Thermodynamics of a Perfect Gas

Thermodynamics of a Perfect Gas.—By definition, a perfect gas in the Boltzmann statistics is one whose equation of state is 

This is a reversal of the argument of Chap. II, Sec. 6, where we used Joule s law as an experimental fact to prove that the gas scale of temperature was identical with the thermodynamic temperature. Here instead we assume the temperature T in Eq. (1.1) to be the thermodynamic temperature, and then Joule s law follows as a thermodynamic consequence of the equation of state. 

No assumption is made thermodynamically about the specific heat of a perfect gas. Some results concerning it follow from thermodynamics and the equation of state, however. We have already seen that 

But from the Table of Thermodynamic Relations in Chap. II we have 

Thermodynamics can state nothing regarding the variation of specific heat with temperature. It actually happens, however, that the heat capacities of all gases approach the values that we have found theoretically for monatomic gases in Eq. (3.18), Chap. IV, namely, 

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