Thermodynamic functions of a perfect gas

We have already had occasion to mention some of the simpler properties of a perfect gas (c/. chap. II, 2-4). Among these was the equation for the difference between the molar heat capacities at constant pressure and constant volume  

Integration of (10.5) from temperature Tq to T gives for the molar internal energy  

Since the specific heat of a gas is readily measured equation (10.7) allows the molar energy to be evaluated, apart from an additive constant. Similarly by integration of (2.17) we find for the enthalpy, 

To obtain the molar entrojpy we integrate (10.4) from an initial state Tq, Vq) to T, v), making use of (10.3). This gives 

The chemical potential of a gas therefore increases logarithmically with the pressure. Comparison of (10.8), (10.10) and (10.11) shows that, for a perfect gas, 

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These equations show that the thermodynamic functions of a perfect gas are determined, apart from additive constants, by the values of the specific heat as a function of temperature. 

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