Heat capacity of a gas in a constant pressure process - to heat capacity in a constant volume process
For an ideal gas the internal energy - u - is a function of temperature and the change in internal energy can be expressed as
du = cv dT (1)
du = change in internal energy
dT = change in temperature
cv varies with temperature, but within a moderate temperature change the heat capacity - cv - can be regarded as constant.
For an ideal gas the enthalpy - h - is function of temperature and the change in enthalpy can be expressed as
dh = cp dT (2)
dh = change in enthalpy
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
ρ = density
Combining (3) and the Ideal Gas Law gives:
h = u + R T (4)
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 Heats
The Ratio of Specific Heats can be expressed as:
k = cp / cv (8)
k = the ratio of specific heats
Ratio of Specific Heats for some common gases:
|Gas||Ratio of Specific Heats|
|Natural Gas (Methane)||1.32|
Since the ratio is dimensionless the value is the same in the SI and the imperial system of units.