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2.3.6 Specific heat capacities
For molar heat capacities and other thermodynamic properties of elements
and chemical compounds, see section 3.10.
Ratio of the principal specific heat capacities for
gases and vapours
The ratio γ of
the specific heat capacity at constant pressure to that at constant volume is
usually determined directly by some method involving an adiabatic expansion,
such as the determination of the velocity of sound in the gas. From a knowledge
of either (1) the pressure or (2) the temperature immediately following an
adiabatic expansion (Clément and Desormes’, Lummer and
Pringsheim’s methods respectively), γ can be deduced from
pvγ =
const, or θvγ−1 = const. (See Adkins
(1983).)
| Gas |
|
|
Temp./°C |
γ |
| |
|
|
|
|
| Monatomic
gases |
|
|
|
|
| |
|
|
|
|
| Helium |
|
|
0 |
1.63 |
| Argon |
|
|
0 |
1.667 |
| Neon |
|
|
19 |
1.642 |
| Krypton
|
|
|
19 |
1.689 |
| Xenon |
|
|
19 |
1.666 |
| Mercury
vapour |
|
|
310 |
1.666 |
| |
|
|
|
|
| Diatomic
gases |
|
|
|
|
| |
|
|
|
|
| Air
(dry) |
|
|
−79.3 |
1.405 |
| Air
(dry) |
|
|
0–17 |
1.401/2 |
| Air
(dry) |
|
|
500 |
1.357 |
| Air
(dry) |
|
|
900 |
1.32 |
| Air
(dry) (200 atm) |
|
|
0 |
1.828 |
| ,, |
|
|
−79.3 |
2.333 |
| Hydrogen |
|
|
4–17 |
1.407/8 |
| Nitrogen
|
|
|
20 |
1.401 |
| Oxygen
|
|
|
5–14 |
1.400 |
| Carbon
monoxide |
|
|
1
800 |
1.297 |
| Nitric
oxide |
|
|
— |
1.394 |
| |
|
|
|
|
| Triatomic
gases |
|
|
|
|
| |
|
|
|
|
| Ozone |
|
|
— |
1.29† |
| Water
vapour |
|
|
100 |
1.334 |
| Carbon
dioxide |
|
|
4–11 |
1.300 |
| Carbon
dioxide |
|
|
300 |
1.22 |
| Carbon
dioxide |
|
|
500 |
1.20 |
| Ammonia,
NH3 |
|
|
50 |
1.306 |
| Nitrous
oxide, N2O |
|
|
— |
1.324 |
| Nitrogen
peroxide N2O4 |
|
|
20 |
1.172 |
| ,, NO2 |
|
|
150 |
1.31 |
| H2S |
|
|
— |
1.340 |
| CS2 |
|
|
— |
1.239 |
| Sulphur
dioxide |
|
|
16–34 |
1.26 |
| ,, |
|
|
500 |
1.2 |
| |
|
|
|
|
| Polyatomic
gases |
|
|
|
|
| |
|
|
|
|
| Methane,
CH4 |
|
|
20 |
1.307 |
| Ethane,
C2H6 |
|
|
20 |
1.197 |
| Propane,
C3H8 |
|
|
20 |
1.136 |
| Acetylene,
C2H2 |
|
|
20 |
1.237 |
| Ethylene,
C2H4 |
|
|
20 |
1.247 |
| Benzene
C6H6 |
|
|
20 |
1.40 |
| Benzene
C6H6 |
|
|
99.7 |
1.105 |
| Chloroform
CHCl3 |
|
|
24–42 |
1.110 |
| ,, |
|
|
99.8 |
1.150 |
| CCl4
|
|
|
— |
1.130 |
| Methyl
alcohol |
|
|
99.7 |
1.256 |
| Methyl
bromide |
|
|
— |
1.274 |
| Methyl
chloride |
|
|
19–30 |
1.279 |
| Methyl
iodide |
|
|
— |
1.286 |
| Ethyl
alcohol |
|
|
53 |
1.133 |
| Ethyl
alcohol |
|
|
99.8 |
1.134 |
| Ethyl
bromide |
|
|
— |
1.188 |
| Ethyl
chloride |
|
|
22.7 |
1.187 |
| Ethyl
ether |
|
|
12–20 |
1.024 |
| Ethyl
ether |
|
|
99.7 |
1.112 |
| Acetic
acid |
|
|
136.5 |
1.147 |
†
Extrapolated.
Specific heat capacity of water
The International Committee for Weights and Measures,
Paris, 1950, accepted W. J. de Haas’s recommended value of 4.1855
Jg−1 °C−1 for the specific heat capacity
of water at 15 °C (cp (15 °C)). Values at
other temperatures are then deduced from the equation:
| |
cp(t °C) |
= 0.996 185 + 0.000 2874 |
|
t + 100 |
|
5.26 |
+ 0.011 160 ×
10−0.036t |
| |
cp(15 °C) |
100 |
due to Osborne, Stimson and Ginnings.
The tabulated values are essentially those appearing in
the IUPAC publication edited by K. N. Marsh (1987). The minimum of 4.1815 in
Cox, Wagman and Medvedev (1989) is higher by 0.08%.
Water cp(t)/(Jg−1
°C−1)
|
°C |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
0 |
4.217 4 |
4.213 8 |
4.210 4 |
4.207 4 |
4.204 5 |
4.201 9 |
4.199 6 |
4.197 4 |
4.195 4 |
4.193 6 |
|
10 |
4.191 9 |
4.190 4 |
4.189 0 |
4.187 7 |
4.186 6 |
4.185 5 |
4.184 6 |
4.183 7 |
4.182 9 |
4.182 2 |
|
20 |
4.181 6 |
4.181 0 |
4.180 5 |
4.180 1 |
4.179 7 |
4.179 3 |
4.179 0 |
4.178 7 |
4.178 5 |
4.178 3 |
|
30 |
4.178 2 |
4.178 1 |
4.178 0 |
4.178 0 |
4.177 9 |
4.177 9 |
4.178 0 |
4.178 0 |
4.178 1 |
4.178 2 |
|
40 |
4.178 3 |
4.178 4 |
4.178 6 |
4.178 8 |
4.178 9 |
4.179 2 |
4.179 4 |
4.179 6 |
4.179 9 |
4.180 1 |
|
50 |
4.180 4 |
4.180 7 |
4.181 1 |
4.181 4 |
4.181 7 |
4.182 1 |
4.182 5 |
4.182 9 |
4.183 3 |
4.183 7 |
|
60 |
4.184 1 |
4.184 6 |
4.185 0 |
4.185 5 |
4.186 0 |
4.186 5 |
4.187 1 |
4.187 6 |
4.188 2 |
4.188 7 |
|
70 |
4.189 3 |
4.189 9 |
4.190 5 |
4.191 2 |
4.191 8 |
4.192 5 |
4.193 2 |
4.193 9 |
4.194 6 |
4.195 4 |
|
80 |
4.196 1 |
4.196 9 |
4.197 7 |
4.198 5 |
4.199 4 |
4.200 2 |
4.201 1 |
4.202 0 |
4.202 9 |
4.203 9 |
|
90 |
4.204 8 |
4.205 8 |
4.206 8 |
4.207 8 |
4.208 9 |
4.210 0 |
4.211 1 |
4.212 2 |
4.213 3 |
4.214 5 |
|
|
|
|
|
|
|
|
|
|
|
|
Specific heat capacities of metals, alloys and
miscellaneous substances
|
Metal |
cp/Jg−1
K−1 |
|
Temperature/K |
|
77 |
173 |
273 |
373 |
573 |
773 |
|
|
|
|
|
|
|
|
|
Aluminium . . . . . . . . .
|
0.336 |
0.743 |
0.880 |
0.937 |
1.021 |
1.130 |
|
Antimony . . . . . . . . .
|
0.150 |
0.196 |
0.206 |
0.212 |
0.221 |
0.238 |
|
Beryllium . . . . . . . . .
|
0.080 |
0.852 |
1.75 |
2.01 |
2.44 |
~ 2.8 |
|
Bismuth . . . . . . . . . .
|
0.104 |
0.119 |
0.122 |
0.125 |
0.143 |
0.135 |
|
Cadmium . . . . . . . . .
|
0.179 |
0.218 |
0.229 |
0.238 |
0.255 |
— |
|
Cerium . . . . . . . . . .
|
— |
— |
0.190 |
0.199 |
0.219 |
— |
|
Chromium . . . . . . . . .
|
0.117 |
0.351 |
0.438 |
0.481 |
0.527 |
0.55 |
|
Cobalt . . . . . . . . . .
|
0.169 |
0.357 |
0.414 |
0.443 |
0.490 |
0.54 |
|
Copper . . . . . . . . . .
|
0.195 |
0.341 |
0.379 |
0.397 |
0.419 |
~ 0.43 |
|
Erbium . . . . . . . . . .
|
0.192 |
0.140 |
0.166 |
0.169 |
0.174 |
0.181 |
|
Gadolinium . . . . . . . . .
|
0.166 |
— |
0.300 |
0.35 |
0.38 |
0.39 |
|
Gold . . . . . . . . . . .
|
0.097 |
0.121 |
0.128 |
0.131 |
0.135 |
0.140 |
|
Hafnium . . . . . . . . . .
|
0.101 |
0.134 |
0.143 |
0.148 |
0.157 |
0.164 |
|
Holmium . . . . . . . . . .
|
— |
0.161 |
0.164 |
0.168 |
— |
— |
|
Indium . . . . . . . . . .
|
0.191 |
0.222 |
0.231 |
0.247 |
0.247 |
0.239 |
|
Iron (α) . . . . . . . . . .
|
0.144 |
0.336 |
0.442 |
0.484 |
0.567 |
0.665 |
|
Lanthanum . . . . . . . . .
|
0.156 |
— |
— |
0.194 |
0.210 |
— |
|
Lead . . . . . . . . . . .
|
0.114 |
0.124 |
0.127 |
0.131 |
0.141 |
0.132 |
|
Lithium . . . . . . . . . .
|
1.30 |
2.89 |
3.48 |
3.87 |
4.28 |
4.17 |
|
Lutetium . . . . . . . . . .
|
— |
0.602 |
0.64 |
— |
— |
— |
|
Magnesium . . . . . . . . .
|
0.488 |
0.887 |
1.00 |
1.06 |
1.14 |
1.27 |
|
Manganese (α) . . . . . . . .
|
0.201 |
0.394 |
0.467 |
0.502 |
0.565 |
0.63 |
|
Mercury . . . . . . . . . .
|
0.115 |
0.132 |
0.140 |
0.137 |
0.135 |
0.137 |
|
Molybdenum . . . . . . . .
|
0.098 |
0.209 |
0.246 |
0.259 |
0.274 |
0.285 |
|
Nickel . . . . . . . . . .
|
0.163 |
0.357 |
0.429 |
0.465 |
0.569 |
0.527 |
|
Niobium . . . . . . . . . .
|
0.167 |
0.247 |
0.265 |
0.272 |
0.28 |
0.29 |
|
Osmium . . . . . . . . . .
|
— |
— |
0.130 |
0.132 |
0.136 |
— |
|
Palladium . . . . . . . . .
|
0.124 |
0.218 |
0.240 |
0.249 |
0.259 |
0.270 |
|
Platinum . . . . . . . . . .
|
0.085 |
0.123 |
0.132 |
0.135 |
0.141 |
0.146 |
|
Plutonium . . . . . . . . .
|
— |
— |
0.146 |
~ 0.17 |
~ 0.20 |
~ 0.18 |
|
Potassium . . . . . . . . .
|
0.604 |
0.677 |
0.732 |
0.813 |
0.774 |
0.761 |
|
Praseodymium . . . . . . . .
|
0.193 |
— |
0.196 |
0.200 |
0.217 |
~ 0.24 |
|
Rhenium . . . . . . . . .
|
0.078 |
0.125 |
0.138 |
0.142 |
0.145 |
0.146 |
|
Rhodium . . . . . . . . .
|
0.088 |
0.209 |
0.238 |
0.252 |
0.269 |
— |
|
Rubidium . . . . . . . . .
|
0.291 |
0.315 |
0.346 |
0.390 |
0.358 |
0.340 |
|
Ruthenium . . . . . . . . .
|
0.094 |
0.202 |
0.235 |
0.241 |
0.251 |
— |
|
Samarium . . . . . . . . .
|
— |
0.177 |
0.192 |
0.214 |
0.263 |
0.296 |
|
Scandium . . . . . . . . .
|
— |
0.497 |
0.557 |
0.582 |
— |
— |
|
Silver . . . . . . . . . .
|
0.162 |
0.219 |
0.235 |
0.239 |
0.249 |
0.257 |
|
Sodium . . . . . . . . .
|
0.888 |
1.101 |
1.200 |
1.383 |
1.304 |
1.261 |
|
Tantalum . . . . . . . . .
|
0.095 |
0.130 |
0.139 |
0.143 |
0.150 |
0.152 |
|
Terbium . . . . . . . . .
|
0.178 |
0.255 |
0.186 |
0.180 |
0.186 |
0.204 |
|
Thallium . . . . . . . . .
|
0.115 |
0.126 |
0.131 |
0.138 |
— |
— |
|
Thorium . . . . . . . . .
|
0.091 |
0.110 |
0.117 |
0.122 |
0.133 |
0.144 |
|
Thulium . . . . . . . . .
|
0.146 |
0.156 |
0.159 |
0.161 |
— |
— |
|
Tin . . . . . . . . . . .
|
0.170 |
0.211 |
0.221 |
0.240 |
0.244 |
0.235 |
|
Titanium . . . . . . . . .
|
0.218 |
0.438 |
0.511 |
0.546 |
0.586 |
0.628 |
|
Tungsten . . . . . . . . .
|
0.068 |
0.120 |
0.133 |
0.135 |
0.140 |
0.143 |
|
Uranium . . . . . . . . .
|
0.085 |
0.106 |
0.114 |
0.119 |
0.144 |
0.167 |
|
Vanadium . . . . . . . . .
|
0.188 |
0.409 |
0.489 |
0.510 |
0.531 |
0.573 |
|
Yttrium . . . . . . . . . .
|
0.200 |
0.273 |
0.294 |
0.304 |
0.320 |
0.336 |
|
Zinc . . . . . . . . . . .
|
0.251 |
0.357 |
0.385 |
0.402 |
0.437 |
0.470 |
|
Zirconium . . . . . . . . .
|
0.170 |
0.257 |
0.273 |
0.294 |
0.319 |
0.339 |
| |
|
|
|
|
|
|
Values in italics refer to liquid state.
|
Alloy |
cp/Jg−1
K−1 |
|
Temperature/K |
|
77 |
173 |
273 |
373 |
573 |
773 |
| |
|
|
|
|
|
|
|
Alumel 72Ni, 25Mn, 2Al . . . . .
|
— |
— |
0.481 |
0.496 |
— |
|
|
Aluminium alloys 93Al,
7Si . . . .
|
— |
— |
0.866 |
0.929 |
1.009 |
— |
|
94Al, 4.5Cu,
1.5Mg . . . . .
|
0.48 |
0.69 |
0.82 |
0.91 |
1.03 |
— |
|
Brass . . . . . . . . . . .
|
0.20 |
0.34 |
0.387 |
0.390 |
0.448 |
— |
|
Chromel 90Ni,
10Cr . . . . . . .
|
— |
— |
— |
0.473 |
0.521 |
— |
|
Constantan 60Cu,
40Ni . . . . . .
|
0.175 |
— |
0.401 |
0.425 |
0.457 |
— |
|
Monel 67Ni, 29Cu + Fe
. . . . .
|
— |
0.35 |
0.406 |
0.448 |
0.489 |
0.514 |
|
Nichrome V, 77Ni, 19.5Cr
. . . . .
|
— |
— |
0.432 |
0.464 |
0.509 |
0.548 |
|
Nickel steels |
|
|
|
|
|
|
|
3.5% Ni
. . . . . . . . .
|
– |
– |
– |
0.496 |
0.569 |
0.694 |
|
5.0% Ni
. . . . . . . . .
|
0.155 |
0.365 |
0.445 |
— |
— |
— |
|
9% Ni
. . . . . . . . . . . .
|
0.154 |
0.364 |
0.454 |
— |
0.557 |
— |
|
Nickel Superalloys |
|
|
|
|
|
|
|
75Ni, 20Cr, 5Fe . . . . . .
|
— |
— |
0.442 |
0.468 |
0.507 |
0.540 |
|
60Ni, 10Co, 10W, 9Cr, 5Al,
2Ta . |
— |
— |
0.403 |
0.428 |
0.459 |
0.481 |
|
Solder 50Pb,
50Sn . . . . . .
|
0.142 |
0.167 |
0.177 |
— |
— |
— |
|
30Bi, 70Sn
. . . . . . . .
|
— |
— |
0.198 |
0.277 |
— |
— |
|
Steels |
|
|
|
|
|
|
|
Low alloy (→5% additions)
. . . |
— |
— |
0.44–45 |
0.48–50 |
0.55–59 |
0.67–70 |
|
18Cr, 10Ni stainless
. . . . .
|
— |
— |
0.460 |
0.504 |
0.593 |
— |
|
18Cr, 12Ni stainless
. . . . .
|
0.197 |
0.401 |
0.47 |
— |
— |
— |
|
25Cr, 20Ni stainless
. . . . .
|
— |
— |
0.450 |
0.490 |
0.530 |
0.560 |
|
24Cr, 20Ni stainless
. . . . .
|
0.195 |
0.393 |
0.463 |
— |
— |
— |
|
Titanium alloys |
|
|
|
|
|
|
|
90Ti, 6Al, 4V
. . . . . . .
|
0.21 |
0.45 |
0.547 |
0.569 |
0.616 |
0.678 |
|
81Ti, 11Sn, 5Zr, 2Al
. . . . .
|
|
|
0.490 |
0.506 |
0.548 |
0.602 |
|
Zircaloy 2 . . . . . . . . .
|
— |
— |
0.280 |
0.295 |
0.316 |
— |
|
|
|
|
|
|
|
|
|
Miscellaneous |
cp/Jg−1
K−1 |
|
Temperature/K |
|
77 |
173 |
273 |
373 |
573 |
773 |
|
|
|
|
|
|
|
|
|
Air (dry) cp . . . . . . . . . .
|
— |
1.008 |
— |
1.011 |
— |
1.092 |
|
Alumina
Al2O3 . . . . . . . . .
|
0.060 |
0.403 |
0.718 |
0.907 |
1.089 |
1.168 |
|
Asbestos . . . . . . . . . . .
|
— |
— |
(~ 0.84)† |
— |
— |
|
Basalt . . . . . . . . . . . .
|
— |
— |
(~ 0.84–1.0)† |
— |
— |
|
Boron . . . . . . . . . . . .
|
0.064 |
0.48 |
~0.96 |
1.37 |
1.84 |
2.22 |
|
Boron
nitride . . . . . . . . . .
|
0.15 |
0.43 |
0.72 |
0.916 |
1.375 |
1.619 |
|
Calcium
silicate . . . . . . . . .
|
— |
— |
0.71 |
0.82 |
0.97 |
1.04 |
|
(CaSiO3) |
|
|
|
|
|
|
|
Carbon
(diamond) . . . . . . . .
|
0.008 |
0.14 |
0.42 |
0.77 |
1.30 |
1.59 |
|
Carbon
(graphite) . . . . . . . . .
|
0.009 |
0.34 |
0.644 |
0.918 |
1.348 |
1.620 |
|
Chalk . . . . . . . . . . . .
|
— |
— |
0.75 |
0.92 |
— |
— |
|
Ebonite . . . . . . . . . . . .
|
— |
— |
(1.38)† |
— |
— |
|
Fluorspar
CaF2 . . . . . . . . .
|
— |
— |
0.83 |
0.93 |
0.99 |
1.07 |
|
Glass
crown . . . . . . . . . .
|
— |
— |
(~ 0.67)‡ |
— |
— |
|
flint . . . . . . . . . . . .
|
— |
— |
(~ 0.5)‡ |
— |
— |
|
Pyrex . . . . . . . . . . .
|
— |
— |
0.70 |
0.85 |
1.1 |
— |
|
Ice . . . . . . . . . . . . .
|
0.686 |
1.372 |
2.097 |
— |
— |
— |
|
India
rubber . . . . . . . . . .
|
— |
— |
1.25 |
1.49 |
— |
— |
|
Magnesia, MgO
. . . . . . . . .
|
0.10 |
0.57 |
0.874 |
1.034 |
1.163 |
1.221 |
|
Porcelain . . . . . . . . . . .
|
— |
— |
— |
(~ 0.75)A§ |
— |
(~ 1.07) B§ |
|
Polymers |
|
|
|
|
|
|
|
Epoxy resin
(cured) . . . . . . .
|
— |
— |
1.11 |
1.52 |
2.11
(473) |
— |
|
Natural rubber |
0.52 |
1.0 |
1.80 |
2.19 |
— |
— |
|
(vulcanised/unvulcanised) . . . . .
|
|
|
|
|
|
|
|
Nylon 6
. . . . . . . . . . .
|
0.48 |
0.91 |
1.31 |
2.10 |
2.75 |
— |
|
PET . . . . . . . . . . . .
|
0.36 |
0.70 |
1.03 |
1.50 |
2.07 |
— |
|
PMMA (Perspex)
. . . . . . . .
|
0.45 |
0.87 |
1.27 |
g |
2.25
(473) |
— |
|
Polycarbonate . . . . . . . . .
|
0.35 |
0.71 |
1.10 |
1.50 |
2.01
(473) |
— |
|
Polyethylene . . . . . . . . .
|
0.54 |
1.06 |
1.55 |
2.45 |
2.73
(473) |
— |
|
Polystyrene . . . . . . . . .
|
0.38 |
0.71 |
1.11 |
g |
2.15
(473) |
— |
|
PTFE (Teflon)
. . . . . . . . .
|
0.30 |
0.65 |
0.97 |
— |
— |
— |
|
PVC (rigid)
. . . . . . . . . .
|
0.36 |
0.62 |
0.88 |
— |
— |
— |
|
Potassium chloride
. . . . . . . .
|
0.44 |
0.63 |
0.68 |
— |
— |
— |
|
Pyroceram . . . . . . . . . . .
|
— |
— |
0.71 |
0.90 |
1.03 |
1.12 |
|
Quartz SiO2
. . . . . . . . . .
|
0.19 |
0.47 |
0.73 |
0.86 |
1.06 |
1.2 |
|
Quartz glass
. . . . . . . . . .
|
— |
— |
0.70 |
0.83 |
1.02 |
1.11 |
|
Silicon . . . . . . . . . . . .
|
0.18 |
0.49 |
0.68 |
0.77 |
0.85 |
0.88 |
|
Silicon Carbide
. . . . . . . . .
|
0.05 |
— |
— |
0.82 |
1.01 |
1.12 |
|
Sodium Chloride
. . . . . . . . .
|
0.48 |
0.77 |
0.84 |
— |
— |
— |
|
Tungsten carbide
. . . . . . . . .
|
0.044 |
0.119 |
0.171 |
0.203 |
0.231 |
0.248 |
|
|
|
|
|
|
|
|
† Mean values 293 K to
373 K.
‡ Mean values 283 K to 323
K.
§ Mean values A 288 K to 473 K,
B 288 K to 1273 K.
g = glass transition region
Values in italics refer to the liquid or rubbery
state
References
C. J. Adkins (1983), Equilibrium Thermodynamics, 3rd edn.,
Cambridge University Press.
J. D. Cox, D. D. Wagman and V. A. Medvedev
(1989), CODATA Key Values for Thermodynamics, Hemisphere, New York.
K. N. Marsh (ed.), (1987), Material for the Realization of Physicochemical
Properties, Blackwell, Oxford.
M. J. Richardson
|
|
