were derived directly from the general expression for c_p - c_v\, . == See also == Heat capacity ratio == References == David R. Gaskell (2008), Introduction to the thermodynamics of materials, Fifth Edition, Taylor & Francis. . Like the specific heat, the measured molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). In modern terms the mass m of the sample divided by molar mass M gives the number of moles n. :m/M = n Therefore, using uppercase C for the full heat capacity (in joule per kelvin), we have: :C(M/m) = C/n = K = 3R or :C/n = 3R. The following table shows the experimental molar heat capacities at constant pressure cP,m of the above polyatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000 °C, and the apparent number of degrees of freedom f* estimated by the formula f* = 2cP,m/R − 2: 25 °C 25 °C 500 °C 500 °C 5000 °C 5000 °C Gas cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* f Notes N≡N=O 38.6 7.3 51.8 10.5 62.0 12.9 13 "Nitrous oxide" NIST Chemistry WebBook, SRD 69, online. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. Said another way, the atom-molar heat capacity of a solid substance is expected to be 3R = 24.94 J⋅K−1⋅mol−1, where "amol" denotes an amount of the solid that contains the Avogadro number of atoms. The following is a table of some constant- pressure molar heat capacities cP,m of various diatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000 °C, and the apparent number of degrees of freedom f* estimated by the formula f* = 2cP,m/R − 2: 25 °C 25 °C 500 °C 500 °C 5000 °C 5000 °C Gas cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* H2 28.9 5.0 29.6 5.1 41.2 7.9 Not saturated."Hydrogen" NIST Chemistry WebBook, SRD 69, online. Like the heat capacity of an object, the molar heat capacity of a substance may vary, sometimes substantially, depending on the starting temperature T of the sample and the pressure P applied to it. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1. Therefore, the word "molar", not "specific", should always be used for this quantity. ==Definition== The molar heat capacity of a substance, which may be denoted by cm, is the heat capacity C of a sample of the substance, divided by the amount (moles) n of the substance in the sample: :cm{} \;=\; \frac{C}{n} \;=\; \frac{1}{n} \lim_{\Delta T \rightarrow 0}\frac{Q}{\Delta T} where Q is the amount of heat needed to raise the temperature of the sample by ΔT. The last value corresponds almost exactly to the predicted value for f = 7. right\|thumb\|upright=1.25\|Constant-volume specific heat capacity of diatomic gases (real gases) between about 200 K and 2000 K. In other words, that theory predicts that the molar heat capacity at constant volume cV,m of all monatomic gases will be the same; specifically, :cV,m = R where R is the ideal gas constant, about 8.31446 J⋅K−1⋅mol−1 (which is the product of the Boltzmann constant kB and the Avogadro constant). At high enough temperature, its molar heat capacity then should be cP,m = 7.5 R = 62.63 J⋅K−1⋅mol−1. The molar heat capacity of the gas will then be determined only by the "active" degrees of freedom — that, for most molecules, can receive enough energy to overcome that quantum threshold.Quantum Physics and the Physics of large systems, Part 1A Physics, University of Cambridge, C.G. Smith, 2008. right\|thumb\|upright=1.25\|Constant- volume specific heat capacity of a diatomic gas (idealised). thumb\|upright=2.2\|Molar heat capacity of most elements at 25 °C is in the range between 2.8 R and 3.4 R: Plot as a function of atomic number with a y range from 22.5 to 30 J/mol K. The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Therefore, the heat capacity of a sample of a solid substance is expected to be 3RNa, or (24.94 J/K)Na, where Na is the number of moles of atoms in the sample, not molecules. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1.324 200 1.310 CO2 0 1.310 20 1.300 100 1.281 400 1.235 1000 1.195 CO 20 1.400 NO 20 1.400 N2O 20 1.310 CH4 −115 1.410 −74 1.350 20 1.320 NH3 15 1.310 SO2 15 1.290 C2H6 15 1.220 C3H8 16 1.130 Dry air -15 1.404 0 1.403 20 1.400 100 1.401 200 1.398 400 1.393 1000 1.365 In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). In modern terms, Dulong and Petit found that the heat capacity of a mole of many solid elements is about 3R, where R is the universal gas constant. The same theory predicts that the molar heat capacity of a monatomic gas at constant pressure will be :cP,m = cV,m \+ R = R This prediction matches the experimental values, which, for helium through xenon, are 20.78, 20.79, 20.85, 20.95, and 21.01 J⋅K−1⋅mol−1, respectively;Shuen-Chen Hwang, Robert D. Lein, Daniel A. Morgan (2005).	7.42	0.0526315789	30.0	+3.60	4	C
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The fugacity coefficient of a certain gas at $200 \mathrm{~K}$ and 50 bar is 0.72. Calculate the difference of its molar Gibbs energy from that of a perfect gas in the same state.	Taken at the same temperature and pressure, the difference between the molar Gibbs free energies of a real gas and the corresponding ideal gas is equal to . The contribution of nonideality to the molar Gibbs energy of a real gas is equal to . For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. ==History== The word fugacity is derived from the Latin fugere, to flee. This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure. This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of nitrogen as an ideal gas at . Thus the Gibbs free energy of a system can be calculated by collecting moles together carefully at a specified T, P and at a constant molar ratio composition (so that the chemical potential doesn't change as the moles are added together), i.e. : \mathbf{G} = \sum_{i=1}^I \mu_i N_i . Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1. Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas. For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H = H(T), dU = C_V (T) dT, dH = C_P (T) dT. In a pure substance, is equal to the Gibbs energy for a mole of the substance, and d\mu = dG_\mathrm{m} = -S_\mathrm{m}dT + V_\mathrm{m}dP, where and are the temperature and pressure, is the volume per mole and is the entropy per mole. ===Gas=== For an ideal gas the equation of state can be written as V_\mathrm{m}^\text{ideal} = \frac{RT}{P}, where is the ideal gas constant. The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absorbed in any changes between different crystal structures). The fugacity coefficient is . In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. A calorically perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, and enthalpy H that are functions of temperature only, i.e., U = U(T), H = H(T) * has heat capacities C_V, C_P that are constant, i.e., dU = C_V dT, dH = C_P dT and \Delta U = C_V \Delta T, \Delta H = C_P \Delta T, where \Delta is any finite (non-differential) change in each quantity. In addition, there are natural reference states for fugacity (for example, an ideal gas makes a natural reference state for gas mixtures since the fugacity and pressure converge at low pressure). ===Gases=== In a mixture of gases, the fugacity of each component has a similar definition, with partial molar quantities instead of molar quantities (e.g., instead of and instead of ): dG_i = R T \,d \ln f_i and \lim_{P\to 0} \frac{f_i}{P_i} = 1, where is the partial pressure of component . The total differential of this expression is : \mathrm{d}\mathbf{G} = \sum_{i=1}^I \mu_i \mathrm{d}N_i + \sum_{i=1}^I N_i \mathrm{d}\mu_i Combining the two expressions for the total differential of the Gibbs free energy gives : \sum_{i=1}^I \mu_i \mathrm{d}N_i + \sum_{i=1}^I N_i \mathrm{d}\mu_i =V \mathrm{d}p-S \mathrm{d}T+\sum_{i=1}^I \mu_i \mathrm{d}N_i which simplifies to the Gibbs–Duhem relation: : \sum_{i=1}^I N_i \mathrm{d}\mu_i = -S \mathrm{d}T + V \mathrm{d}p === Alternative derivation === Another way of deriving the Gibbs-Duhem equation can be found be taking the extensivity of energy into account. In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., U=U(n,T), where is the amount of substance in moles. In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle.	7.136	0.000216	0.0	3.8	-0.55	E
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Given the reactions (1) and (2) below, determine $\Delta_{\mathrm{r}} U^{\ominus}$ for reaction (3). (1) $\mathrm{H}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^{\ominus}=-184.62 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (2) $2 \mathrm{H}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^\ominus=-483.64 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (3) $4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{Cl}_2(\mathrm{g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$	==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.18 1.293 65 KAL 33.2 1.297 65.0 SMI −239.9 13.2 kgf/cm² 0.0310 1 H hydrogen (equilibrium) LNG −240.17 1.294 12.77 atm 65.4 0.0308 1 H hydrogen (normal) LNG −239.91 1.297 12.8 atm 65.0 0.0310 1 D deuterium KAL 38.2 1.65 60 1 D deuterium (equilibrium) LNG −234.8 1.650 16.28 atm 60.4 0.0668 1 D deuterium (normal) LNG −234.7 1.665 16.43 atm 60.3 0.0669 2 He helium use 5.19 −267.96 0.227 CRC.a 5.19 −267.96 0.227 57 KAL 5.19 0.227 57.2 SMI −267.9 2.34 kgf/cm² 0.0693 2 He helium (equilibrium) LNG −267.96 0.2289 2.261 atm 0.06930 2 He helium-3 LNG −269.85 0.1182 1.13 atm 72.5 0.0414 2 He helium-4 LNG −267.96 0.227 2.24 atm 57.3 0.0698 3 Li lithium use (3223) (2950) (67) CRC.b (3223) 2950 (67) (66) 7 N nitrogen use 126.21 −146.94 3.39 CRC.a 126.21 −146.94 3.39 90 KAL 126.2 3.39 89.5 SMI −147.1 34.7 kgf/cm² 0.3110 7 N nitrogen-14 LNG −146.94 3.39 33.5 atm 89.5 0.313 7 N nitrogen-15 LNG −146.8 3.39 33.5 atm 90.4 0.332 8 O oxygen use 154.59 −118.56 5.043 CRC.a 154.59 −118.56 5.043 73 LNG −118.56 5.043 49.77 atm 73.4 0.436 KAL 154.6 5.04 73.4 SMI −118.8 51.4 kgf/cm² 0.430 9 F fluorine use 144.13 −129.02 5.172 CRC.a 144.13 −129.02 5.172 66 LNG −129.0 5.215 51.47 atm 66.2 0.574 KAL 144.3 5.22 66 10 Ne neon use 44.4 −228.7 2.76 CRC.a 44.4 −228.7 2.76 42 LNG −228.71 2.77 27.2 atm 41.7 0.4835 KAL 44.4 2.76 41.7 SMI −228.7 26.8 kgf/cm² 0.484 11 Na sodium use (2573) (2300) (35) CRC.b (2573) 2300 (35) (116) 15 P phosphorus use 994 721 CRC.a 994 721 LNG 721 16 S sulfur use 1314 1041 20.7 CRC.a 1314 1041 20.7 LNG 1041 11.7 116 atm KAL 1314 20.7 SMI 1040 17 Cl chlorine use 416.9 143.8 7.991 CRC.a 416.9 143.8 7.991 123 LNG 143.8 7.71 76.1 atm 124 0.573 KAL 416.9 7.98 124 SMI 144.0 78.7 kgf/cm² 0.573 18 Ar argon use 150.87 −122.28 4.898 CRC.a 150.87 −122.28 4.898 75 LNG −122.3 4.87 48.1 atm 74.6 0.536 KAL 150.9 4.90 74.6 SMI −122 49.7 kgf/cm² 0.531 19 K potassium use (2223) (1950) (16) CRC.b (2223) 1950 (16) (209) 33 As arsenic use 1673 1400 CRC.a 1673 1400 35 LNG 1400 34 Se selenium use 1766 1493 27.2 CRC.a 1766 1493 27.2 LNG 1493 35 Br bromine use 588 315 10.34 CRC.a 588 315 10.34 127 LNG 315 10.3 102 atm 135 1.184 KAL 588 10.3 127 SMI 302 1.18 36 Kr krypton use 209.41 −63.74 5.50 CRC.a 209.41 −63.74 5.50 91 LNG −63.75 5.50 54.3 atm 91.2 0.9085 KAL 209.4 5.50 91.2 37 Rb rubidium use (2093) (1820) (16) CRC.b (2093) 1820 (16) (247) LNG 1832 250 0.34 53 I iodine use 819 546 11.7 CRC.a 819 546 155 LNG 546 11.7 115 atm 155 0.164 KAL 819 155 SMI 553 54 Xe xenon use 289.77 16.62 5.841 CRC.c 289.77 16.62 5.841 118 LNG 16.583 5.84 57.64 atm 118 1.105 KAL 289.7 5.84 118 SMI 16.6 60.2 kgf/cm² 1.155 55 Cs caesium use 1938 1665 9.4 CRC.d 1938 1665 9.4 341 LNG 1806 300 0.44 80 Hg mercury use 1750 1477 172.00 CRC.a 1750 1477 172.00 43 LNG 1477 160.8 1587 atm KAL 1750 172 42.7 SMI 1460±20 1640±50 kgf/cm² 0.5 86 Rn radon use 377 104 6.28 CRC.a 377 104 6.28 LNG 104 6.28 62 atm 139 1.6 KAL 377 6.3 SMI 104 64.1 kgf/cm² ==References== ===CRC.a-d=== David R. Lide (ed), CRC Handbook of Chemistry and Physics, 85th Edition, online version. == Specific heat capacity == J/(mol·K) J/(g·K) 1 H hydrogen (H2, gas) use 28.836 14.304 CRC 28.836 14.304 WEL 28.82 LNG 28.84 2 He helium (gas) use 20.786 5.193 CRC 20.786 5.193 WEL 20.786 LNG 20.786 3 Li lithium use 24.860 3.582 CRC 24.860 3.582 WEL 24.8 LNG 24.8 4 Be beryllium use 16.443 1.825 CRC 16.443 1.825 WEL 16.4 LNG 16.38 5 B boron (rhombic) use 11.087 1.026 CRC 11.087 1.026 WEL 11.1 LNG 11.1 6 C carbon (graphite) use 8.517 0.709 CRC 8.517 0.709 WEL 8.53 LNG 8.517 6 C carbon (diamond, nonstd state) use 6.115 0.509 WEL 6.115 LNG 6.116 7 N nitrogen (N2, gas) use 29.124 1.040 CRC 29.124 1.040 WEL 29.12 LNG 29.124 8 O oxygen (O2, gas) use 29.378 0.918 CRC 29.378 0.918 WEL 29.4 LNG 29.4 9 F fluorine (F2, gas) use 31.304 0.824 CRC 31.304 0.824 WEL 31.3 LNG 31.30 10 Ne neon (gas) use 20.786 1.030 CRC 20.786 1.030 WEL 20.786 LNG 20.786 11 Na sodium use 28.230 1.228 CRC 28.230 1.228 WEL 28.2 LNG 28.15 12 Mg magnesium use 24.869 1.023 CRC 24.869 1.023 WEL 24.9 LNG 24.87 13 Al aluminium use 24.200 0.897 CRC 24.200 0.897 WEL 24.4 LNG 24.4 14 Si silicon use 19.789 0.705 CRC 19.789 0.705 WEL 20.0 LNG 20.00 15 P phosphorus (white) use 23.824 0.769 CRC 23.824 0.769 WEL 23.84 LNG 23.83 15 P phosphorus (red, nonstd state) use 21.19 0.684 WEL 21.2 LNG 21.19 16 S sulfur (rhombic) use 22.75 0.710 CRC 22.75 0.710 WEL 22.6 LNG 22.60 16 S sulfur (monoclinic, nonstd state) use 23.23 0.724 LNG 23.23 17 Cl chlorine (Cl2 gas) use 33.949 0.479 CRC 33.949 0.479 WEL 33.91 LNG 33.95 18 Ar argon (gas) use 20.786 0.520 CRC 20.786 0.520 WEL 20.786 LNG 20.79 19 K potassium use 29.600 0.757 CRC 29.600 0.757 WEL 29.6 LNG 29.60 20 Ca calcium use 25.929 0.647 CRC 25.929 0.647 WEL 25.3 LNG 25.9 21 Sc scandium use 25.52 0.568 CRC 25.52 0.568 WEL 25.5 LNG 25.52 22 Ti titanium use 25.060 0.523 CRC 25.060 0.523 WEL 25.0 LNG 25.0 23 V vanadium use 24.89 0.489 CRC 24.89 0.489 WEL 24.9 LNG 24.90 24 Cr chromium use 23.35 0.449 CRC 23.35 0.449 WEL 23.3 LNG 23.43 25 Mn manganese use 26.32 0.479 CRC 26.32 0.479 WEL 26.3 LNG 26.30 26 Fe iron (alpha) use 25.10 0.449 CRC 25.10 0.449 WEL 25.1 LNG 25.09 27 Co cobalt use 24.81 0.421 CRC 24.81 0.421 WEL 24.8 LNG 24.8 28 Ni nickel use 26.07 0.444 CRC 26.07 0.444 WEL 26.1 LNG 26.1 29 Cu copper use 24.440 0.385 CRC 24.440 0.385 WEL 24.43 LNG 24.44 30 Zn zinc use 25.390 0.388 CRC 25.390 0.388 WEL 25.4 LNG 25.40 31 Ga gallium use 25.86 0.371 CRC 25.86 0.371 WEL 25.9 LNG 26.06 32 Ge germanium use 23.222 0.320 CRC 23.222 0.320 WEL 23.35 LNG 23.3 33 As arsenic (alpha, gray) use 24.64 0.329 CRC 24.64 0.329 WEL 24.6 LNG 24.64 34 Se selenium (hexagonal) use 25.363 0.321 CRC 25.363 0.321 WEL 25.36 LNG 24.98 35 Br bromine use (Br2) 75.69 0.474 CRC 36.057 0.226 WEL (liquid) 75.69 WEL (Br2, gas, nonstd state) 36.0 LNG (Br2, liquid) 75.67 36 Kr krypton (gas) use 20.786 0.248 CRC 20.786 0.248 WEL 20.786 LNG 20.786 37 Rb rubidium use 31.060 0.363 CRC 31.060 0.363 WEL 31.1 LNG 31.06 38 Sr strontium use 26.4 0.301 CRC 26.4 0.301 WEL 26 LNG 26.79 39 Y yttrium use 26.53 0.298 CRC 26.53 0.298 WEL 26.5 LNG 26.51 40 Zr zirconium use 25.36 0.278 CRC 25.36 0.278 WEL 25.4 LNG 25.40 41 Nb niobium use 24.60 0.265 CRC 24.60 0.265 WEL 24.6 LNG 24.67 42 Mo molybdenum use 24.06 0.251 CRC 24.06 0.251 WEL 24.1 LNG 24.13 43 Tc technetium use 24.27 LNG 24.27 44 Ru ruthenium use 24.06 0.238 CRC 24.06 0.238 WEL 24.1 LNG 24.1 45 Rh rhodium use 24.98 0.243 CRC 24.98 0.243 WEL 25.0 LNG 24.98 46 Pd palladium use 25.98 0.244 CRC 25.98 0.246 [sic] WEL 26.0 LNG 25.94 47 Ag silver use 25.350 0.235 CRC 25.350 0.235 WEL 25.4 LNG 25.4 48 Cd cadmium use 26.020 0.232 CRC 26.020 0.232 WEL 26.0 LNG 25.9 49 In indium use 26.74 0.233 CRC 26.74 0.233 WEL 26.7 LNG 26.7 50 Sn tin (white) use 27.112 0.228 CRC 27.112 0.228 WEL 27.0 LNG 26.99 50 Sn tin (gray, nonstd state) use 25.77 0.217 WEL 25.8 LNG 25.77 51 Sb antimony use 25.23 0.207 CRC 25.23 0.207 WEL 25.2 LNG 25.2 52 Te tellurium use 25.73 0.202 CRC 25.73 0.202 WEL 25.7 LNG 25.70 53 I iodine use (I2) 54.44 0.214 CRC 36.888 0.145 WEL (solid) 54.44 WEL (I2, gas, nonstd state) 36.9 LNG (I2, solid) 54.44 LNG (I2, gas, nonstd state) 36.86 54 Xe xenon (gas) use 20.786 0.158 CRC 20.786 0.158 WEL 20.786 LNG 20.786 55 Cs caesium use 32.210 0.242 CRC 32.210 0.242 WEL 32.2 LNG 32.20 56 Ba barium use 28.07 0.204 CRC 28.07 0.204 WEL 28.1 LNG 28.10 57 La lanthanum use 27.11 0.195 CRC 27.11 0.195 WEL 27.1 LNG 27.11 58 Ce cerium (gamma, fcc) use 26.94 0.192 CRC 26.94 0.192 WEL 26.9 LNG 26.9 59 Pr praseodymium use 27.20 0.193 CRC 27.20 0.193 WEL 27.2 LNG 27.20 60 Nd neodymium use 27.45 0.190 CRC 27.45 0.190 WEL 27.4 LNG 27.5 62 Sm samarium use 29.54 0.197 CRC 29.54 0.197 WEL 29.5 LNG 29.54 63 Eu europium use 27.66 0.182 CRC 27.66 0.182 WEL 27.7 LNG 27.66 64 Gd gadolinium use 37.03 0.236 CRC 37.03 0.236 WEL 37.0 LNG 37.03 65 Tb terbium use 28.91 0.182 CRC 28.91 0.182 WEL 28.9 LNG 28.91 66 Dy dysprosium use 27.7 0.170 CRC 27.7 0.170 WEL 27.2 LNG 27.7 67 Ho holmium use 27.15 0.165 CRC 27.15 0.165 WEL 27.2 LNG 27.15 68 Er erbium use 28.12 0.168 CRC 28.12 0.168 WEL 28.1 LNG 28.12 69 Tm thulium use 27.03 0.160 CRC 27.03 0.160 WEL 27.0 LNG 27.03 70 Yb ytterbium use 26.74 0.155 CRC 26.74 0.155 WEL 26.7 LNG 26.74 71 Lu lutetium use 26.86 0.154 CRC 26.86 0.154 WEL 26.9 LNG 26.86 72 Hf hafnium (hexagonal) use 25.73 0.144 CRC 25.73 0.144 WEL 25.7 LNG 25.69 73 Ta tantalum use 25.36 0.140 CRC 25.36 0.140 WEL 25.4 LNG 25.40 74 W tungsten use 24.27 0.132 CRC 24.27 0.132 WEL 24.3 LNG 24.3 75 Re rhenium use 25.48 0.137 CRC 25.48 0.137 WEL 25.5 LNG 25.5 76 Os osmium use 24.7 0.130 CRC 24.7 0.130 WEL 25 LNG 24.7 77 Ir iridium use 25.10 0.131 CRC 25.10 0.131 WEL 25.1 LNG 25.06 78 Pt platinum use 25.86 0.133 CRC 25.86 0.133 WEL 25.9 79 Au gold use 25.418 0.129 CRC 25.418 0.129 WEL 25.42 LNG 25.36 80 Hg mercury (liquid) use 27.983 0.140 CRC 27.983 0.140 WEL 27.98 LNG 28.00 81 Tl thallium use 26.32 0.129 CRC 26.32 0.129 WEL 26.3 LNG 26.32 82 Pb lead use 26.650 0.129 CRC 26.650 0.129 WEL 26.4 LNG 26.84 83 Bi bismuth use 25.52 0.122 CRC 25.52 0.122 WEL 25.5 LNG 25.5 84 Po polonium use 26.4 LNG 26.4 86 Rn radon (gas) use 20.786 0.094 CRC 20.786 0.094 WEL 20.79 LNG 20.79 87 Fr francium use 31.80 LNG 31.80 89 Ac actinium use 27.2 0.120 CRC 27.2 0.120 WEL 27.2 LNG 27.2 90 Th thorium use 26.230 0.113 CRC 26.230 0.113 WEL 27.3 LNG 27.32 92 U uranium use 27.665 0.116 CRC 27.665 0.116 WEL 27.7 LNG 27.66 93 Np neptunium use 29.46 LNG 29.46 94 Pu plutonium use 35.5 LNG 35.5 95 Am americium use 62.7 LNG 62.7 == Notes == * All values refer to 25 °C and to the thermodynamically stable standard state at that temperature unless noted. == Heat of fusion == kJ/mol 1 H hydrogen (H2) use (H2) 0.1 CRC (H2) 0.12 LNG (H2) 0.117 WEL (per mol H atoms) 0.0585 2 He helium use 0.0138 LNG 0.0138 WEL 0.02 3 Li lithium use 3.00 CRC 3.00 LNG 3.00 WEL 3.0 4 Be beryllium use 7.895 CRC 7.895 LNG 7.895 WEL 7.95 5 B boron use 50.2 CRC 50.2 LNG 50.2 WEL 50 6 C carbon (graphite) use (graphite) 117 CRC (graphite) 117 LNG (graphite) 117 7 N nitrogen (N2) use (N2) 0.720 CRC (N2) 0.71 LNG (N2) 0.720 WEL (per mol N atoms) 0.36 8 O oxygen (O2) use (O2) 0.444 CRC (O2) 0.44 LNG (O2) 0.444 WEL (per mol O atoms) 0.222 9 F fluorine (F2) use (F2) 0.510 CRC (F2) 0.51 LNG (F2) 0.510 WEL (per mol F atoms) 0.26 10 Ne neon use 0.335 CRC 0.328 LNG 0.335 WEL 0.34 11 Na sodium use 2.60 CRC 2.60 LNG 2.60 WEL 2.60 12 Mg magnesium use 8.48 CRC 8.48 LNG 8.48 WEL 8.7 13 Al aluminium use 10.71 CRC 10.789 LNG 10.71 WEL 10.7 14 Si silicon use 50.21 CRC 50.21 LNG 50.21 WEL 50.2 15 P phosphorus use 0.66 CRC (white) 0.66 LNG 0.66 WEL 0.64 16 S sulfur use (mono) 1.727 CRC (mono) 1.72 LNG (mono) 1.727 WEL 1.73 17 Cl chlorine (Cl2) use (Cl2) 6.406 CRC (Cl2) 6.40 LNG (Cl2) 6.406 WEL (per mol Cl atoms) 3.2 18 Ar argon use 1.18 CRC 1.18 LNG 1.12 WEL 1.18 19 K potassium use 2.321 CRC 2.33 LNG 2.321 WEL 2.33 20 Ca calcium use 8.54 CRC 8.54 LNG 8.54 WEL 8.54 21 Sc scandium use 14.1 CRC 14.1 LNG 14.1 WEL 16 22 Ti titanium use 14.15 CRC 14.15 LNG 14.15 WEL 18.7 23 V vanadium use 21.5 CRC 21.5 LNG 21.5 WEL 22.8 24 Cr chromium use 21.0 CRC 21.0 LNG 21.0 WEL 20.5 25 Mn manganese use 12.91 CRC 12.91 LNG 12.9 WEL 13.2 26 Fe iron use 13.81 CRC 13.81 LNG 13.81 WEL 13.8 27 Co cobalt use 16.06 CRC 16.06 LNG 16.2 WEL 16.2 28 Ni nickel use 17.48 CRC 17.04 LNG 17.48 WEL 17.2 29 Cu copper use 13.26 CRC 12.93 LNG 13.26 WEL 13.1 30 Zn zinc use 7.32 CRC 7.068 LNG 7.32 WEL 7.35 31 Ga gallium use 5.59 CRC 5.576 LNG 5.59 WEL 5.59 32 Ge germanium use 36.94 CRC 36.94 LNG 36.94 WEL 31.8 33 As arsenic use (gray) 24.44 CRC (gray) 24.44 LNG 24.44 WEL 27.7 34 Se selenium use (gray) 6.69 CRC (gray) 6.69 LNG 6.69 WEL 5.4 35 Br bromine (Br2) use (Br2) 10.57 CRC (Br2) 10.57 LNG (Br2) 10.57 WEL (per mol Br atoms) 5.8 36 Kr krypton use 1.64 CRC 1.64 LNG 1.37 WEL 1.64 37 Rb rubidium use 2.19 CRC 2.19 LNG 2.19 WEL 2.19 38 Sr strontium use 7.43 CRC 7.43 LNG 7.43 WEL 8 39 Y yttrium use 11.42 CRC 11.4 LNG 11.42 WEL 11.4 40 Zr zirconium use 14 13.96 ± 0.36 CRC 21.00 LNG 21.00 WEL 21 41 Nb niobium use 30 CRC 30 LNG 30 WEL 26.8 42 Mo molybdenum use 37.48 CRC 37.48 LNG 37.48 WEL 36 43 Tc technetium use 33.29 CRC 33.29 LNG 33.29 WEL 23 44 Ru ruthenium use 38.59 CRC 38.59 LNG 38.59 WEL 25.7 45 Rh rhodium use 26.59 CRC 26.59 LNG 26.59 WEL 21.7 46 Pd palladium use 16.74 CRC 16.74 LNG 16.74 WEL 16.7 47 Ag silver use 11.28 CRC 11.28 LNG 11.95 WEL 11.3 48 Cd cadmium use 6.21 CRC 6.21 LNG 6.19 WEL 6.3 49 In indium use 3.281 CRC 3.281 LNG 3.28 WEL 3.26 50 Sn tin use (white) 7.03 CRC (white) 7.173 LNG (white) 7.03 WEL 7.0 51 Sb antimony use 19.79 CRC 19.79 LNG 19.87 WEL 19.7 52 Te tellurium use 17.49 CRC 17.49 LNG 17.49 WEL 17.5 53 I iodine (I2) use (I2) 15.52 CRC (I2) 15.52 LNG (I2) 150.66 [sic] WEL (per mol I atoms) 7.76 54 Xe xenon use 2.27 CRC 2.27 LNG 1.81 WEL 2.30 55 Cs caesium use 2.09 CRC 2.09 LNG 2.09 WEL 2.09 56 Ba barium use 7.12 CRC 7.12 LNG 7.12 WEL 8.0 57 La lanthanum use 6.20 CRC 6.20 LNG 6.20 WEL 6.2 58 Ce cerium use 5.46 CRC 5.46 LNG 5.46 WEL 5.5 59 Pr praseodymium use 6.89 CRC 6.89 LNG 6.89 WEL 6.9 60 Nd neodymium use 7.14 CRC 7.14 LNG 7.14 WEL 7.1 61 Pm promethium use 7.13 LNG 7.13 WEL about 7.7 62 Sm samarium use 8.62 CRC 8.62 LNG 8.62 WEL 8.6 63 Eu europium use 9.21 CRC 9.21 LNG 9.21 WEL 9.2 64 Gd gadolinium use 10.05 CRC 10.0 LNG 10.05 WEL 10.0 65 Tb terbium use 10.15 CRC 10.15 LNG 10.15 WEL 10.8 66 Dy dysprosium use 11.06 CRC 11.06 LNG 11.06 WEL 11.1 67 Ho holmium use 17.0 CRC 17.0 LNG 16.8 WEL 17.0 68 Er erbium use 19.90 CRC 19.9 LNG 19.90 WEL 19.9 69 Tm thulium use 16.84 CRC 16.84 LNG 16.84 WEL 16.8 70 Yb ytterbium use 7.66 CRC 7.66 LNG 7.66 WEL 7.7 71 Lu lutetium use ca. 22 CRC 22 LNG (22) WEL about 22 72 Hf hafnium use 27.2 CRC 27.2 LNG 27.2 WEL 25.5 73 Ta tantalum use 36.57 CRC 36.57 LNG 36.57 WEL 36 74 W tungsten use 52.31 CRC 52.31 LNG 52.31 WEL 35 75 Re rhenium use 60.43 CRC 60.43 LNG 60.43 WEL 33 76 Os osmium use 57.85 CRC 57.85 LNG 57.85 WEL 31 77 Ir iridium use 41.12 CRC 41.12 LNG 41.12 WEL 26 78 Pt platinum use 22.17 CRC 22.17 LNG 22.17 WEL 20 79 Au gold use 12.55 CRC 12.72 LNG 12.55 WEL 12.5 80 Hg mercury use 2.29 CRC 2.29 LNG 2.29 WEL 2.29 81 Tl thallium use 4.14 CRC 4.14 LNG 4.14 WEL 4.2 82 Pb lead use 4.77 CRC 4.782 LNG 4.77 WEL 4.77 83 Bi bismuth use 11.30 CRC 11.145 LNG 11.30 WEL 10.9 84 Po polonium use ca. 13 WEL about 13 85 At astatine use WEL (per mol At atoms) about 6 86 Rn radon use 3.247 LNG 3.247 WEL 3 87 Fr francium use ca. 2 WEL about 2 88 Ra radium use 8.5 LNG 8.5 WEL about 8 89 Ac actinium use 14 WEL 14 90 Th thorium use 13.81 CRC 13.81 LNG 13.81 WEL 16 91 Pa protactinium use 12.34 CRC 12.34 LNG 12.34 WEL 15 92 U uranium use 9.14 CRC 9.14 LNG 9.14 WEL 14 93 Np neptunium use 3.20 CRC 3.20 LNG 3.20 WEL 10 94 Pu plutonium use 2.82 CRC 2.82 LNG 2.82 95 Am americium use 14.39 CRC 14.39 LNG 14.39 == Notes == * Values refer to the enthalpy change between the liquid phase and the most stable solid phase at the melting point (normal, 101.325 kPa). == References == === CRC === As quoted from various sources in an online version of: * David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. ==Earth bulk continental crust and upper continental crust== C1 — Crust: CRC Handbook C2 — Crust: Kaye and Laby C3 — Crust: Greenwood C4 — Crust: Ahrens (Taylor) C5 — Crust: Ahrens (Wänke) C6 — Crust: Ahrens (Weaver) U1 — Upper crust: Ahrens (Taylor) U2 — Upper crust: Ahrens (Shaw) Element C1 C2 C3 C4 C5 C6 U1 U2 01 H hydrogen 1.40×10−3 1.52 _0_ ×10−3 02 He helium 8×10−9 03 Li lithium 2.0×10−5 2.0×10−5 1.8×10−5 1.3×10−5 1.37×10−5 2. _0_ ×10−5 2.2×10−5 04 Be beryllium 2.8×10−6 2.0×10−6 2×10−6 1.5 _00_ ×10−6 3. _000_ ×10−6 05 B boron 1.0×10−5 7.0×10−6 9×10−6 1. _0000_ ×10−5 1.5 _000_ ×10−5 06 C carbon 2.00×10−4 1.8 _0_ ×10−4 3.76×10−3 07 N nitrogen 1.9×10−5 2.0×10−5 1.9×10−5 08 O oxygen 4.61×10−1 3.7×10−1 4.55 _000_ ×10−1 09 F fluorine 5.85×10−4 4.6×10−4 5.44×10−4 5.25×10−4 10 Ne neon 5×10−9 11 Na sodium 2.36×10−2 2.3×10−2 2.27 _00_ ×10−2 2.3 _000_ ×10−2 2.44 _00_ ×10−2 3.1 _000_ ×10−2 2.89×10−2 2.57×10−2 12 Mg magnesium 2.33×10−2 2.8×10−2 2.764 _0_ ×10−2 3.20×10−2 2.37×10−2 1.69×10−2 1.33×10−2 1.35×10−2 13 Al aluminium 8.23×10−2 8.0×10−2 8.3 _000_ ×10−2 8.41 _00_ ×10−2 8.305 _0_ ×10−2 8.52 _00_ ×10−2 8.04 _00_ ×10−2 7.74 _00_ ×10−2 14 Si silicon 2.82×10−1 2.7×10−1 2.72 _000_ ×10−1 2.677×10−1 2.81×10−1 2.95×10−1 3.08×10−1 3.04×10−1 15 P phosphorus 1.05×10−3 1.0×10−3 1.12 _0_ ×10−3 7.63×10−4 8.3 _0_ ×10−4 16 S sulfur 3.50×10−4 3.0×10−4 3.4 _0_ ×10−4 8.81×10−4 17 Cl chlorine 1.45×10−4 1.9×10−4 1.26×10−4 1.9 _00_ ×10−3 18 Ar argon 3.5×10−6 19 K potassium 2.09×10−2 1.7×10−2 1.84 _00_ ×10−2 9.1 _00_ ×10−3 1.76 _00_ ×10−2 1.7 _000_ ×10−2 2.8 _000_ ×10−2 2.57 _00_ ×10−2 20 Ca calcium 4.15×10−2 5.1×10−2 4.66 _00_ ×10−2 5.29 _00_ ×10−2 4.92 _00_ ×10−2 3.4 _000_ ×10−2 3. _0000_ ×10−2 2.95 _00_ ×10−2 21 Sc scandium 2.2×10−5 2.2×10−5 2.5×10−5 3. _0_ ×10−5 2.14×10−5 1.1×10−5 7×10−6 22 Ti titanium 5.65×10−3 8.6×10−3 6.32 _0_ ×10−3 5.4 _00_ ×10−3 5.25 _0_ ×10−3 3.6 _00_ ×10−3 3. _000_ ×10−3 3.12 _0_ ×10−3 23 V vanadium 1.20×10−4 1.7×10−4 1.36×10−4 2.3 _0_ ×10−4 1.34×10−4 6. _0_ ×10−5 5.3×10−5 24 Cr chromium 1.02×10−4 9.6×10−5 1.22×10−4 1.85×10−4 1.46×10−4 5.6×10−5 3.5×10−5 3.5×10−5 25 Mn manganese 9.50×10−4 1.0×10−3 1.06 _0_ ×10−3 1.4 _00_ ×10−3 8.47×10−4 1. _000_ ×10−3 6. _00_ ×10−4 5.27×10−4 26 Fe iron 5.63×10−2 5.8×10−2 6.2 _000_ ×10−2 7.07×10−2 4.92×10−2 3.8×10−2 3.50×10−2 3.09×10−2 27 Co cobalt 2.5×10−5 2.8×10−5 2.9×10−5 2.9×10−5 2.54×10−5 1. _0_ ×10−5 1.2×10−5 28 Ni nickel 8.4×10−5 7.2×10−5 9.9×10−5 1.05×10−4 6.95×10−5 3.5×10−5 2×10−5 1.9×10−5 29 Cu copper 6.0×10−5 5.8×10−5 6.8×10−5 7.5×10−5 4.7×10−5 2.5×10−5 1.4×10−5 30 Zn zinc 7.0×10−5 8.2×10−5 7.6×10−5 8. _0_ ×10−5 7.6×10−5 7.1×10−5 5.2×10−5 31 Ga gallium 1.9×10−5 1.7×10−5 1.9×10−5 1.8×10−5 1.86×10−5 1.7×10−5 1.4×10−5 32 Ge germanium 1.5×10−6 1.3×10−6 1.5×10−6 1.6×10−6 1.32×10−6 1.6×10−6 33 As arsenic 1.8×10−6 2.0×10−6 1.8×10−6 1.0×10−6 2.03×10−6 1.5×10−6 34 Se selenium 5×10−8 5×10−8 5×10−8 5×10−8 1.53×10−7 5×10−8 35 Br bromine 2.4×10−6 4.0×10−6 2.5×10−6 6.95×10−6 36 Kr krypton 1×10−10 37 Rb rubidium 9.0×10−5 7.0×10−5 7.8×10−5 3.2×10−5 7.90×10−5 6.1×10−5 1.12×10−4 1.1 _0_ ×10−4 38 Sr strontium 3.70×10−4 4.5×10−4 3.84×10−4 2.6 _0_ ×10−4 2.93×10−4 5.03×10−4 3.5 _0_ ×10−4 3.16×10−4 39 Y yttrium 3.3×10−5 3.5×10−7 3.1×10−5 2. _0_ ×10−5 1.4×10−5 2.2×10−5 2.1×10−5 40 Zr zirconium 1.65×10−4 1.4×10−4 1.62×10−4 1. _00_ ×10−4 2.1 _0_ ×10−4 1.9 _0_ ×10−4 2.4 _0_ ×10−4 41 Nb niobium 2.0×10−5 2.0×10−5 2. _0_ ×10−5 1.1 _000_ ×10−5 1.3 _000_ ×10−5 2.5 _000_ ×10−5 2.6 _000_ ×10−5 42 Mo molybdenum 1.2×10−6 1.2×10−6 1.2×10−6 1. _000_ ×10−6 1.5 _00_ ×10−6 43 Tc technetium 44 Ru ruthenium 1×10−9 1×10−10 45 Rh rhodium 1×10−9 1×10−10 46 Pd palladium 1.5×10−8 3×10−9 1.5×10−8 1.0×10−9 5×10−10 47 Ag silver 7.5×10−8 8×10−8 8×10−8 8. _0_ ×10−8 6.95×10−8 5. _0_ ×10−8 48 Cd cadmium 1.5×10−7 1.8×10−7 1.6×10−7 9.8×10−8 1. _00_ ×10−7 9.8×10−8 49 In indium 2.5×10−7 2×10−7 2.4×10−7 5. _0_ ×10−8 6.95×10−8 5. _0_ ×10−8 50 Sn tin 2.3×10−6 1.5×10−6 2.1×10−6 2.5 _00_ ×10−6 5.5 _00_ ×10−6 51 Sb antimony 2×10−7 2×10−7 2×10−7 2. _00_ ×10−7 2.03×10−7 2. _00_ ×10−7 52 Te tellurium 1×10−9 1×10−9 2.03×10−9 53 I iodine 4.5×10−7 5×10−7 4.6×10−7 1.54 _0_ ×10−6 54 Xe xenon 3×10−11 55 Cs caesium 3×10−6 1.6×10−6 2.6×10−6 1. _000_ ×10−6 1.31 _0_ ×10−6 3.7 _00_ ×10−6 56 Ba barium 4.25×10−4 3.8×10−4 3.9 _0_ ×10−4 2.5 _0000_ ×10−4 5.42 _000_ ×10−4 7.07 _000_ ×10−4 5.5 _0000_ ×10−4 1.07 _0000_ ×10−3 57 La lanthanum 3.9×10−5 5.0×10−5 3.5×10−5 1.6 _000_ ×10−5 2.9 _000_ ×10−5 2.8 _000_ ×10−5 3. _0000_ ×10−5 3.2 _00_ ×10−6 58 Ce cerium 6.65×10−5 8.3×10−5 6.6×10−5 3.3 _000_ ×10−5 5.42 _00_ ×10−5 5.7 _000_ ×10−5 6.4 _000_ ×10−5 6.5 _000_ ×10−5 59 Pr praseodymium 9.2×10−6 1.3×10−5 9.1×10−6 3.9 _00_ ×10−6 7.1 _00_ ×10−6 60 Nd neodymium 4.15×10−5 4.4×10−5 4. _0_ ×10−5 1.6 _000_ ×10−5 2.54 _00_ ×10−5 2.3 _000_ ×10−5 2.6 _000_ ×10−5 2.6 _000_ ×10−5 61 Pm promethium 62 Sm samarium 7.05×10−6 7.7×10−6 7.0×10−6 3.5 _00_ ×10−6 5.59 _0_ ×10−6 4.1 _00_ ×10−6 4.5 _00_ ×10−6 4.5 _00_ ×10−6 63 Eu europium 2.0×10−6 2.2×10−6 2.1×10−6 1.1 _00_ ×10−6 1.407×10−6 1.09 _0_ ×10−6 8.8 _0_ ×10−7 9.4 _0_ ×10−7 64 Gd gadolinium 6.2×10−6 6.3×10−6 6.1×10−6 3.3 _00_ ×10−6 8.14 _0_ ×10−6 3.8 _00_ ×10−6 2.8 _00_ ×10−6 65 Tb terbium 1.2×10−6 1.0×10−6 1.2×10−6 6. _00_ ×10−7 1.02 _0_ ×10−6 5.3 _0_ ×10−7 6.4 _0_ ×10−7 4.8 _0_ ×10−7 66 Dy dysprosium 5.2×10−6 8.5×10−6 3.7 _00_ ×10−6 6.102×10−6 3.5 _00_ ×10−6 67 Ho holmium 1.3×10−6 1.6×10−6 1.3×10−6 7.8 _0_ ×10−7 1.86 _0_ ×10−6 8. _00_ ×10−7 6.2 _0_ ×10−7 68 Er erbium 3.5×10−6 3.6×10−6 3.5×10−6 2.2 _00_ ×10−6 3.39 _0_ ×10−6 2.3 _00_ ×10−6 69 Tm thulium 5.2×10−7 5.2×10−7 5×10−7 3.2 _0_ ×10−7 2.4 _0_ ×10−7 3.3 _0_ ×10−7 70 Yb ytterbium 3.2×10−6 3.4×10−6 3.1×10−6 2.2 _00_ ×10−6 3.39 _0_ ×10−6 1.53 _0_ ×10−6 2.2 _00_ ×10−6 1.5 _00_ ×10−6 71 Lu lutetium 8×10−7 8×10−7 3. _00_ ×10−7 5.76×10−7 2.3 _0_ ×10−7 3.2 _0_ ×10−7 2.3 _0_ ×10−7 72 Hf hafnium 3.0×10−6 4×10−6 2.8×10−6 3. _000_ ×10−6 3.46 _0_ ×10−6 4.7 _00_ ×10−6 5.8 _00_ ×10−6 5.8 _00_ ×10−6 73 Ta tantalum 2.0×10−6 2.4×10−6 1.7×10−6 1. _000_ ×10−6 2.203×10−6 2.2 _00_ ×10−6 74 W tungsten 1.25×10−6 1.0×10−6 1.2×10−6 1. _000_ ×10−6 1.31 _0_ ×10−6 2. _000_ ×10−6 75 Re rhenium 7×10−10 4×10−10 7×10−10 5×10−10 1.02×10−9 5×10−10 76 Os osmium 1.5×10−9 2×10−10 5×10−9 1.02×10−9 77 Ir iridium 1×10−9 2×10−10 1×10−9 1×10−10 1.02×10−9 2×10−11 78 Pt platinum 5×10−9 1×10−8 79 Au gold 4×10−9 2×10−9 4×10−9 3.0×10−9 4.07×10−9 1.8×10−9 80 Hg mercury 8.5×10−8 2×10−8 8×10−8 81 Tl thallium 8.5×10−7 4.7×10−7 7×10−7 3.6 _0_ ×10−7 7.5 _0_ ×10−7 5.2 _0_ ×10−7 82 Pb lead 1.4×10−5 1.0×10−5 1.3×10−5 8. _000_ ×10−6 1.5 _000_ ×10−5 2. _0000_ ×10−5 1.7 _000_ ×10−5 83 Bi bismuth 8.5×10−9 4×10−9 8×10−9 6. _0_ ×10−8 1.27×10−7 84 Po polonium 2×10−16 85 At astatine 86 Rn radon 4×10−19 87 Fr francium 88 Ra radium 9×10−13 89 Ac actinium 5.5×10−16 90 Th thorium 9.6×10−6 5.8×10−6 8.1×10−6 3.5 _00_ ×10−6 5.7 _00_ ×10−6 1.07 _00_ ×10−5 1. _0000_ ×10−5 91 Pa protactinium 1.4×10−12 92 U uranium 2.7×10−6 1.6×10−6 2.3×10−6 9.1 _0_ ×10−7 1.2 _00_ ×10−6 1.3 _00_ ×10−6 2.8 _00_ ×10−6 2.5 _00_ ×10−6 93 Np neptunium 94 Pu plutonium ==Urban soils== The established abundances of chemical elements in urban soils can be considered a geochemical (ecological and geochemical) characteristic, the accumulated impact of technogenic and natural processes at the beginning of the 21st century. ==Thermal conductivity== 1 H hydrogen use 180.5 mW/(m·K) CR2 (P=0) 186.9 mW/(m·K) LNG 0.1805 W/(m·K) WEL 0.1805 W/(m·K) 2 He helium use 151.3 mW/(m·K) CR2 (P=0) 156.7 mW/(m·K) LNG 0.1513 W/(m·K) WEL 0.1513 W/(m·K) 3 Li lithium use 84.8 W/(m·K) CRC 0.847 W/(cm·K) LNG 84.8 W/(m·K) WEL 85 W/(m·K) 4 Be beryllium use 200 W/(m·K) CRC 2.00 W/(cm·K) LNG 200 W/(m·K) WEL 190 W/(m·K) 5 B boron use 27.4 W/(m·K) LNG 27.4 W/(m·K) WEL 27 W/(m·K) 6 C carbon (graphite) use (graphite) (119-165) W/(m·K) LNG (119-165) W/(m·K) LNG (amorphous) 1.59 W/(m·K) WEL 140 W/(m·K) CRC pyrolytic graphite (parallel to the layer planes) 19.5 W/(cm·K) (perpendicular) 0.0570 W/(cm·K) 6 C carbon (diamond) use (diamond) (900-2320) W/(m·K) LNG (900-2320) W/(m·K) CRC (type I) 8.95 W/(cm·K) (type IIa) 23.0 W/(cm·K) (type IIb) 13.5 W/(cm·K) 7 N nitrogen use 25.83 mW/(m·K) CR2 26.0 mW/(m·K) LNG 0.02583 W/(m·K) WEL 0.02583 W/(m·K) 8 O oxygen use 26.58 mW/(m·K) CR2 26.3 mW/(m·K) LNG (gas) 0.02658 W/(m·K) LNG (liquid) 0.149 W/(m·K) WEL 0.02658 W/(m·K) 9 F fluorine use 27.7 mW/(m·K) LNG 0.0277 W/(m·K) WEL 0.0277 W/(m·K) 10 Ne neon use 49.1 mW/(m·K) CR2 (P=0) 49.8 mW/(m·K) LNG 0.0491 W/(m·K) WEL 0.0491 W/(m·K) 11 Na sodium use 142 W/(m·K) CRC 1.41 W/(cm·K) LNG 142 W/(m·K) WEL 140 W/(m·K) 12 Mg magnesium use 156 W/(m·K) CRC 1.56 W/(cm·K) LNG 156 W/(m·K) WEL 160 W/(m·K) 13 Al aluminium use 237 W/(m·K) CRC 2.37 W/(cm·K) LNG 237 W/(m·K) WEL 235 W/(m·K) 14 Si silicon use 149 W/(m·K) LNG 149 W/(m·K) WEL 150 W/(m·K) 15 P phosphorus use (white) 0.236 W/(m·K) LNG (white) 0.23617 W/(m·K) [sic] WEL 0.236 W/(m·K) 16 S sulfur use (amorphous) 0.205 W/(m·K) LNG (amorphous) 0.205 W/(m·K) WEL 0.205 W/(m·K) 17 Cl chlorine use 8.9 mW/(m·K) LNG 0.0089 W/(m·K) WEL 0.0089 W/(m·K) 18 Ar argon use 17.72 mW/(m·K) CR2 17.9 mW/(m·K) LNG 0.01772 W/(m·K) WEL 0.01772 W/(m·K) 19 K potassium use 102.5 W/(m·K) CRC 1.024 W/(cm·K) LNG 102.5 W/(m·K) WEL 100 W/(m·K) 20 Ca calcium use 201 W/(m·K) CRC 2.00 W/(cm·K) LNG 201 W/(m·K) WEL 200 W/(m·K) 21 Sc scandium use 15.8 W/(m·K) CRC 0.158 W/(cm·K) LNG 15.8 W/(m·K) WEL 16 W/(m·K) 22 Ti titanium use 21.9 W/(m·K) CRC 0.219 W/(cm·K) LNG 21.9 W/(m·K) WEL 22 W/(m·K) 23 V vanadium use 30.7 W/(m·K) CRC 0.307 W/(cm·K) LNG 30.7 W/(m·K) WEL 31 W/(m·K) 24 Cr chromium use 93.9 W/(m·K) CRC 0.937 W/(cm·K) LNG 93.9 W/(m·K) WEL 94 W/(m·K) 25 Mn manganese use 7.81 W/(m·K) CRC 0.0782 W/(cm·K) LNG 7.81 W/(m·K) WEL 7.8 W/(m·K) 26 Fe iron use 80.4 W/(m·K) CRC 0.802 W/(cm·K) LNG 80.4 W/(m·K) WEL 80 W/(m·K) 27 Co cobalt use 100 W/(m·K) CRC 1.00 W/(cm·K) LNG 100 W/(m·K) WEL 100 W/(m·K) 28 Ni nickel use 90.9 W/(m·K) CRC 0.907 W/(cm·K) LNG 90.9 W/(m·K) WEL 91 W/(m·K) 29 Cu copper use 401 W/(m·K) CRC 4.01 W/(cm·K) LNG 401 W/(m·K) WEL 400 W/(m·K) 30 Zn zinc use 116 W/(m·K) CRC 1.16 W/(cm·K) LNG 116 W/(m·K) WEL 120 W/(m·K) 31 Ga gallium use 40.6 W/(m·K) CRC 0.406 W/(cm·K) LNG (liquid) 29.4 W/(m·K) LNG (solid) 40.6 W/(m·K) WEL 29 W/(m·K) 32 Ge germanium use 60.2 W/(m·K) LNG 60.2 W/(m·K) WEL 60 W/(m·K) 33 As arsenic use 50.2 W/(m·K) LNG 50.2 W/(m·K) WEL 50 W/(m·K) 34 Se selenium use (amorphous) 0.519 W/(m·K) LNG (amorphous) 0.519 W/(m·K) WEL 0.52 W/(m·K) 35 Br bromine use 0.122 W/(m·K) LNG 0.122 W/(m·K) WEL 0.12 W/(m·K) 36 Kr krypton use 9.43 mW/(m·K) CR2 (P=0) 9.5 mW/(m·K) LNG 9.43 W/(m·K) [sic] WEL 0.00943 W/(m·K) 37 Rb rubidium use 58.2 W/(m·K) CRC 0.582 W/(cm·K) LNG 58.2 W/(m·K) WEL 58 W/(m·K) 38 Sr strontium use 35.4 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.4 W/(m·K) WEL 35 W/(m·K) 39 Y yttrium use 17.2 W/(m·K) CRC 0.172 W/(cm·K) LNG 17.2 W/(m·K) WEL 17 W/(m·K) 40 Zr zirconium use 22.6 W/(m·K) CRC 0.227 W/(cm·K) LNG 22.6 W/(m·K) WEL 23 W/(m·K) 41 Nb niobium use 53.7 W/(m·K) CRC 0.537 W/(cm·K) LNG 53.7 W/(m·K) WEL 54 W/(m·K) 42 Mo molybdenum use 138 W/(m·K) CRC 1.38 W/(cm·K) LNG 138 W/(m·K) WEL 139 W/(m·K) 43 Tc technetium use 50.6 W/(m·K) CRC 0.506 W/(cm·K) LNG 50.6 W/(m·K) WEL 51 W/(m·K) 44 Ru ruthenium use 117 W/(m·K) CRC 1.17 W/(cm·K) LNG 117 W/(m·K) WEL 120 W/(m·K) 45 Rh rhodium use 150 W/(m·K) CRC 1.50 W/(cm·K) LNG 150 W/(m·K) WEL 150 W/(m·K) 46 Pd palladium use 71.8 W/(m·K) CRC 0.718 W/(cm·K) LNG 71.8 W/(m·K) WEL 72 W/(m·K) 47 Ag silver use 429 W/(m·K) CRC 4.29 W/(cm·K) LNG 429 W/(m·K) WEL 430 W/(m·K) 48 Cd cadmium use 96.6 W/(m·K) CRC 0.968 W/(cm·K) LNG 96.6 W/(m·K) WEL 97 W/(m·K) 49 In indium use 81.8 W/(m·K) CRC 0.816 W/(cm·K) LNG 81.8 W/(m·K) WEL 82 W/(m·K) 50 Sn tin use 66.8 W/(m·K) CRC 0.666 W/(cm·K) LNG 66.8 W/(m·K) WEL 67 W/(m·K) 51 Sb antimony use 24.4 W/(m·K) CRC 0.243 W/(cm·K) LNG 24.4 W/(m·K) WEL 24 W/(m·K) 52 Te tellurium use (1.97-3.38) W/(m·K) LNG (1.97-3.38) W/(m·K) WEL 3 W/(m·K) 53 I iodine use 0.449 W/(m·K) CRC (300 K) 0.45 W/(m·K) LNG 449 W/(m·K) [sic] WEL 0.449 W/(m·K) 54 Xe xenon use 5.65 mW/(m·K) CR2 (P=0) 5.5 mW/(m·K) LNG 0.00565 W/(m·K) WEL 0.00565 W/(m·K) 55 Cs caesium use 35.9 W/(m·K) CRC 0.359 W/(cm·K) LNG 35.9 W/(m·K) WEL 36 W/(m·K) 56 Ba barium use 18.4 W/(m·K) CRC 0.184 W/(cm·K) LNG 18.4 W/(m·K) WEL 18 W/(m·K) 57 La lanthanum use 13.4 W/(m·K) CRC 0.134 W/(cm·K) LNG 13.4 W/(m·K) WEL 13 W/(m·K) 58 Ce cerium use 11.3 W/(m·K) CRC 0.113 W/(cm·K) LNG 11.3 W/(m·K) WEL 11 W/(m·K) 59 Pr praseodymium use 12.5 W/(m·K) CRC 0.125 W/(cm·K) LNG 12.5 W/(m·K) WEL 13 W/(m·K) 60 Nd neodymium use 16.5 W/(m·K) CRC 0.165 W/(cm·K) LNG 16.5 W/(m·K) WEL 17 W/(m·K) 61 Pm promethium use 17.9 W/(m·K) CRC (est.) 0.15 W/(cm·K) LNG 17.9 W/(m·K) WEL 15 W/(m·K) 62 Sm samarium use 13.3 W/(m·K) CRC 0.133 W/(cm·K) LNG 13.3 W/(m·K) WEL 13 W/(m·K) 63 Eu europium use (est.) 13.9 W/(m·K) CRC (est.) 0.139 W/(cm·K) LNG 13.9 W/(m·K) WEL 14 W/(m·K) 64 Gd gadolinium use 10.6 W/(m·K) (300 K) 10.6 W/(m·K) CRC (100 °C) 0.105 W/(cm·K) LNG 10.5 W/(m·K) WEL 11 W/(m·K) 65 Tb terbium use 11.1 W/(m·K) CRC 0.111 W/(cm·K) LNG 11.1 W/(m·K) WEL 11 W/(m·K) 66 Dy dysprosium use 10.7 W/(m·K) CRC 0.107 W/(cm·K) LNG 10.7 W/(m·K) WEL 11 W/(m·K) 67 Ho holmium use 16.2 W/(m·K) CRC 0.162 W/(cm·K) LNG 16.2 W/(m·K) WEL 16 W/(m·K) 68 Er erbium use 14.5 W/(m·K) CRC 0.145 W/(cm·K) LNG 14.5 W/(m·K) WEL 15 W/(m·K) 69 Tm thulium use 16.9 W/(m·K) CRC 0.169 W/(cm·K) LNG 16.9 W/(m·K) WEL 17 W/(m·K) 70 Yb ytterbium use 38.5 W/(m·K) CRC 0.385 W/(cm·K) LNG 38.5 W/(m·K) WEL 39 W/(m·K) 71 Lu lutetium use 16.4 W/(m·K) CRC 0.164 W/(cm·K) LNG 16.4 W/(m·K) WEL 16 W/(m·K) 72 Hf hafnium use 23.0 W/(m·K) CRC 0.230 W/(cm·K) LNG 23.0 W/(m·K) WEL 23 W/(m·K) 73 Ta tantalum use 57.5 W/(m·K) CRC 0.575 W/(cm·K) LNG 57.5 W/(m·K) WEL 57 W/(m·K) 74 W tungsten use 173 W/(m·K) CRC 1.74 W/(cm·K) LNG 173 W/(m·K) WEL 170 W/(m·K) 75 Re rhenium use 48.0 W/(m·K) CRC 0.479 W/(cm·K) LNG 48.0 W/(m·K) WEL 48 W/(m·K) 76 Os osmium use 87.6 W/(m·K) CRC 0.876 W/(cm·K) LNG 87.6 W/(m·K) WEL 88 W/(m·K) 77 Ir iridium use 147 W/(m·K) CRC 1.47 W/(cm·K) LNG 147 W/(m·K) WEL 150 W/(m·K) 78 Pt platinum use 71.6 W/(m·K) CRC 0.716 W/(cm·K) LNG 71.6 W/(m·K) WEL 72 W/(m·K) 79 Au gold use 318 W/(m·K) CRC 3.17 W/(cm·K) LNG 318 W/(m·K) WEL 320 W/(m·K) 80 Hg mercury use 8.30 W/(m·K) CRC 0.0834 W/(cm·K) LNG 8.30 W/(m·K) WEL 8.3 W/(m·K) 81 Tl thallium use 46.1 W/(m·K) CRC 0.461 W/(cm·K) LNG 46.1 W/(m·K) WEL 46 W/(m·K) 82 Pb lead use 35.3 W/(m·K) CRC 0.353 W/(cm·K) LNG 35.3 W/(m·K) WEL 35 W/(m·K) 83 Bi bismuth use 7.97 W/(m·K) CRC 0.0787 W/(cm·K) LNG 7.97 W/(m·K) WEL 8 W/(m·K) 84 Po polonium use CRC 0.20 W/(cm·K) LNG 0.2 W/(m·K) 85 At astatine use 1.7 W/(m·K) LNG 1.7 W/(m·K) WEL 2 W/(m·K) 86 Rn radon use 3.61 mW/(m·K) LNG 0.00361 W/(m·K) WEL 0.00361 W/(m·K) 88 Ra radium use 18.6 W/(m·K) LNG 18.6 W/(m·K) WEL 19 W/(m·K) 89 Ac actinium use 12 W/(m·K) LNG 12 W/(m·K) WEL 12 W/(m·K) 90 Th thorium use 54.0 W/(m·K) CRC 0.540 W/(cm·K) LNG 54.0 W/(m·K) WEL 54 W/(m·K) 91 Pa protactinium use 47 W/(m·K) LNG 47 W/(m·K) WEL 47 W/(m·K) 92 U uranium use 27.5 W/(m·K) CRC 0.276 W/(cm·K) LNG 27.5 W/(m·K) WEL 27 W/(m·K) 93 Np neptunium use 6.3 W/(m·K) CRC 0.063 W/(cm·K) LNG 6.3 W/(m·K) WEL 6 W/(m·K) 94 Pu plutonium use 6.74 W/(m·K) CRC 0.0674 W/(cm·K) LNG 6.74 W/(m·K) WEL 6 W/(m·K) 95 Am americium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) 97 Bk berkelium use 10 W/(m·K) LNG 10 W/(m·K) WEL 10 W/(m·K) ==Notes== * Ref. CRC: Values refer to 27 °C unless noted. J/(mol K) Gas properties Std enthalpy change of formation ΔfH ~~o~~ gas ? kJ/mol Standard molar entropy S ~~o~~ gas ? Element S1 Y1 Y2 01 H hydrogen 2.8×104 2.8×104* 2.79×104 02 He helium 2.7×103 2.7×103* 2.72×103 03 Li lithium 4.0×10−7 5.7×10−5 5.71×10−5 (9.2%) 04 Be beryllium 4.0×10−7 7.0×10−7 7.30×10−7 (9.5%) 05 B boron 1.1×10−5 2.1×10−5 2.12×10−5 (10%) 06 C carbon 1.0×101 1.0×101* 1.01×101 07 N nitrogen 3.1×100 3.1×100* 3.13×100 08 O oxygen 2.4×101 2.4×101* 2.38×101 (10%) 09 F fluorine about 1.0×10−3 8.5×10−4 8.43×10−4 (15%) 10 Ne neon 3.0×100 3.0×100* 3.44×100 (14%) 11 Na sodium 6.0×10−2 5.7×10−2 5.74×10−2 (7.1%) 12 Mg magnesium 1.0×100 1.1×100 1.074×100 (3.8%) 13 Al aluminium 8.3×10−2 8.5×10−2 8.49×10−2 (3.6%) 14 Si silicon 1.0×100 1.0×100 1.0×100 (4.4%) 15 P phosphorus 8.0×10−3 1.0×10−2 1.04×10−2 (10%) 16 S sulfur 4.5×10−1 5.2×10−1 5.15×10−1 (13%) 17 Cl chlorine about 9.0×10−3 5.2×10−3 5.24×10−3 (15%) 18 Ar argon 1.0×10−1* 1.0×10−1* 1.01×10−1 (6%) 19 K potassium 3.7×10−3 3.8×10−3 3.77×10−3 (7.7%) 20 Ca calcium 6.4×10−2 6.1×10−2 6.11×10−2 (7.1%) 21 Sc scandium 3.5×10−5 3.4×10−5 3.42×10−5 (8.6%) 22 Ti titanium 2.7×10−3 2.4×10−3 2.40×10−3 (5.0%) 23 V vanadium 2.8×10−4 2.9×10−4 2.93×10−4 (5.1%) 24 Cr chromium 1.3×10−2 1.3×10−2 1.35×10−2 (7.6%) 25 Mn manganese 6.9×10−3 9.5×10−3 9.55×10−3 (9.6%) 26 Fe iron 9.0×10−1 9.0×10−1 9.00×10−1 (2.7%) 27 Co cobalt 2.3×10−3 2.3×10−3 2.25×10−3 (6.6%) 28 Ni nickel 5.0×10−2 5.0×10−2 4.93×10−2 (5.1%) 29 Cu copper 4.5×10−4 5.2×10−4 5.22×10−4 (11%) 30 Zn zinc 1.1×10−3 1.3×10−3 1.26×10−3 (4.4%) 31 Ga gallium 2.1×10−5 3.8×10−5 3.78×10−5 (6.9%) 32 Ge germanium 7.2×10−5 1.2×10−4 1.19×10−4 (9.6%) 33 As arsenic 6.6×10−6 6.56×10−6 (12%) 34 Se selenium 6.3×10−5 6.21×10−5 (6.4%) 35 Br bromine 1.2×10−5 1.18×10−5 (19%) 36 Kr krypton 4.8×10−5 4.50×10−5 (18%) 37 Rb rubidium 1.1×10−5 7.0×10−6 7.09×10−6 (6.6%) 38 Sr strontium 2.2×10−5 2.4×10−5 2.35×10−5 (8.1%) 39 Y yttrium 4.9×10−6 4.6×10−6 4.64×10−6 (6.0%) 40 Zr zirconium 1.12×10−5 1.14×10−5 1.14×10−5 (6.4%) 41 Nb niobium 7.0×10−7 7.0×10−7 6.98×10−7 (1.4%) 42 Mo molybdenum 2.3×10−6 2.6×10−6 2.55×10−6 (5.5%) 43 Tc technetium 44 Ru ruthenium 1.9×10−6 1.9×10−6 1.86×10−6 (5.4%) 45 Rh rhodium 4.0×10−7 3.4×10−7 3.44×10−7 (8%) 46 Pd palladium 1.4×10−6 1.4×10−6 1.39×10−6 (6.6%) 47 Ag silver about 2.0×10−7 4.9×10−7 4.86×10−7 (2.9%) 48 Cd cadmium 2.0×10−6 1.6×10−6 1.61×10−6 (6.5%) 49 In indium about 1.3×10−6 1.9×10−7 1.84×10−7 (6.4%) 50 Sn tin about 3.0×10−6 3.9×10−6 3.82×10−6 (9.4%) 51 Sb antimony about 3.0×10−7 3.1×10−7 3.09×10−7 (18%) 52 Te tellurium 4.9×10−6 4.81×10−6 (10%) 53 I iodine 9.0×10−7 9.00×10−7 (21%) 54 Xe xenon 4.8×10−6 4.70×10−6 (20%) 55 Cs caesium 3.7×10−7 3.72×10−7 (5.6%) 56 Ba barium 3.8×10−6 4.5×10−6 4.49×10−6 (6.3%) 57 La lanthanum 5.0×10−7 4.4×10−7 4.46×10−7 (2.0%) 58 Ce cerium 1.0×10−6 1.1×10−6 1.136×10−6 (1.7%) 59 Pr praseodymium 1.4×10−7 1.7×10−7 1.669×10−7 (2.4%) 60 Nd neodymium 9.0×10−7 8.3×10−7 8.279×10−7 (1.3%) 61 Pm promethium 62 Sm samarium 3.0×10−7 2.6×10−7 2.582×10−7 (1.3%) 63 Eu europium 9.0×10−8 9.7×10−8 9.73×10−8 (1.6%) 64 Gd gadolinium 3.7×10−7 3.3×10−7 3.30×10−7 (1.4%) 65 Tb terbium about 2.0×10−8 6.0×10−8 6.03×10−8 (2.2%) 66 Dy dysprosium 3.5×10−7 4.0×10−7 3.942×10−7 (1.4%) 67 Ho holmium about 5.0×10−8 8.9×10−8 8.89×10−8 (2.4%) 68 Er erbium 2.4×10−7 2.5×10−7 2.508×10−7 (1.3%) 69 Tm thulium about 3.0×10−8 3.8×10−8 3.78×10−8 (2.3%) 70 Yb ytterbium 3.4×10−7 2.5×10−7 2.479×10−7 (1.6%) 71 Lu lutetium about 1.5×10−7 3.7×10−8 3.67×10−8 (1.3%) 72 Hf hafnium 2.1×10−7 1.5×10−7 1.54×10−7 (1.9%) 73 Ta tantalum 3.8×10−8 2.07×10−8 (1.8%) 74 W tungsten about 3.6×10−7 1.3×10−7 1.33×10−7 (5.1%) 75 Re rhenium 5.0×10−8 5.17×10−8 (9.4%) 76 Os osmium 8.0×10−7 6.7×10−7 6.75×10−7 (6.3%) 77 Ir iridium 6.0×10−7 6.6×10−7 6.61×10−7 (6.1%) 78 Pt platinum about 1.8×10−6 1.34×10−6 1.34×10−6 (7.4%) 79 Au gold about 3.0×10−7 1.9×10−7 1.87×10−7 (15%) 80 Hg mercury 3.4×10−7 3.40×10−7 (12%) 81 Tl thallium about 2.0×10−7 1.9×10−7 1.84×10−7 (9.4%) 82 Pb lead 2.0×10−6 3.1×10−6 3.15×10−6 (7.8%) 83 Bi bismuth 1.4×10−7 1.44×10−7 (8.2%) 84 Po polonium 85 At astatine 86 Rn radon 87 Fr francium 88 Ra radium 89 Ac actinium 90 Th thorium 5.0×10−8 4.5×10−8 3.35×10−8 (5.7%) 91 Pa protactinium 92 U uranium 1.8×10−8 9.00×10−9 (8.4%) 93 Np neptunium 94 Pu plutonium ==See also== Chemical elements data references ==Notes== Due to the estimate nature of these values, no single recommendations are given. :(d) N.B. Vargaftik, Int. J. Thermophys. 11, 467, (1990). ===LNG=== J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6; Table 6.5 Critical Properties ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; D. Ambrose, M.B. Ewing, M.L. McGlashan, Critical constants and second virial coefficients of gases (retrieved Dec 2005) ===SMI=== W.E. Forsythe (ed.), Smithsonian Physical Tables 9th ed., online version (1954; Knovel 2003). Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? J/(mol·K) Solid properties Std enthalpy change of formation -ΔfH ~~o~~ solid 448.9 kcal/mol Std entropy change of formation -ΔfS ~~o~~ solid 71.9 kcal/mol Std Gibbs free energy change of formation -ΔfG ~~o~~ solid 427.5 kcal/mol Std enthalpy change of absorption -ΔaH ~~o~~ solid ? kJ/mol Standard molar entropy S ~~o~~ solid ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? (The average density of sea water in the surface is 1.025 kg/L) Element W1 W2 01 H hydrogen 1.08×10−1 1.1×10−1 02 He helium 7×10−12 7.2×10−12 03 Li lithium 1.8×10−7 1.7×10−7 04 Be beryllium 5.6×10−12 6×10−13 05 B boron 4.44×10−6 4.4×10−6 06 C carbon 2.8×10−5 2.8×10−5 07 N nitrogen 5×10−7 1.6×10−5 08 O oxygen 8.57×10−1 8.8×10−1 09 F fluorine 1.3×10−6 1.3×10−6 10 Ne neon 1.2×10−10 1.2×10−10 11 Na sodium 1.08×10−2 1.1×10−2 12 Mg magnesium 1.29×10−3 1.3×10−3 13 Al aluminium 2×10−9 1×10−9 14 Si silicon 2.2×10−6 2.9×10−6 15 P phosphorus 6×10−8 8.8×10−8 16 S sulfur 9.05×10−4 9.0×10−4 17 Cl chlorine 1.94×10−2 1.9×10−2 18 Ar argon 4.5×10−7 4.5×10−7 19 K potassium 3.99×10−4 3.9×10−4 20 Ca calcium 4.12×10−4 4.1×10−4 21 Sc scandium 6×10−13 < 4×10−12 22 Ti titanium 1×10−9 1×10−9 23 V vanadium 2.5×10−9 1.9×10−9 24 Cr chromium 3×10−10 2×10−10 25 Mn manganese 2×10−10 1.9×10−9 26 Fe iron 2×10−9 3.4×10−9 27 Co cobalt 2×10−11 3.9×10−10 28 Ni nickel 5.6×10−10 6.6×10−9 29 Cu copper 2.5×10−10 2.3×10−8 30 Zn zinc 4.9×10−9 1.1×10−8 31 Ga gallium 3×10−11 3×10−11 32 Ge germanium 5×10−11 6×10−11 33 As arsenic 3.7×10−9 2.6×10−9 34 Se selenium 2×10−10 9.0×10−11 35 Br bromine 6.73×10−5 6.7×10−5 36 Kr krypton 2.1×10−10 2.1×10−10 37 Rb rubidium 1.2×10−7 1.2×10−7 38 Sr strontium 7.9×10−6 8.1×10−6 39 Y yttrium 1.3×10−11 1.3×10−12 40 Zr zirconium 3×10−11 2.6×10−11 41 Nb niobium 1×10−11 1.5×10−11 42 Mo molybdenum 1×10−8 1.0×10−8 43 Tc technetium 44 Ru ruthenium 7×10−13 45 Rh rhodium 46 Pd palladium 47 Ag silver 4×10−11 2.8×10−10 48 Cd cadmium 1.1×10−10 1.1×10−10 49 In indium 2×10−8 50 Sn tin 4×10−12 8.1×10−10 51 Sb antimony 2.4×10−10 3.3×10−10 52 Te tellurium 53 I iodine 6×10−8 6.4×10−8 54 Xe xenon 5×10−11 4.7×10−11 55 Cs caesium 3×10−10 3.0×10−10 56 Ba barium 1.3×10−8 2.1×10−8 57 La lanthanum 3.4×10−12 3.4×10−12 58 Ce cerium 1.2×10−12 1.2×10−12 59 Pr praseodymium 6.4×10−13 6.4×10−13 60 Nd neodymium 2.8×10−12 2.8×10−12 61 Pm promethium 62 Sm samarium 4.5×10−13 4.5×10−13 63 Eu europium 1.3×10−13 1.3×10−13 64 Gd gadolinium 7×10−13 7.0×10−13 65 Tb terbium 1.4×10−13 1.4×10−12 66 Dy dysprosium 9.1×10−13 9.1×10−13 67 Ho holmium 2.2×10−13 2.2×10−13 68 Er erbium 8.7×10−13 8.7×10−12 69 Tm thulium 1.7×10−13 1.7×10−13 70 Yb ytterbium 8.2×10−13 8.2×10−13 71 Lu lutetium 1.5×10−13 1.5×10−13 72 Hf hafnium 7×10−12 < 8×10−12 73 Ta tantalum 2×10−12 < 2.5×10−12 74 W tungsten 1×10−10 < 1×10−12 75 Re rhenium 4×10−12 76 Os osmium 77 Ir iridium 78 Pt platinum 79 Au gold 4×10−12 1.1×10−11 80 Hg mercury 3×10−11 1.5×10−10 81 Tl thallium 1.9×10−11 82 Pb lead 3×10−11 3×10−11 83 Bi bismuth 2×10−11 2×10−11 84 Po polonium 1.5×10−20 85 At astatine 86 Rn radon 6×10−22 87 Fr francium 88 Ra radium 8.9×10−17 89 Ac actinium 90 Th thorium 1×10−12 1.5×10−12 91 Pa protactinium 5×10−17 92 U uranium 3.2×10−9 3.3×10−9 93 Np neptunium 94 Pu plutonium ==Sun and solar system== S1 — Sun: Kaye & Laby Y1 — Solar system: Kaye & Laby Y2 — Solar system: Ahrens, with uncertainty s (%) Atom mole fraction relative to silicon = 1. :(c) O. Sifner, J. Klomfar, J. Phys. Chem. Ref. Data 23, 63, (1994). K (? °C), ? K (? °C), ? :(b) I.G. Dillon, P.A. Nelson, B.S. Swanson, J. Chem. Phys. 44, 4229, (1966). Boca Raton, Florida, 2003; Section 6, Fluid Properties; Thermal Conductivity of Gases ===LNG=== As quoted from this source in an online version of: J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 4; Table 4.1, Electronic Configuration and Properties of the Elements Ho, C. Y., Powell, R. W., and Liley, P. E., J. Phys. Chem. Ref. Data 3:Suppl. 1 (1974) ===WEL=== As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. Boca Raton, Florida, 2003; Section 6, Fluid Properties; Enthalpy of Fusion === LNG === As quoted from various sources in: * J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6, Thermodynamic Properties; Table 6.4, Heats of Fusion, Vaporization, and Sublimation and Specific Heat at Various Temperatures of the Elements and Inorganic Compounds === WEL === As quoted at http://www.webelements.com/ from these sources: * G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993. Ellis (Ed.) in Nuffield Advanced Science Book of Data, Longman, London, UK, 1972. == See also == Category:Thermodynamic properties Category:Chemical element data pages Table 259, Critical Temperatures, Pressures, and Densities of Gases == See also == Category:Phase transitions Category:Units of pressure Category:Temperature Category:Properties of chemical elements Category:Chemical element data pages J/(mol K) Liquid properties Std enthalpy change of formation ΔfH ~~o~~ liquid ? kJ/mol Standard molar entropy S ~~o~~ liquid ? Bodek et al., Environmental Inorganic Chemistry, Pergamon Press, New York, (1988).	91.17	0.7854	2.19	-0.28	-111.92	E
Radiation from an X-ray source consists of two components of wavelengths $154.433 \mathrm{pm}$ and $154.051 \mathrm{pm}$. Calculate the difference in glancing angles $(2 \theta)$ of the diffraction lines arising from the two components in a diffraction pattern from planes of separation $77.8 \mathrm{pm}$.	In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). right\|thumb\|Grazing incidence diffraction geometry. * The diffraction angles are invariant under scaling; that is, they depend only on the ratio of the wavelength to the size of the diffracting object. * The diffraction angles are invariant under scaling; that is, they depend only on the ratio of the wavelength to the size of the diffracting object. The amount of diffraction depends on the size of the gap. When the incident angle \theta_\text{i} of the light onto the slit is non-zero (which causes a change in the path length), the intensity profile in the Fraunhofer regime (i.e. far field) becomes: :I(\theta) = I_0 \,\operatorname{sinc}^2 \left[ \frac{d \pi}{\lambda} (\sin\theta \pm \sin\theta_i)\right] The choice of plus/minus sign depends on the definition of the incident angle \theta_\text{i}.right\|thumb\|2-slit (top) and 5-slit diffraction of red laser light thumb\|left\|Diffraction of a red laser using a diffraction grating. right\|thumb\|A diffraction pattern of a 633 nm laser through a grid of 150 slits ===Diffraction grating=== thumb\|Diffraction grating A diffraction grating is an optical component with a regular pattern. The beam is diffracted in the plane of the surface of the sample by the angle 2θ, and often also out of the plane. The main central beam, nulls, and phase reversals are apparent. right\|thumb\|300px\|Graph and image of single-slit diffraction As an example, an exact equation can now be derived for the intensity of the diffraction pattern as a function of angle in the case of single-slit diffraction. Given that \delta_A-\delta_B\ll 1 and \alpha_A-\alpha_B\ll 1, at a second-order development it turns that \cos\delta_A\cos\delta_B \frac{(\alpha_A - \alpha_B)^2}{2} \approx \cos^2\delta_A \frac{(\alpha_A - \alpha_B)^2}{2}, so that :\theta \approx \sqrt{\left[(\alpha_A - \alpha_B)\cos\delta_A\right]^2 + (\delta_A-\delta_B)^2} === Small angular distance: planar approximation === thumb\|Planar approximation of angular distance on sky If we consider a detector imaging a small sky field (dimension much less than one radian) with the y-axis pointing up, parallel to the meridian of right ascension \alpha, and the x-axis along the parallel of declination \delta, the angular separation can be written as: : \theta \approx \sqrt{\delta x^2 + \delta y^2} where \delta x = (\alpha_A - \alpha_B)\cos\delta_A and \delta y=\delta_A-\delta_B. Note that the y-axis is equal to the declination, whereas the x-axis is the right ascension modulated by \cos\delta_A because the section of a sphere of radius R at declination (latitude) \delta is R' = R \cos\delta_A (see Figure). ==See also== * Milliradian * Gradian * Hour angle * Central angle * Angle of rotation * Angular diameter * Angular displacement * Great-circle distance * ==References== * CASTOR, author(s) unknown. Grazing incidence diffraction is used in X-ray spectroscopy and atom optics, where significant reflection can be achieved only at small values of the grazing angle. thumb\|425x425px\|The plane of incidence is defined by the incoming radiation's propagation vector and the normal vector of the surface. Determining the angle of reflection with respect to a planar surface is trivial, but the computation for almost any other surface is significantly more difficult. thumb\|center\|650px\|Refraction of light at the interface between two media. ==Grazing angle or glancing angle== thumb\|Focusing X-rays with glancing reflection When dealing with a beam that is nearly parallel to a surface, it is sometimes more useful to refer to the angle between the beam and the surface tangent, rather than that between the beam and the surface normal. Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. Diffraction is greatest when the size of the gap is similar to the wavelength of the wave. The 90-degree complement to the angle of incidence is called the grazing angle or glancing angle. Angular distance or angular separation, also known as apparent distance or apparent separation, denoted \theta, is the angle between the two sightlines, or between two point objects as viewed from an observer. The path difference is approximately \frac{d \sin(\theta)}{2} so that the minimum intensity occurs at an angle \theta_{min} given by :d\,\sin\theta_\text{min} = \lambda, where d is the width of the slit, \theta_\text{min} is the angle of incidence at which the minimum intensity occurs, and \lambda is the wavelength of the light. Now, substituting in \frac{2\pi}{\lambda} = k, the intensity (squared amplitude) I of the diffracted waves at an angle θ is given by: I(\theta) = I_0 {\left[ \operatorname{sinc} \left( \frac{\pi a}{\lambda} \sin \theta \right) \right] }^2 ==Multiple slits== right\|frame\|Double-slit diffraction of red laser light right\|frame\|2-slit and 5-slit diffraction Let us again start with the mathematical representation of Huygens' principle. File:Two-Slit Diffraction.png\|Generation of an interference pattern from two-slit diffraction. The figure shows the light diffracted by 2-element and 5-element gratings where the grating spacings are the same; it can be seen that the maxima are in the same position, but the detailed structures of the intensities are different. thumb\|A computer-generated image of an Airy disk. thumb\| Computer-generated light diffraction pattern from a circular aperture of diameter 0.5 micrometre at a wavelength of 0.6 micrometre (red-light) at distances of 0.1 cm – 1 cm in steps of 0.1 cm. We can find the angle at which a first minimum is obtained in the diffracted light by the following reasoning. The main central beam, nulls, and phase reversals are apparent. right\|thumb\|Graph and image of single-slit diffraction.	+37	3.38	0.14	2.14	0.020	D
A chemical reaction takes place in a container of cross-sectional area $50 \mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $15 \mathrm{~cm}$ against an external pressure of $1.0 \mathrm{~atm}$. Calculate the work done by the system.	The work done is given by the dot product of the two vectors. The work is the product of the distance times the spring force, which is also dependent on distance; hence the result. ===Work by a gas=== The work W done by a body of gas on its surroundings is: W = \int_a^b P \, dV where is pressure, is volume, and and are initial and final volumes. ==Work–energy principle== The principle of work and kinetic energy (also known as the work–energy principle) states that the work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle. The work is due to change of system volume by expansion or contraction of the system. Then for a given amount of work transferred, the exchange of volumes involves different pressures, inversely with the piston areas, for mechanical equilibrium. The work of the net force is calculated as the product of its magnitude and the particle displacement. The quantity of thermodynamic work is defined as work done by the system on its surroundings. This force will act through the distance along the circular arc l=s=r\phi, so the work done is W = F s = F r \phi . The work done by the system on its surroundings is calculated from the quantities that constitute the whole cycle.Lavenda, B.H. (2010). work is represented by the following equation between differentials: \delta W = P \, dV where \delta W (inexact differential) denotes an infinitesimal increment of work done by the system, transferring energy to the surroundings; P denotes the pressure inside the system, that it exerts on the moving wall that transmits force to the surroundings.Borgnakke, C., Sontag, R. E. (2009). Pressure–volume work is a kind of contact work, because it occurs through direct material contact with the surrounding wall or matter at the boundary of the system. When work, for example pressure–volume work, is done on its surroundings by a closed system that cannot pass heat in or out because it is confined by an adiabatic wall, the work is said to be adiabatic for the system as well as for the surroundings. That is, the work W done by the resultant force on a particle equals the change in the particle's kinetic energy E_\text{k}, W = \Delta E_\text{k} = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2 where v_1 and v_2 are the speeds of the particle before and after the work is done, and is its mass. Given only the initial state and the final state of the system, one can only say what the total change in internal energy was, not how much of the energy went out as heat, and how much as work. If an object with weight is displaced upwards or downwards a vertical distance , the work done on the object is: W = F_g (y_2 - y_1) = F_g\Delta y = mg\Delta y where Fg is weight (pounds in imperial units, and newtons in SI units), and Δy is the change in height y. When a force component is perpendicular to the displacement of the object (such as when a body moves in a circular path under a central force), no work is done, since the cosine of 90° is zero. As a result, the work done by the system also depends on the initial and final states. Then, for instance, to calculate the percent of the piston's stroke at which steam admission is cut off: Calculate the angle whose cosine is twice the lap divided by the valve travel Calculate the angle whose cosine is twice the (lap plus lead), divided by the valve travel Add the two angles and take the cosine of their sum; subtract 1 from that cosine and multiply the result by -50. Work done on a thermodynamic system, by devices or systems in the surroundings, is performed by actions such as compression, and includes shaft work, stirring, and rubbing. Therefore, work need only be computed for the gravitational forces acting on the bodies. Such work is adiabatic for the surroundings, even though it is associated with friction within the system. If the torque \tau is aligned with the angular velocity vector so that, \mathbf{T} = \tau \mathbf{S}, and both the torque and angular velocity are constant, then the work takes the form, W = \int_{t_1}^{t_2} \tau \dot{\phi} \, dt = \tau(\phi_2 - \phi_1). 250px\|thumb\|right\|alt=Work on lever arm\|A force of constant magnitude and perpendicular to the lever arm This result can be understood more simply by considering the torque as arising from a force of constant magnitude , being applied perpendicularly to a lever arm at a distance r, as shown in the figure. Because it does not change the volume of the system it is not measured as pressure–volume work, and it is called isochoric work.	-75	30	0.042	0.000216	6.07	A
A mixture of water and ethanol is prepared with a mole fraction of water of 0.60 . If a small change in the mixture composition results in an increase in the chemical potential of water by $0.25 \mathrm{~J} \mathrm{~mol}^{-1}$, by how much will the chemical potential of ethanol change?	Specific heat = 2.44 kJ/(kg·K) === Acid-base chemistry === Ethanol is a neutral molecule and the pH of a solution of ethanol in water is nearly 7.00. Ethanol-water mixtures have less volume than the sum of their individual components at the given fractions. It can be calculated from this table that at 25 °C, 45 g of ethanol has volume 57.3 ml, 55 g of water has volume 55.2 ml; these sum to 112.5 ml. Whereas to make a 50% v/v ethanol solution, 50 ml of ethanol and 50 ml of water could be mixed but the resulting volume of solution will measure less than 100 ml due to the change of volume on mixing, and will contain a higher concentration of ethanol. Mixing equal volumes of ethanol and water results in only 1.92 volumes of mixture. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. The volume of alcohol in the solution can then be estimated. For example, to make 100 ml of 50% ABV ethanol solution, water would be added to 50 ml of ethanol to make up exactly 100 ml. The number of millilitres of pure ethanol is the mass of the ethanol divided by its density at , which is .Haynes, William M., ed. (2011). Mixing ethanol and water is exothermic, with up to 777 J/mol being released at 298 K. Mixtures of ethanol and water form an azeotrope at about 89 mole-% ethanol and 11 mole-% water or a mixture of 95.6% ethanol by mass (or about 97% alcohol by volume) at normal pressure, which boils at 351 K (78 °C). Ethanol can be quantitatively converted to its conjugate base, the ethoxide ion (CH3CH2O−), by reaction with an alkali metal such as sodium: :2 CH3CH2OH + 2 Na → 2 CH3CH2ONa + H2 or a very strong base such as sodium hydride: :CH3CH2OH + NaH → CH3CH2ONa + H2 The acidities of water and ethanol are nearly the same, as indicated by their pKa of 15.7 and 16 respectively. As high as 30-50 kcal/mol changes in the potential energy surface (activation energies and relative stability) were calculated if the charge of the metal species was changed during the chemical transformation. ===Free radical syntheses=== Many free radical-based syntheses show large kinetic solvent effects that can reduce the rate of reaction and cause a planned reaction to follow an unwanted pathway. ==See also== * Cage effect ==References== Category:Physical chemistry Category:Reaction mechanisms A solution will have a lower and hence more negative water potential than that of pure water. For example, in a binary mixture, at constant temperature and pressure, the chemical potentials of the two participants A and B are related by : d\mu_\text{B} = -\frac{n_\text{A}}{n_\text{B}}\,d\mu_\text{A} where n_\text{A} is the number of moles of A and n_\text{B} is the number of moles of B. Water potential is the potential energy of water per unit volume relative to pure water in reference conditions. Ethanol is slightly more refractive than water, having a refractive index of 1.36242 (at λ=589.3 nm and ). From the above equation, the chemical potential is given by : \mu_i = \left(\frac{\partial U}{\partial N_i} \right)_{S,V, N_{j e i}}. It is defined as the number of millilitres (mL) of pure ethanol present in of solution at . Furthermore, the more solute molecules present, the more negative the solute potential is. This source gives density data for ethanol:water mixes by %weight ethanol in 5% increments and against temperature including at 25 °C, used here. Under such nomenclature, the ethanol was mixed with 25% water to reduce the combustion chamber temperature. The addition of even a few percent of ethanol to water sharply reduces the surface tension of water.	-0.38	131	1.81	2	8.7	A
The enthalpy of fusion of mercury is $2.292 \mathrm{~kJ} \mathrm{~mol}^{-1}$, and its normal freezing point is $234.3 \mathrm{~K}$ with a change in molar volume of $+0.517 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$ on melting. At what temperature will the bottom of a column of mercury (density $13.6 \mathrm{~g} \mathrm{~cm}^{-3}$ ) of height $10.0 \mathrm{~m}$ be expected to freeze?	T_M(d) = T_{MB}(1-\frac{4\sigma\,_{sl}}{H_f\rho\,_sd}) Where: TMB = bulk melting temperature ::σsl = solid–liquid interface energy ::Hf = Bulk heat of fusion ::ρs = density of solid ::d = particle diameter ==Semiconductor/covalent nanoparticles== Equation 2 gives the general relation between the melting point of a metal nanoparticle and its diameter. T_M(d)=\frac{4T_{MB}}{H_fd}\left(\sigma\,_{sv}-\sigma\,_{lv}\left(\frac{\rho\,_s}{\rho\,_l}\right)^{2/3}\right) Where: σsv=solid-vapor interface energy ::σlv=liquid-vapor interface energy ::Hf=Bulk heat of fusion ::ρs=density of solid ::ρl=density of liquid ::d=diameter of nanoparticle ===Liquid shell nucleation model=== The liquid shell nucleation model (LSN) predicts that a surface layer of atoms melts prior to the bulk of the particle. :This article deals with melting/freezing point depression due to very small particle size. The theoretical size-dependent melting point of a material can be calculated through classical thermodynamic analysis. Equation 4 gives the normalized, size-dependent melting temperature of a material according to the liquid-drop model. The behavior of the heat capacity near the peak is described by the formula C\approx A_\pm t^{-\alpha}+B_\pm where t=\|1-T/T_c\| is the reduced temperature, T_c is the Lambda point temperature, A_\pm,B_\pm are constants (different above and below the transition temperature), and is the critical exponent: \alpha=-0.0127(3). T_M(d)=T_{MB}(1-(\frac{c}{d})^2) Where: TMB=bulk melting temperature ::c=materials constant ::d=particle diameter Equation 3 indicates that melting point depression is less pronounced in covalent nanoparticles due to the quadratic nature of particle size dependence in the melting Equation. ==Proposed mechanisms== The specific melting process for nanoparticles is currently unknown. K (? °C), ? K (? °C), ? K (? °C), ? K (? °C), ? T_M(d)=\frac{4T_{MB}}{H_fd}(\frac{\sigma\,_{sv}}{1-\frac{d_0}{d}}-\sigma\,_{lv}(1-\frac{\rho\,_s}{\rho\,_l})) Where: d0=atomic diameter ===Liquid nucleation and growth model=== The liquid nucleation and growth model (LNG) treats nanoparticle melting as a surface- initiated process. Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? The decrease in melting temperature can be on the order of tens to hundreds of degrees for metals with nanometer dimensions. J/(mol·K) Solid properties Std enthalpy change of formation ΔfH ~~o~~ solid −118 kJ/mol Standard molar entropy S ~~o~~ solid ? The melting temperature of a nanoparticle decreases sharply as the particle reaches critical diameter, usually < 50 nm for common engineering metals. The melting temperature of a nanoparticle is a function of its radius of curvature according to the LSN. The model calculates melting conditions as a function of two competing order parameters using Landau potentials. thumb\|0 °C = 32 °F A degree of frost is a non-standard unit of measure for air temperature meaning degrees below melting point (also known as "freezing point") of water (0 degrees Celsius or 32 degrees Fahrenheit). The Mollier diagram coordinates are enthalpy h and humidity ratio x. More recently, researchers developed nanocalorimeters that directly measure the enthalpy and melting temperature of nanoparticles.	0	1.154700538	0.6	16.3923	234.4	E
Suppose a nanostructure is modelled by an electron confined to a rectangular region with sides of lengths $L_1=1.0 \mathrm{~nm}$ and $L_2=2.0 \mathrm{~nm}$ and is subjected to thermal motion with a typical energy equal to $k T$, where $k$ is Boltzmann's constant. How low should the temperature be for the thermal energy to be comparable to the zero-point energy？	When L is comparable to or smaller than the mean free path (which is of the order 1 µm for carbon nanostructures ), the continuous energy model used for bulk materials no longer applies and nonlocal and nonequilibrium aspects to heat transfer also need to be considered. These issues can be addressed with phonon engineering, once nanoscale thermal behaviors have been studied and understood. ==The effect of the limited length of structure== In general two carrier types can contribute to thermal conductivity - electrons and phonons. Modeling of the low-temperature specific heat allows determination of the on-tube phonon velocity, the splitting of phonon subbands on a single tube, and the interaction between neighboring tubes in a bundle. ===Thermal conductivity measurements=== Measurements show a single-wall carbon nanotubes (SWNTs) room-temperature thermal conductivity about 3500 W/(m·K), and over 3000 W/(m·K) for individual multiwalled carbon nanotubes (MWNTs). Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state, then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature. ==Context== In quantum mechanics, a group of particles known as fermions (for example, electrons, protons and neutrons) obey the Pauli exclusion principle. The Fermi temperature is defined as T_\text{F} = \frac{E_\text{F}}{k_\text{B}}, where k_\text{B} is the Boltzmann constant, and E_\text{F} the Fermi energy. Only when the temperature exceeds the related Fermi temperature, do the particles begin to move significantly faster than at absolute zero. The Fermi temperature for a metal is a couple of orders of magnitude above room temperature. Junction temperature, short for transistor junction temperature, is the highest operating temperature of the actual semiconductor in an electronic device. In physics, the thermal conductance quantum g_0 describes the rate at which heat is transported through a single ballistic phonon channel with temperature T. For CNT, represented as 1-D ballistic electronic channel, the electronic conductance is quantized, with a universal value of :G_0 = \frac{2e^2}{h} Similarly, for a single ballistic 1-D channel, the thermal conductance is independent of materials parameters, and there exists a quantum of thermal conductance, which is linear in temperature: :G_{th} = \frac{\pi^2 {k_B}^2 T}{3h} Possible conditions for observation of this quantum were examined by Rego and Kirczenow. The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. These measurements employed suspended silicon nitride () nanostructures that exhibited a constant thermal conductance of 16 g_0 at temperatures below approximately 0.6 kelvin. == Relation to the quantum of electrical conductance == For ballistic electrical conductors, the electron contribution to the thermal conductance is also quantized as a result of the electrical conductance quantum and the Wiedemann–Franz law, which has been quantitatively measured at both cryogenic (~20 mK) and room temperature (~300K). Then : \kappa = L T \sigma = {\pi^2 k_{\rm B}^2 \over 3e^2}\times {n e^2 \over h} T = {\pi^2 k_{\rm B}^2 \over 3h} n T = g_0 n, where g_0 is the thermal conductance quantum defined above. ==References== ==See also== * Thermal properties of nanostructures Category:Mesoscopic physics Category:Nanotechnology Category:Quantum mechanics Category:Condensed matter physics Category:Physical quantities Category:Heat conduction It was shown that, using this formula and atomistically computed phonon dispersions (with interatomic potentials developed in ), it is possible to predictively calculate lattice thermal conductivity curves for nanowires, in good agreement with experiments. In materials science, the threshold displacement energy () is the minimum kinetic energy that an atom in a solid needs to be permanently displaced from its site in the lattice to a defect position. Berber et al. have calculated the phonon thermal conductivity of isolated nanotubes. In condensed matter physics, the recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes, and corresponds to the kinetic energy imparted in an atom initially at rest by the spontaneous emission of a photon. It may be that this weak coupling, which is problematic for mechanical applications of nanotubes, is an advantage for thermal applications. ====Phonon density of states for nanotubes==== The phonon density of states is to calculated through band structure of isolated nanotubes, which is studied in Saito et al. and Sanchez-Portal et al. Threshold displacement energies in typical solids are of the order of 10-50 eV. M. Nastasi, J. Mayer, and J. Hirvonen, Ion-Solid Interactions - Fundamentals and Applications, Cambridge University Press, Cambridge, Great Britain, 1996 P. Lucasson, The production of Frenkel defects in metals, in Fundamental Aspects of Radiation Damage in Metals, edited by M. T. Robinson and F. N. Young Jr., pages 42--65, Springfield, 1975, ORNL R. S. Averback and T. Diaz de la Rubia, Displacement damage in irradiated metals and semiconductors, in Solid State Physics, edited by H. Ehrenfest and F. Spaepen, volume 51, pages 281--402, Academic Press, New York, 1998.R. Smith (ed.), Atomic & ion collisions in solids and at surfaces: theory, simulation and applications, Cambridge University Press, Cambridge, UK, 1997 == Theory and simulation == The threshold displacement energy is a materials property relevant during high- energy particle radiation of materials. The Fermi temperature can be thought of as the temperature at which thermal effects are comparable to quantum effects associated with Fermi statistics. As the devices continue to shrink further into the sub-100 nm range following the trend predicted by Moore’s law, the topic of thermal properties and transport in such nanoscale devices becomes increasingly important. Therefore, the phonon thermal conductivity displays a peak and decreases with increasing temperature.	-8	1.5	5.5	0.7812	0.0761	C
Calculate the change in Gibbs energy of $35 \mathrm{~g}$ of ethanol (mass density $0.789 \mathrm{~g} \mathrm{~cm}^{-3}$ ) when the pressure is increased isothermally from 1 atm to 3000 atm.	The Gibbs energy of any system is and an infinitesimal change in G, at constant temperature and pressure, yields :dG=dU+pdV-TdS. The Gibbs free energy is expressed as : G(p,T) = U + pV - TS = H - TS where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy. This implies that at equilibrium Q_\text{r} = K_\text{eq} and \Delta_\text{r} G = 0. ==Standard Gibbs energy change of formation== Table of selected substancesCRC Handbook of Chemistry and Physics, 2009, pp. 5-4–5-42, 90th ed., Lide. Alcoholic fermentation converts one mole of glucose into two moles of ethanol and two moles of carbon dioxide, producing two moles of ATP in the process. In isothermal, isobaric systems, Gibbs free energy can be thought of as a "dynamic" quantity, in that it is a representative measure of the competing effects of the enthalpic and entropic driving forces involved in a thermodynamic process. thumb\|upright=1.9\|Relation to other relevant parameters The temperature dependence of the Gibbs energy for an ideal gas is given by the Gibbs–Helmholtz equation, and its pressure dependence is given by \frac{G}{N} = \frac{G^\circ}{N} + kT\ln \frac{p}{p^\circ}. or more conveniently as its chemical potential: \frac{G}{N} = \mu = \mu^\circ + kT\ln \frac{p}{p^\circ}. The standard Gibbs free energy of formation (Gf°) of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 1 bar of pressure and the specified temperature, usually 298.15 K or 25 °C). The Gibbs free energy change , measured in joules in SI) is the maximum amount of non-volume expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. The Gibbs energy is the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature when not driven by an applied electrolytic voltage. In an isobaric process, the pressure remains constant, so the heat interaction is the change in enthalpy. Each quantity in the equations above can be divided by the amount of substance, measured in moles, to form molar Gibbs free energy. Substance (state) ΔfG° ΔfG° Substance (state) (kJ/mol) (kcal/mol) NO(g) 87.6 20.9 NO2(g) 51.3 12.3 N2O(g) 103.7 24.78 H2O(g) −228.6 −54.64 H2O(l) −237.1 −56.67 CO2(g) −394.4 −94.26 CO(g) −137.2 −32.79 CH4(g) −50.5 −12.1 C2H6(g) −32.0 −7.65 C3H8(g) −23.4 −5.59 C6H6(g) 129.7 29.76 C6H6(l) 124.5 31.00 The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, in their standard states (the most stable form of the element at 25 °C and 100 kPa). Moreover, we also have \begin{align} K_\text{eq} &= e^{-\frac{\Delta_\text{r} G^\circ}{RT}}, \\\ \Delta_\text{r} G^\circ &= -RT\left(\ln K_\text{eq}\right) = -2.303\,RT\left(\log_{10} K_\text{eq}\right), \end{align} which relates the equilibrium constant with Gibbs free energy. At constant pressure the above equation produces a Maxwell relation that links the change in open cell voltage with temperature T (a measurable quantity) to the change in entropy S when charge is passed isothermally and isobarically. Further, Gibbs stated: In this description, as used by Gibbs, ε refers to the internal energy of the body, η refers to the entropy of the body, and ν is the volume of the body... In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. The entropy of vaporization is then equal to the heat of vaporization divided by the boiling point: : \Delta S_\text{vap} = \frac{\Delta H_\text{vap}}{T_\text{vap}}. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces. Approximately 2.8 gallons of ethanol are produced from one bushel of corn (0.42 liter per kilogram). However, simply substituting the above integrated result for U into the definition of G gives a standard expression for G: :\begin{align} G &= U + p V - TS\\\ &= \left(T S - p V + \sum_i \mu_i N_i \right) + p V - T S\\\ &= \sum_i \mu_i N_i. \end{align} This result shows that the chemical potential of a substance i is its (partial) mol(ecul)ar Gibbs free energy. At standard pressure , the value is denoted as and normally expressed in joules per mole-kelvin, J/(mol·K). thumb\|400px\|Diagram showing pressure difference induced by a temperature difference. The quantities on the right are all directly measurable. ==Useful identities to derive the Nernst equation== During a reversible electrochemical reaction at constant temperature and pressure, the following equations involving the Gibbs free energy hold: \Delta_\text{r} G = \Delta_\text{r} G^\circ + R T \ln Q_\text{r} (see chemical equilibrium), \Delta_\text{r} G^\circ = -R T \ln K_\text{eq} (for a system at chemical equilibrium), \Delta_\text{r} G = w_\text{elec,rev} = -nF\mathcal{E} (for a reversible electrochemical process at constant temperature and pressure), \Delta_\text{r} G^\circ = -nF\mathcal{E}^\circ (definition of \mathcal{E}^\circ), and rearranging gives \begin{align} nF\mathcal{E}^\circ &= RT \ln K_\text{eq}, \\\ nF\mathcal{E} &= nF\mathcal{E}^\circ - R T \ln Q_\text{r}, \\\ \mathcal{E} &= \mathcal{E}^\circ - \frac{R T}{n F} \ln Q_\text{r}, \end{align} which relates the cell potential resulting from the reaction to the equilibrium constant and reaction quotient for that reaction (Nernst equation), where * , Gibbs free energy change per mole of reaction, * , Gibbs free energy change per mole of reaction for unmixed reactants and products at standard conditions (i.e. 298K, 100kPa, 1M of each reactant and product), * , gas constant, * , absolute temperature, * , natural logarithm, * , reaction quotient (unitless), * , equilibrium constant (unitless), * , electrical work in a reversible process (chemistry sign convention), * , number of moles of electrons transferred in the reaction, * , Faraday constant (charge per mole of electrons), * \mathcal{E}, cell potential, * \mathcal{E}^\circ, standard cell potential.	12	0.00539	6.0	14.5115	-17	A
The promotion of an electron from the valence band into the conduction band in pure $\mathrm{TIO}_2$ by light absorption requires a wavelength of less than $350 \mathrm{~nm}$. Calculate the energy gap in electronvolts between the valence and conduction bands.	Within the concept of bands, the energy gap between the valence band and the conduction band is the band gap. For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In graphs of the electronic band structure of solids, the band gap refers to the energy difference (often expressed in electronvolts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. This formula is valid only for light with photon energy larger, but not too much larger, than the band gap (more specifically, this formula assumes the bands are approximately parabolic), and ignores all other sources of absorption other than the band-to-band absorption in question, as well as the electrical attraction between the newly created electron and hole (see exciton). By plotting certain powers of the absorption coefficient against photon energy, one can normally tell both what value the band gap is, and whether or not it is direct. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band. A band gap is an energy range in a solid where no electron states can exist due to the quantization of energy. However, in order for a valence band electron to be promoted to the conduction band, it requires a specific minimum amount of energy for the transition. Especially in condensed-matter physics, an energy gap is often known more abstractly as a spectral gap, a term which need not be specific to electrons or solids. ==Band gap== If an energy gap exists in the band structure of a material, it is called band gap. The relationship between band gap energy and temperature can be described by Varshni's empirical expression (named after Y. P. Varshni), :E_g(T)=E_g(0)-\frac{\alpha T^2}{T+\beta}, where Eg(0), α and β are material constants. A semiconductor will not absorb photons of energy less than the band gap; and the energy of the electron-hole pair produced by a photon is equal to the bandgap energy. The band gap is called "direct" if the crystal momentum of electrons and holes is the same in both the conduction band and the valence band; an electron can directly emit a photon. On the other hand, for an indirect band gap, the formula is: :\alpha \propto \frac{(h u- E_{\text{g}}+E_{\text{p}})^2}{\exp(\frac{E_{\text{p}}}{kT})-1} + \frac{(h u- E_{\text{g}}-E_{\text{p}})^2}{1-\exp(-\frac{E_{\text{p}}}{kT})} where: E_{\text{p}} is the energy of the phonon that assists in the transition k is Boltzmann's constant *T is the thermodynamic temperature This formula involves the same approximations mentioned above. For the same reason as above, light with a photon energy close to the band gap can penetrate much farther before being absorbed in an indirect band gap material than a direct band gap one (at least insofar as the light absorption is due to exciting electrons across the band gap). In solid-state physics, the most important spectral gap is for the many-body system of electrons in a solid material, in which case it is often known as an energy gap. Since the mid-gap states do exist within some depth of the semiconductor, they must be a mixture (a Fourier series) of valence and conduction band states from the bulk. In solid-state physics, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. Group Material Symbol Band gap (eV) @ 302K Reference III–V Aluminium nitride AlN 6.0 IV Diamond C 5.5 IV Silicon Si 1.14 IV Germanium Ge 0.67 III–V Gallium nitride GaN 3.4 III–V Gallium phosphide GaP 2.26 III–V Gallium arsenide GaAs 1.43 IV–V Silicon nitride Si3N4 5 IV–VI Lead(II) sulfide PbS 0.37 IV–VI Silicon dioxide SiO2 9 Copper(I) oxide Cu2O 2.1 ==Optical versus electronic bandgap== In materials with a large exciton binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. In contrast, for materials with an indirect band gap, a photon and phonon must both be involved in a transition from the valence band top to the conduction band bottom, involving a momentum change. If there is a small band gap (Eg), then the flow of electrons from valence to conduction band is possible only if an external energy (thermal, etc.) is supplied; these groups with small Eg are called semiconductors. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.	0.139	5.4	3.54	-0.0301	0.6321205588	C
Although the crystallization of large biological molecules may not be as readily accomplished as that of small molecules, their crystal lattices are no different. Tobacco seed globulin forms face-centred cubic crystals with unit cell dimension of $12.3 \mathrm{~nm}$ and a density of $1.287 \mathrm{~g} \mathrm{~cm}^{-3}$. Determine its molar mass.	The molecular formula C18H22O6 (molar mass: 334.36 g/mol, exact mass: 334.1416 u) may refer to: * Combretastatin * Combretastatin B-1 The molecular formula C3H9O6P (molar mass: 172.07 g/mol, exact mass: 172.0137 u) may refer to: * Glycerol 1-phosphate * Glycerol 2-phosphate (BGP) * Glycerol 3-phosphate Category:Molecular formulas A seed crystal is a small piece of single crystal or polycrystal material from which a large crystal of typically the same material is grown in a laboratory. The molecular formula C21H26O3 (molar mass: 326.42 g/mol, exact mass: 326.1882 u) may refer to: * Acitretin * Buparvaquone * Moxestrol * Octabenzone * RU-16117 * 11-Hydroxycannabinol Category:Molecular formulas The molecular formula C9H16N3O14P3 (molar mass: 483.16 g/mol) may refer to: * Cytidine triphosphate * Arabinofuranosylcytosine triphosphate Used to replicate material, the use of seed crystal to promote growth avoids the otherwise slow randomness of natural crystal growth and allows manufacture on a scale suitable for industry. ==Crystal enlargement== The large crystal can be grown by dipping the seed into a supersaturated solution, into molten material that is then cooled, or by growth on the seed face by passing vapor of the material to be grown over it. ==Theory== The theory behind this effect is thought to derive from the physical intermolecular interaction that occurs between compounds in a supersaturated solution (or possibly vapor). This was especially important in pharmaceutical applications where slight changes in molar mass (e.g. aggregation) or shape may result in different biological activity. The placement of a seed crystal into solution allows the recrystallization process to expedite by eliminating the need for random molecular collision or interaction. Absolute molar mass is a process used to determine the characteristics of molecules. == History == The first absolute measurements of molecular weights (i.e. made without reference to standards) were based on fundamental physical characteristics and their relation to the molar mass. In order to gain information about a polydisperse mixture of molar masses, a method for separating the different sizes was developed. To obtain molar mass, light scattering instruments need to measure the intensity of light scattered at zero angle. The purely mathematical root mean square radius is defined as the radii making up the molecule multiplied by the mass at that radius. == Bibliography == A. Einstein, Ann. Phys. 33 (1910), 1275 C.V. Raman, Indian J. Phys. 2 (1927), 1 P.Debye, J. Appl. Phys. 15 (1944), 338 B.H. Zimm, J. Chem. Phys. 13 (1945), 141 B.H. Zimm, J. Chem. Phys. 16 (1948), 1093 B.H. Zimm, R.S. Stein and P. Dotty, Pol. Bull. 1,(1945), 90 M. Fixman, J. Chem. Phys. 23 (1955), 2074 A.C. Ouano and W. Kaye J. Poly. Sci. A1(12) (1974), 1151 Z. Grubisic, P. Rempp, and H. Benoit, J. Polym. The problem was that the system was calibrated according to the Vh characteristics of polymer standards that are not directly related to the molar mass. Also during the process of tempering chocolate, seed crystals can be used to promote the growth of favorable type V crystals ==See also== Crystal structure * Crystallization * Laser heated pedestal growth * Micro-pulling-down * Polycrystal * Single crystal * Wafer (electronics) * Disappearing polymorphs ==References== Category:Crystals The next step is to convert the time at which the samples eluted into a measurement of molar mass. This information is the Root Mean Square radius of the molecule (RMS or Rg). As the demands on polymer properties increased, the necessity of getting absolute information on the molar mass and size also increased. Seeding is therefore said to decrease the necessary amount of time needed for nucleation to occur in a recrystallization process. ==Uses== One example where a seed crystal is used to grow large boules or ingots of a single crystal is the semiconductor industry where methods such as the Czochralski process or Bridgman technique are employed. This interaction can potentiate intermolecular forces between the separate molecules and form a basis for a crystal lattice. As previously noted, the MALS detector can also provide information about the size of the molecule. If the relationship between the molar mass and Vh of the standard is not the same as that of the unknown sample, then the calibration is invalid. A low angle light scattering system was developed in the early 1970s that allowed a single measurement to be used to calculate the molar mass.	0.6296296296	0.5	22.0	1.8	3.61	E
An electron is accelerated in an electron microscope from rest through a potential difference $\Delta \phi=100 \mathrm{kV}$ and acquires an energy of $e \Delta \phi$. What is its final speed?	The kinetic energy Ke of an electron moving with velocity v is: :\displaystyle K_{\mathrm{e}} = (\gamma - 1)m_{\mathrm{e}} c^2, where me is the mass of electron. This wavelength, for example, is equal to 0.0037 nm for electrons accelerated across a 100,000-volt potential. The speed of an electron can approach, but never reach, the speed of light in vacuum, c. Given sufficient voltage, the electron can be accelerated sufficiently fast to exhibit measurable relativistic effects. For an electron with rest mass m0, the rest energy is equal to: :\textstyle E_{\mathrm p} = m_0 c^2, where c is the speed of light in vacuum. Electron optics calculations are crucial for the design of electron microscopes and particle accelerators. thumb\|420x420px\|A schematic of electron excitation, showing excitation by photon (left) and by particle collision (right) Electron excitation is the transfer of a bound electron to a more energetic, but still bound state. The electron (symbol e) is on the left. For example, the Stanford linear accelerator can accelerate an electron to roughly 51 GeV. This energy is assumed to equal the electron's rest energy, defined by special relativity (E = mc2). The energy emission in turn causes a recoil of the electron, known as the Abraham–Lorentz–Dirac Force, which creates a friction that slows the electron. Electrons can be accelerated by suitable electric (or magnetic) fields, thereby acquiring kinetic energy. This can be done by photoexcitation (PE), where the electron absorbs a photon and gains all its energy or by collisional excitation (CE), where the electron receives energy from a collision with another, energetic electron. The required energy of the electrons is typically in the range 20–200 eV. The electron microscope directs a focused beam of electrons at a specimen. Electrons radiate or absorb energy in the form of photons when they are accelerated. For an electron, it has a value of . Relativistic electron beams are streams of electrons moving at relativistic speeds. For the special case of an electrostatic field that is surpassed by a particle, the acceleration voltage is directly given by integrating the electric field along its path. The upper bound of the electron radius of 10−18 meters can be derived using the uncertainty relation in energy. In accelerator physics, the term acceleration voltage means the effective voltage surpassed by a charged particle along a defined straight line. When an excited electron falls back to a state of lower energy, it undergoes electron relaxation (deexcitationSakho, Ibrahima.	1.88	8	0.28209479	1.51	0.333333	A
The following data show how the standard molar constant-pressure heat capacity of sulfur dioxide varies with temperature. By how much does the standard molar enthalpy of $\mathrm{SO}_2(\mathrm{~g})$ increase when the temperature is raised from $298.15 \mathrm{~K}$ to $1500 \mathrm{~K}$ ?	The molar heat capacity generally increases with the molar mass, often varies with temperature and pressure, and is different for each state of matter. The following is a table of some constant- pressure molar heat capacities cP,m of various diatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000 °C, and the apparent number of degrees of freedom f* estimated by the formula f* = 2cP,m/R − 2: 25 °C 25 °C 500 °C 500 °C 5000 °C 5000 °C Gas cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* H2 28.9 5.0 29.6 5.1 41.2 7.9 Not saturated."Hydrogen" NIST Chemistry WebBook, SRD 69, online. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.Lange's Handbook of Chemistry, 10th ed. p. 1524 All methods for the measurement of specific heat apply to molar heat capacity as well. ==Units== The SI unit of molar heat capacity heat is joule per kelvin per mole (J/(K⋅mol), J/(K mol), J K−1 mol−1, etc.). On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows: : C_{P,m} - C_{V,m} = \frac{C_{P} - C_{V}}{n} = \frac{n R}{n} = R This result would be consistent if the specific difference were derived directly from the general expression for c_p - c_v\, . == See also == Heat capacity ratio == References == David R. Gaskell (2008), Introduction to the thermodynamics of materials, Fifth Edition, Taylor & Francis. . The following table shows the experimental molar heat capacities at constant pressure cP,m of the above polyatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000 °C, and the apparent number of degrees of freedom f* estimated by the formula f* = 2cP,m/R − 2: 25 °C 25 °C 500 °C 500 °C 5000 °C 5000 °C Gas cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* cP,m J⋅K−1⋅mol−1 f* f Notes N≡N=O 38.6 7.3 51.8 10.5 62.0 12.9 13 "Nitrous oxide" NIST Chemistry WebBook, SRD 69, online. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1. Therefore, the word "molar", not "specific", should always be used for this quantity. ==Definition== The molar heat capacity of a substance, which may be denoted by cm, is the heat capacity C of a sample of the substance, divided by the amount (moles) n of the substance in the sample: :cm{} \;=\; \frac{C}{n} \;=\; \frac{1}{n} \lim_{\Delta T \rightarrow 0}\frac{Q}{\Delta T} where Q is the amount of heat needed to raise the temperature of the sample by ΔT. Like the heat capacity of an object, the molar heat capacity of a substance may vary, sometimes substantially, depending on the starting temperature T of the sample and the pressure P applied to it. The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. * Standard enthalpy of combustion is the enthalpy change when one mole of an organic compound reacts with molecular oxygen (O2) to form carbon dioxide and liquid water. Then the molar heat capacity (at constant volume) would be :cV,m = fR where R is the ideal gas constant. On the other hand, the vibration modes only start to become active around 350 K (77 °C) Accordingly, the molar heat capacity cP,m is nearly constant at 29.1 J⋅K−1⋅mol−1 from 100 K to about 300 °C. According to Mayer's relation, the molar heat capacity at constant pressure would be :cP,m = cV,m \+ R = fR + R = (f + 2)R Thus, each additional degree of freedom will contribute R to the molar heat capacity of the gas (both cV,m and cP,m). Since the molar heat capacity of a substance is the specific heat c times the molar mass of the substance M/N its numerical value is generally smaller than that of the specific heat. Regardless, if each reactant and product can be prepared in its respective standard state, then the contribution of each species is equal to its molar enthalpy of formation multiplied by its stoichiometric coefficient in the reaction, and the enthalpy of reaction at constant (standard) pressure P^{\ominus} and constant temperature (usually 298 K) may be written as : Q_{P^{\ominus}} = \Delta_{\text {rxn}} H^\ominus = \sum_{products,~p} u_{p}\Delta_{\text {f}} H_{p}^{\ominus} - \sum_{reactants,~r} u_{r}\Delta_{\text {f}} H_{r}^{\ominus} As shown above, at constant pressure the heat of the reaction is exactly equal to the enthalpy change, \Delta_{\text {rxn}} H, of the reacting system. == Variation with temperature or pressure == The variation of the enthalpy of reaction with temperature is given by Kirchhoff's Law of Thermochemistry, which states that the temperature derivative of ΔH for a chemical reaction is given by the difference in heat capacity (at constant pressure) between products and reactants: :\left(\frac{\partial \Delta H}{\partial T}\right)_p = \Delta C_p. In modern terms the mass m of the sample divided by molar mass M gives the number of moles n. :m/M = n Therefore, using uppercase C for the full heat capacity (in joule per kelvin), we have: :C(M/m) = C/n = K = 3R or :C/n = 3R. Like the specific heat, the measured molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). The value thus obtained is said to be the molar heat capacity at constant pressure (or isobaric), and is often denoted cP,m, cp,m, cP,m, etc. For example, "H2O: 75.338 J⋅K−1⋅mol−1 (25 °C, 101.325 kPa)" W. Wagner, J. R. Cooper, A. Dittmann, J. Kijima, H.-J. Kretzschmar, A. Kruse, R. Mare, K. Oguchi, H. Sato, I. Stöcker, O. Šifner, Y. Takaishi, I. Tanishita, J. Trübenbach and Th. Willkommen (2000): "The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam", ASME J. Eng. Gas Turbines and Power, volume 122, pages 150–182 When not specified, published values of the molar heat capacity cm generally are valid for some standard conditions for temperature and pressure. thumb\|upright=2.2\|Molar heat capacity of most elements at 25 °C is in the range between 2.8 R and 3.4 R: Plot as a function of atomic number with a y range from 22.5 to 30 J/mol K. These parameters are usually specified when giving the molar heat capacity of a substance. At high enough temperature, its molar heat capacity then should be cP,m = 7.5 R = 62.63 J⋅K−1⋅mol−1.	1.94	1.07	1.2	62.2	1.06	D
Suppose that the normalized wavefunction for an electron in a carbon nanotube of length $L=10.0 \mathrm{~nm}$ is: $\psi=(2 / L)^{1 / 2} \sin (\pi x / L)$. Calculate the probability that the electron is between $x=4.95 \mathrm{~nm}$ and $5.05 \mathrm{~nm}$.	b) Linear dependence of the electron energy on the wave vector in CNTs; c) Dispersion relation near the Fermi energy for a semiconducting CNT; d) Dispersion relation near the Fermi energy for a metallic CNT Conduction in single-walled carbon nanotubes is quantized due to their one-dimensionality and the number of allowed electronic states is limited, if compared to bulk graphite. If a carbon nanotube is a ballistic conductor, but the contacts are nontransparent, the transmission probability, T, is reduced by back- scattering in the contacts. Scattering of electrons by optical phonons in carbon nanotube channels has two requirements: * The traveled length in the conduction channel between source and drain has to be greater than the optical phonon mean free path * The electron energy has to be greater than the critical optical phonon emission energy === Schottky barrier Ballistic conduction === thumb\|400px\|Figure 2: Example of the band structure of a ballistic CNT FET. In order to estimate the current in the carbon nanotube channel, the Landauer formula can be applied, which considers a one-dimensional channel, connected to two contacts – source and drain. In semiconducting CNTs at room temperature and for low energies, the mean free path is determined by the electron scattering from acoustic phonons, which results in lm ≈ 0.5μm. Single-walled carbon nanotubes in the fields of quantum mechanics and nanoelectronics, have the ability to conduct electricity. When ballistically conducted, the electrons travel through the nanotubes channel without experiencing scattering due to impurities, local defects or lattice vibrations. "Carbon Nanotube and Graphene Device Physics", Cambridge UP, 2011. Another way to make carbon nanotube transistors has been to use random networks of them. Carbon nanotube transistors as logic-gate circuits with densities comparable to modern CMOS technology has not yet been demonstrated. The potential of carbon nanotubes was demonstrated in 2003 when room- temperature ballistic transistors with ohmic metal contacts and high-k gate dielectric were reported, showing 20–30x higher ON current than state-of-the- art Si MOSFETs. Carbon nanotube chemistry involves chemical reactions, which are used to modify the properties of carbon nanotubes (CNTs). In order to derive the current-voltage (I-V) characteristics for a ballistic CNT FET, one can start with Planck's postulate, which relates the energy of the i-th state to its frequency: E_i=h u_i=\frac{h}{2e}\frac{2e}{T_i}=\frac{h}{2e}I_i The total current for a many-state system is then the sum over the energy of each state multiplied by the occupation probability function, in this case the Fermi–Dirac statistics: I_i=\frac{2e}{h}\sum_{i}E_i\frac{1}{1+e^{\frac{E-E_f}{k_BT}}} For a system with dense states, the discrete sum can be approximated by an integral: I_i=\frac{2e}{h}\int \frac{1}{1+e^{\frac{E-E_f}{k_BT}}}dE In CNT FETs, the charge carriers move either left (negative velocity) or right (positive velocity) and the resulting net current is called drain current. When ballistic in nature conductance can be treated as if the electrons experience no scattering. == Conductance quantization and Landauer formula == thumb\|400px\|Figure 1: a) Energy contour plot of the electronic band structure in CNTs.; thumbnail\|right\|Plot of probit function In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. The exceptional electrical and mechanical properties of carbon nanotubes have made them alternatives to the traditional electrical actuators for both microscopic and macroscopic applications. These processes were essential for low yield production of carbon nanotubes where carbon particles, amorphous carbon particles and coatings comprised a significant percentage of the overall material and are still important for the introduction of surface functional groups. A carbon nanotube quantum dot (CNT QD) is a small region of a carbon nanotube in which electrons are confined. ==Formation== A CNT QD is formed when electrons are confined to a small region within a carbon nanotube. The CNT QD is modelled as an Anderson-type model, which can be reduced by Schrieffer-Wolff transformation to an effective Kondo-type model at low temperature. ==Other nanotube system== Similar mesoscopic devices have been constructed from elements other than carbon. "Nanowelded Carbon Nanotubes from Field-effect Transistors to Solar Microcells", Heidelberg: Springer, 2009. Major obstacles to nanotube-based microelectronics include the absence of technology for mass production, circuit density, positioning of individual electrical contacts, sample purity, control over length, chirality and desired alignment, thermal budget and contact resistance. Carbon nanotubes (CNTs) are cylinders of one or more layers of graphene (lattice).	0.08	226	1.0	0.020	0.011	D
A sample of the sugar D-ribose of mass $0.727 \mathrm{~g}$ was placed in a calorimeter and then ignited in the presence of excess oxygen. The temperature rose by $0.910 \mathrm{~K}$. In a separate experiment in the same calorimeter, the combustion of $0.825 \mathrm{~g}$ of benzoic acid, for which the internal energy of combustion is $-3251 \mathrm{~kJ} \mathrm{~mol}^{-1}$, gave a temperature rise of $1.940 \mathrm{~K}$. Calculate the enthalpy of formation of D-ribose.	However the standard enthalpy of combustion is readily measurable using bomb calorimetry. The standard enthalpy of formation is then determined using Hess's law. That is, the heat of combustion, ΔH°comb, is the heat of reaction of the following process: : (std.) + (c + - ) (g) → c (g) + (l) + (g) Chlorine and sulfur are not quite standardized; they are usually assumed to convert to hydrogen chloride gas and or gas, respectively, or to dilute aqueous hydrochloric and sulfuric acids, respectively, when the combustion is conducted in a bomb calorimeter containing some quantity of water. == Ways of determination == ===Gross and net=== Zwolinski and Wilhoit defined, in 1972, "gross" and "net" values for heats of combustion. The calorific value is the total energy released as heat when a substance undergoes complete combustion with oxygen under standard conditions. They may also be calculated as the difference between the heat of formation ΔH of the products and reactants (though this approach is somewhat artificial since most heats of formation are typically calculated from measured heats of combustion). For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol . == Hess's law == For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). The temperature may depend on pressure, because at lower pressure there will be more dissociation of the combustion products, implying a lower adiabatic temperature. ≈6332 Aluminium Oxygen 3732 6750 Lithium Oxygen 2438 4420 Phosphorus (white) Oxygen 2969 5376 Zirconium Oxygen 4005 7241 ==Thermodynamics== thumb\|right\|300px\|First law of thermodynamics for a closed reacting system From the first law of thermodynamics for a closed reacting system we have :{}_RQ_P - {}_RW_P = U_P - U_R where, {}_RQ_P and {}_RW_P are the heat and work transferred from the system to the surroundings during the process, respectively, and U_R and U_P are the internal energy of the reactants and products, respectively. The experimental heat of formation of ethane is -20.03 kcal/mol and ethane consists of 2 P groups. Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. It may be expressed with the quantities: * energy/mole of fuel * energy/mass of fuel * energy/volume of the fuel There are two kinds of enthalpy of combustion, called high(er) and low(er) heat(ing) value, depending on how much the products are allowed to cool and whether compounds like are allowed to condense. The temperatures mentioned here are for a stoichiometric fuel-oxidizer mixture (i.e. equivalence ratio φ = 1). alt=\|thumb\| Fischer Projection Ribose is a simple sugar and carbohydrate with molecular formula C5H10O5 and the linear-form composition H−(C=O)−(CHOH)4−H. 150px 150px Comparison of the chemical structures of ribose (top) and deoxyribose (bottom). This is the same as the thermodynamic heat of combustion since the enthalpy change for the reaction assumes a common temperature of the compounds before and after combustion, in which case the water produced by combustion is condensed to a liquid. It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method. == Use in calculation for other reactions == The standard enthalpy change of any reaction can be calculated from the standard enthalpies of formation of reactants and products using Hess's law. Since the heat of combustion of these elements is known, the heating value can be calculated using Dulong's Formula: LHV [kJ/g]= 33.87mC \+ 122.3(mH \- mO ÷ 8) + 9.4mS where mC, mH, mO, mN, and mS are the contents of carbon, hydrogen, oxygen, nitrogen, and sulfur on any (wet, dry or ash free) basis, respectively. === Higher heating value === The higher heating value (HHV; gross energy, upper heating value, gross calorific value GCV, or higher calorific value; HCV) indicates the upper limit of the available thermal energy produced by a complete combustion of fuel. The enthalpy of reaction can then be analyzed by applying Hess's Law, which states that the sum of the enthalpy changes for a number of individual reaction steps equals the enthalpy change of the overall reaction. However O2 is an element in its standard state, so that \Delta_{\text{f}} H^{\ominus }(\text{O}_2) = 0, and the heat of reaction is simplified to :\Delta_{\text{r}} H^{\ominus } = [\Delta_{\text{f}} H^{\ominus }(\text{CO}_2) + 2\Delta_{\text{f}} H^{\ominus } (\text{H}_2{}\text{O})] - \Delta_{\text{f}} H^{\ominus }(\text{CH}_4), which is the equation in the previous section for the enthalpy of combustion \Delta_{\text{comb}}H^{\ominus }. == Key concepts for enthalpy calculations == *When a reaction is reversed, the magnitude of ΔH stays the same, but the sign changes. The following figure illustrates that the effects of dissociation tend to lower the adiabatic flame temperature. Incomplete reaction at higher temperature further curtails the effect of a larger heat of combustion. There are a number of programs available that can calculate the adiabatic flame temperature taking into account dissociation through equilibrium constants (Stanjan, NASA CEA, AFTP).	-0.347	-1270	0.4772	1.3	7.136	B
An electron confined to a metallic nanoparticle is modelled as a particle in a one-dimensional box of length $L$. If the electron is in the state $n=1$, calculate the probability of finding it in the following regions: $0 \leq x \leq \frac{1}{2} L$.	To a first approximation (i.e. assuming that the charges are distributed randomly), the molar configurational electronic entropy is given by: :S \approx n_\text{sites} \left [ x \ln x + (1-x) \ln (1-x) \right ] where is the fraction of sites on which a localized electron/hole could reside (typically a transition metal site), and is the concentration of localized electrons/holes. Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. 180px\|thumb\|right\|Diagram of a helium atom, showing the electron probability density as shades of gray. The probability of occupation of each eigenstate is given by the Fermi function, : :p(E)=f=\frac{1}{e^{(E-E_{\rm F}) / k_{\rm B} T} + 1} where is the Fermi energy and is the absolute temperature. For one-electron systems, the electron density at any point is proportional to the square magnitude of the wavefunction. == Definition == The electronic density corresponding to a normalised N-electron wavefunction \Psi (with \textbf r and s denoting spatial and spin variables respectively) is defined as : \rho(\mathbf{r}) = \langle\Psi\|\hat{\rho}(\mathbf{r})\|\Psi\rangle, where the operator corresponding to the density observable is :\hat{\rho}(\mathbf{r}) = \sum_{i=1}^{N}\ \delta(\mathbf{r}-\mathbf{r}_{i}). The density is determined, through definition, by the normalised N-electron wavefunction which itself depends upon 4N variables (3N spatial and N spin coordinates). Some softwareor example, the Spartan program from Wavefunction, Inc. also allows for specification of the electron density in terms of percentage of total electrons enclosed. For every possible transfer of an electron from an occupied site i to an unoccupied site j , the energy invested should be positive, since we are assuming we are in the ground state of the system, i.e., \Delta E>=0 . In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The Fermi–Dirac distribution implies that each eigenstate of a system, , is occupied with a certain probability, . Of course, the localized charges are not distributed randomly, as the charges will interact electrostatically with one another, and so the above formula should only be regarded as an approximation to the configurational atomic entropy. We will solve for each independently: Let E be an energy value above the well (E>0) * For 0 < x < (a-b): \begin{align} \frac{-\hbar^2}{2m} \psi_{xx} &= E \psi \\\ \Rightarrow \psi &= A e^{i \alpha x} + A' e^{-i \alpha x} & \left( \alpha^2 = {2mE \over \hbar^2} \right) \end{align} For -b : \begin{align} \frac{-\hbar^2}{2m} \psi_{xx} &= (E+V_0)\psi \\\ \Rightarrow \psi &= B e^{i \beta x} + B' e^{-i \beta x} & \left( \beta^2 = {2m(E+V_0) \over \hbar^2} \right). \end{align} To find u(x) in each region, we need to manipulate the electron's wavefunction: \begin{align} \psi(0 And in the same manner: u(-b To complete the solution we need to make sure the probability function is continuous and smooth, i.e.: \psi(0^{-})=\psi(0^{+}) \qquad \psi'(0^{-})=\psi'(0^{+}). In these situations, the density simplifies to :\rho(\mathbf{r})=\sum_{k=1}^N n_{k}\|\varphi_k(\mathbf{r})\|^2. == General properties == From its definition, the electron density is a non-negative function integrating to the total number of electrons. Moreover, in condensed matter and molecules, the electron clouds of the atoms usually overlap to some extent, and some of the electrons may roam over a large region encompassing two or more atoms. Switching from summing over individual states to integrating over energy levels, the entropy can be written as: :S=-k_{\rm B} \int n(E) \left [ p(E) \ln p(E) +(1- p(E)) \ln \left ( 1- p(E)\right ) \right ]dE where is the density of states of the solid. Metals have non-zero density of states at the Fermi level. As the density of states at the Fermi level varies widely between systems, this approximation is a reasonable heuristic for inferring when it may be necessary to include electronic entropy in the thermodynamic description of a system; only systems with large densities of states at the Fermi level should exhibit non-negligible electronic entropy (where large may be approximately defined as ). == Application to different materials classes == Insulators have zero density of states at the Fermi level due to their band gaps. The occupation numbers are not limited to the range of zero to two, and therefore sometimes even the response density can be negative in certain regions of space. ==Overview== In molecules, regions of large electron density are usually found around the atom, and its bonds. Electrons and Holes in Semiconductors: With Applications to Transistor Electronics, Bell Telephone Laboratories series, Van Nostrand. The observation of this is expected to occur below a certain temperature, such that the optimal energy of hopping would be smaller than the width of the Coulomb gap. An earlier version containing some of the material appeared in the Bell Labs Technical Journal in 1949. ==Contents== The arrangement of chapters is as follows: Part I INTRODUCTION TO TRANSISTOR ELECTRONICS Chapter 1: THE BULK PROPERTIES OF SEMICONDUCTORS Chapter 2: THE TRANSISTOR AS A CIRCUIT ELEMENT Chapter 3: QUANTITATIVE STUDIES OF INJECTION OF HOLES AND ELECTRONS Chapter 4: ON THE PHYSICAL THEORY OF TRANSISTORS Chapter 5: QUANTUM STATES, ENERGY BANDS, AND BRILLOUIN ZONES PART II DESCRIPTIVE THEORY OF SEMICONDUCTORS Chapter 6: VELOCITIES AND CURRENTS FOR ELECTRONS I N CRYSTALS Chapter 7: ELECTRONS AND HOLES IN ELECTRIC AND MAGNETIC FIELDS Chapter 8: INTRODUCTORY THEORY OF CONDUCTIVITY AND HALL EFFECT Chapter 9: DISTRIBUTIONS OF QUANTUM STATES IN ENERGY Chapter 10: FERMI-DIRAC STATISTICS FOR SEMICONDUCTORS Chapter 11: MATHEMATICAL THEORY OF CONDUCTIVITY AND HALL EFFECT Chapter 12: APPLICATIONS TO TRANSISTOR ELECTRONICS PART III QUANTUM MECHANICAL FOUNDATIONS Chapter 13: INTRODUCTION TO PART III Chapter 14: ELEMENTARY QUANTUM MECHANICS WITH CIRCUIT THEORY ANALOGUES Chapter 15: THEORY OF ELECTRON AND HOLE VELOCITIES, CURRENTS AND ACCELERATIONS Chapter 16: STATISTICAL MECHANICS FOR SEMICONDUCTORS Chapter 17: THE THEORY OF TRANSITION PROBABILITIES FOR HOLES AND ELECTRONS APPENDIX A Units APPENDIX B Periodic Table APPENDIX C Values of the physical constants APPENDIX D Energy conversion chart NAME INDEX SUBJECT INDEX Category:1950 non-fiction books Category:1950 in science Category:Physics textbooks Together with the normalization property places acceptable densities within the intersection of L1 and L3 – a superset of \mathcal{J}_{N}. == Topology == The ground state electronic density of an atom is conjectured to be a monotonically decaying function of the distance from the nucleus. === Nuclear cusp condition === The electronic density displays cusps at each nucleus in a molecule as a result of the unbounded electron- nucleus Coulomb potential.	6	0.829	'-20.0'	4500	0.5	E