Ratios of specific heat for gases in constant pressure and volume processes (Cp &Cv)
For an ideal gas the internal energy (U) is a function of temperature.
The internal energy of a thermodynamic system is the energy contained within it.
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) isothermal 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
Value of Ratio of Specific Heat Of Different Gases :
|Gas||Ratio of Specific Heat
– k –
|Natural Gas (Methane)||1.32|
The Ratio of Specific Heat is dimensionless and the value is the same in the SI and the Imperial system of units.