Gases - Ratios of Specific Heats

Ratio of specific heats for gases in constant pressure and constant volume processes

Internal Energy

For an ideal gas the internal energy - u - is a function of the temperature. The change in internal energy can be expressed as

du = cv dT         (1)


du = change in internal energy

cv = specific heat for the gas in a constant volume process

dT = change in temperature

cv varies with temperature but within a moderate temperature change the specific heat - cv - can be regarded as constant.


For an ideal gas the enthalpy - h - is function of temperature. The change in enthalpy can be expressed as

dh = cp dT         (2)


dh = change in enthalpy

cp= specific heat for the gas in a constant pressure process

cp can within a moderate temperature change be regarded as constant.

The enthalpy in a fluid is defined as:

h = u + p / ρ         (3)


h = enthalpy

u = internal energy

p = absolute pressure

ρ = density

Combining (3) and the Ideal Gas Law gives:

h = u + R T         (4)


R = the individual gas constant

The change in enthalpy can be expressed by differentiating (4):

dh = du + R dT         (5)

Dividing (5) with dT gives:

(dh / dT) - (du / dT) = R         (6)

Modifying (6) with (1) and (2):

cp - cv = R         (7)

The difference cp - cv is constant for an ideal gas.

The Ratio of Specific Heat

The Ratio of Specific Heat can be expressed as:

k = cp / cv         (8)


k = Ratio of Specific Heat

Ratio of Specific Heat for some common gases:

Gas Ratio of Specific Heat
- k -
Acetylene 1.30
Air, Standard 1.40
Ammonia 1.32
Argon 1.66
Benzene 1.12
N-butane 1.18
Iso-butane 1.19
Carbon Dioxide 1.28
Carbon Disulphide 1.21
Carbon Monoxide 1.40
Chlorine 1.33
Ethane 1.18
Ethyl alcohol 1.13
Ethyl chloride 1.19
Ethylene 1.24
Helium 1.66
N-heptane 1.05
Hexane 1.06
Hydrochloric acid 1.41
Hydrogen 1.41
Hydrogen chloride 1.41
Hydrogen sulphide 1.32
Methane 1.32
Methyl alcohol 1.20
Methyl butane 1.08
Methyl chloride 1.20
Natural Gas (Methane) 1.32
Nitric oxide 1.40
Nitrogen 1.40
Nitrous oxide 1.31
N-octane 1.05
Oxygen 1.40
N-pentane 1.08
Iso-pentane 1.08
Propane 1.13
R-11 1.14
R-12 1.14
R-22 1.18
R-114 1.09
R-123 1.10
R-134a 1.20
Steam (water) 1.33
Sulphur dioxide 1.26
Toulene 1.09

Since the Ratio of Specific Heat is dimensionless the value is the same in the SI and the imperial system of units.

Related Topics

  • Fluid Mechanics - The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.

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