Guggenheims smoothed potential model

This model [GUG32] is extrapolated from the imperfect gas model, which can be used to calculate the second coefficient of the virial (see section A.3.4 in Appendix 3). The canonical partition function then takes the form of equation [A.3.41]. 

From this, we deduce the configuration integral due to the interactions and to the volmne, in this case the volume of slightly imperfect gases  

Using the notation to represent the volume per molecule (V/N), or the molecular volume (which must not be confused with the volume of a molecule), and using Stirling s approximation [A.3.1], this expression takes the following equivalent form  

According to relation [A.3.40], the term Baa is a function only of the temperature. 

We can use such an expression for a highly-imperfect gas or a liquid, supposing that the term Baa is also a function of the volume. The difference Vm-BAA(T,Vm) will therefore represent the free volume per molecule v/and the above relation will then be written  

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The model of the liquid chosen is Guggenheim s smoothed potential... 

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