This is a derivation to obtain an expression for  for an ideal gas.
An ideal gas has the equation of state:  
where
:P = pressure
:V = volume
:n = number of moles
:R = universal gas constant
:T = temperature
The ideal gas equation of state can be arranged to give:
:    or  
The following partial derivatives are obtained from the above equation of state:
The following simple expressions are obtained for thermal expansion coefficient :
and for isothermal compressibility :
One can now calculate  for ideal gases from the previously obtained general formula:
Substituting from the ideal gas equation gives finally:
where n = number of moles of gas in the thermodynamic system under consideration and R = universal gas constant.  On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows:
This result would be consistent if the specific difference were derived directly from the general expression for .