Virial Coefficients in Terms of Interaction Potential Energies: Mayer’s Theory

Abstract

It is proved that the experimental coefficients of the virial expansion are related to some parameters coming from the theory of statistical thermodynamics. This is a very important point since it permits to link theoretical results (coming from statistical thermodynamics) with experimental ones. Above all, it permits to attribute a physical origin to each virial coefficient, that is to say to attribute interactions between well-known numbers of particles to every coefficient of the virial expansion. The theory, mentioned in this chapter, leads to mathematical expressions relating parameters stemming from the statistical theory to purely thermodynamic quantities and inversely. The demonstration is done within the framework of the great ensemble. It is based on some series developments. Intervene in it some parameters such the absolute activity λ of the compound, canonical partition functions, configuration integrals, and also, of course, the virial coefficients B(n). The expression of the latter involve an integral, which is also introduced from another starting viewpoint, i.e., within the framework of the Kirkwood–Buff’s theory, which has a different nature than that studied in this chapter and which will be considered later.