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Gases - Ratios of Specific Heat

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Internal Energy

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

du =cv dT                            (1)


du = change in internal energy (kJ/kg)

cv = specific heat for gas in a constant volume process (kJ/kgK)

dT = change in temperature (K)

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


For an ideal gas the enthalpy - h - is a function of temperature. Change of enthalpy can be expressed as

dh = cp dT                         (2)


dh = change in enthalpy (kJ/kg)

cp= specific heat for gas in a constant pressure process (kJ/kgK

Specific heat cp can within moderate temperature changes be regarded as constant.

The enthalpy in a fluid is defined as:

h = u + p / ρ                           (3)    


h = enthalpy  (kJ/kg)

u = internal energy    (kJ/kg)

p = absolute pressure (Pa)

ρ = density (kg/m3)

Combining (3) and the Ideal Gas Law:

h = u + R T                         (4)


R = the individual gas constant (kJ/kgK)

Change in enthalpy can be expressed by differentiating (4):

dh = du + R dT                      (5)

Dividing (5) with dT:

(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.


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 gases:

Gases - Ratios of Specific Heat
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
Toluene 1.09

The Ratio of Specific Heat is dimensionless and the value is the same in the SI and the Imperial system of units.

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