Calculation of Virial Coefficients. Squares and Cubes with Attractive Forces

A general combinatorial formulation of the star integrals occurring in calculations of virial coefficients is presented. The usefulness of the formulation is demonstrated by the exact calculation of the first five virial coefficients for gases of hard parallel squares and cubes with attractive forces. For these gases the three-, four-, and five-term virial series are examined, and each series is found to have a critical point. Most of the critical properties of these truncated virial series are sensitive to the number of terms included, but the product PcVc remains nearly constant as more terms are added. It is shown that any two- or three-dimensional square-well virial coefficient is negative at low temperature. Despite this, the low-temperature contribution of the complete star integral can be either positive or negative.