On the generalized Bernoulli construction. II. Extension to two and three dimensions

The generalized Bernoulli construction is used to study the equation of state of rigid particles in two and three dimensions. A system of hard squares is considered in detail, and results for hard cubes, disks, and spheres are also presented. The discussion permits the introduction of the mean‐free‐path problem in the equation of state, and the result of the virial theorem of Clausius is obtained for these systems. This heuristic method can be used to discuss the equation of state at low and high densities without the use of formal theories.