Gases - Ratios of Specific Heat

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 =c_v dT                            (1)

where

du = change in internal energy (kJ/kg)

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

dT = change in temperature (K)

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

• Specific Heat of Gases

Enthalpy

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

dh = c_p dT                         (2)

where

dh = change in enthalpy (kJ/kg)

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

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

• more about gases and specific heats

The enthalpy in a fluid is defined as:

h = u + p / ρ                           (3)    

where

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)

where

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):

c_p - c_v = R                                 (7)

The difference c_p - c_v is constant for an ideal gas.

Ratio of Specific Heat

The Ratio of Specific Heat can be expressed as:

k = c_p / c_v                                  (8)

where

k = Ratio of Specific Heat

Ratio of Specific Heat for some gases:

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