Evaluation of Virial Coefficients

Virial coefficients can be evaluated through Statistical Mechanics, using expressions for the intermolecular potential that are not, unfortunately, available in the typical case. Virial coefficients are available, therefore, in practice from two sources  

Determination of virial coefficients from PVT data is discussed in Example 8.4, which should be of interest to Graduate Students only. It demonstrates, however, that the reliability of their values fails considerably beyond the second one. This is why experimental values for third virial coefficients are scarce, and practically non-existing for higher ones. 

As a result, the virial equation is typically used truncated after the second term. We will concentrate, therefore, our attention on the second coefficient only. 

For a qualitative understanding of this temperature effect, we solve the volume series, Eq.8.9.1, truncated after B, for the pressure  

Notice that the first term represents the ideal gas pressure, i.e. the pressure in the absence of interraolecular forces, at the same temperature T and volume V as those of the real gas. 

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