Generalized Bernoulli Construction—A Heuristic Approach to the Equation of State

The equation of state (ES) is a subject of the greatest interest in Statistical Mechanics and Chemical Physics. In this paper we present a simple and rigorous method by which the ES of simple systems can be obtained. The derivation requires at most the knowledge of the Maxwell distribution. The well known formula for the ES of a one-dimensional system of hard rods is derived exactly, as an illustration. The method can be generalized to higher dimensionality and to include other types of potential.