Enthalpy of a Pure Real Gas

In this section we make use of the virial expansion of the equation of state in the calculation of the molal enthalpy, h(T,p), of a pure real gas at temperature T and pressure p. 

The difference in molal enthalpy between a state at temperature T, and pressure pi and a state at temperature T2 and pressure p2 is given by 

Since the heat capacity at constant pressure is given by 

The virial expansion in powers of the pressure [Eq. (7-15)] can be manipulated to yield 

Equation (7-38) is an expression for the enthalpy of a pure real gas that has been evaluated expUcitly up to terms proportional to p. Evaluation of the enthalpy thus demands information concerning the dependence of the second virial coefficient on temperature and thermal data on the behavior of the heat capacity at constant pressure in the limit of zero pressure. In addition, there is an undetermined constant of integration. We note that the enthalpy of an ideal gas at T and p is given by h T). Thus the zero-pressure limit of the enthalpy of a pure real gas is the same as the enthalpy of a corresponding ideal gas. 

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