Synonym: Heat Capacity Ratio (γ) = Adiabatic Index (γ) = Isentropic expansion factor (κ) = Isentropic exponent (κ)
Ratio between Isobaric heat capacity
C_P and Isochoric heat capacity
C_V:
(1) | \gamma = \frac{C_P}{C_V} |
Since (1) is the ratio it can be equivalently represented by intensive properties:
(2) | \gamma = \frac{c_P}{c_V} = \frac{c_{Pm}}{c_{Vm}}= \frac{c_{Pv}}{c_{Vv}} |
where
c_P | c_{Pm} | Isobaric specific heat capacity | c_{Pv} | Isobaric volumetric heat capacity | |
c_V | Isochoric molar heat capacity | c_{Vm} | Isochoric specific heat capacity | c_{Vv} | Isochoric volumetric heat capacity |
The Heat Capacity Ratio can be equivalently represented as ratio of Isothermal Compressibility \beta_T and Isentropic Compressibility \beta_S:
(3) | \gamma=\frac{c_P}{c_V}=\frac{\beta_T}{\beta_S}= \kappa |
wich is often denoted as \kappa and referred as Isentropic exponent.
The Heat Capacity Ratio for ideal gases is:
(4) | \gamma = 1 + \frac{2}{f} |
where
f | number of molecular freedom degrees |
Heat capacity ratio for various fluids [1]:
Temp | Fluid | γ | Temp | Fluid | γ | Temp | Fluid | γ | ||
---|---|---|---|---|---|---|---|---|---|---|
−181 °C | H2 | 1.597 | 200 °C | Dry air | 1.398 | 20 °C | NO | 1.400 | ||
−76 °C | 1.453 | 400 °C | 1.393 | 20 °C | N2O | 1.310 | ||||
20 °C | 1.410 | 1000 °C | 1.365 | −181 °C | N2 | 1.470 | ||||
100 °C | 1.404 | 15 °C | 1.404 | |||||||
400 °C | 1.387 | 0 °C | CO2 | 1.310 | 20 °C | Cl2 | 1.340 | |||
1000 °C | 1.358 | 20 °C | 1.300 | −115 °C | CH4 | 1.410 | ||||
2000 °C | 1.318 | 100 °C | 1.281 | −74 °C | 1.350 | |||||
20 °C | He | 1.660 | 400 °C | 1.235 | 20 °C | 1.320 | ||||
20 °C | H2O | 1.330 | 1000 °C | 1.195 | 15 °C | NH3 | 1.310 | |||
100 °C | 1.324 | 20 °C | CO | 1.400 | 19 °C | Ne | 1.640 | |||
200 °C | 1.310 | −181 °C | O2 | 1.450 | 19 °C | Xe | 1.660 | |||
−180 °C | Ar | 1.760 | −76 °C | 1.415 | 19 °C | Kr | 1.680 | |||
20 °C | 1.670 | 20 °C | 1.400 | 15 °C | SO2 | 1.290 | ||||
0 °C | Dry air | 1.403 | 100 °C | 1.399 | 360 °C | Hg | 1.670 | |||
20 °C | 1.400 | 200 °C | 1.397 | 15 °C | C2H6 | 1.220 | ||||
100 °C | 1.401 | 400 °C | 1.394 | 16 °C | C3H8 | 1.130 |
In express analysis of petroleum fluids (including liquid water and vapour) the Heat Capacity Ratio can be assumed
\gamma \sim 1.3.
See also
Physics / Thermodynamics / Thermodynamic process
[ Mayer's relation ]
References
White, Frank M. (October 1998). Fluid Mechanics (4th ed.). New York: McGraw Hill. ISBN 978-0-07-228192-7.