ABSTRACT
Mayer’s theory of imperfect gases constitutes perhaps the first fully microscopic statistical mechanical analysis of interacting many body systems, in the sense that the theory starts with a given intermolecular potential and attempts to evaluate the partition function from first principles. In this theory Joseph Mayer introduced what later became well known as graph theory for liquids and gases. Among many successes, the most prominent one is the derivation of Virial expansion of pressure in terms of density. The theory provides molecular expressions of the Virial coefficients in terms of intermolecular potential. It also introduces the concept and language of cluster size distribution. It offers a quantifiable microscopic picture of gas-liquid condensation. More recently, it was shown that Mayer’s partition function belongs to a generalized class of polynomials, known as Bell polynomials. This mapping allows numerical evaluation of a Mayer partition function by using a set of recursion relations. Despite several limitations Mayer’s theory still remains as a cornerstone of equilibrium Statistical Mechanics.
