Potential of Pure Real Gases

In this section we derive an expression for the chemical potential of a pure real gas at temperature Tand pressure p. The difference in chemical potentials between states characterized by temperature Ti and pressure Pi and by temperature and pressure pi can be written in the form 

We wish to obtain an expression for p T,p) in terms of a properly selected zero-pressure quantity. In order to do this we must investigate the behavior of (dpldpjf in the zero-pressure limit. The zero-pressure quantities here, as well as in the preceding sections, are independent of the forces between the gas molecules. In particular, they can be computed from molecular considerations of ideal-gas systems they may vary from gas to gas since they do depend upon the internal degrees of freedom of the molecules. 

It is clear that Eq. (7-131) diverges in the zero-pressure limit. In order to obtain a convergent quantity, we subtract RTjp from both sides of Eq. (7-131). Since 

Integration of Eq. (7-133) along a constant-temperature path yields 

As in the expression for the free energy of a pure gas, we make a purely notational change and write 

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