The virial expansion re-visited: A new interpretation

as an empirical formula expressing P in a power series of particle density ρ = N/V , where N is the number of particles. A first-principle understanding of the virial expansion was provided years later by the advent of the Mayer cluster expansion in statistical mechanics in the 1930s. However, following Onnes the virial expansion has since been generally regarded as an expansion in density. Here we re-visit the virial expansion using the Mayer expansion, and show that the virial expansion should be considered as an expansion in specific volume, the ratio of the effective volume of a gas molecule and its allotted mean volume. This consideration is illustrated in the case of the hard sphere gas.