Derivation of Van der Waal's equation of state in microcanonical ensemble formulation

TL;DR

This paper derives Van der Waal's equation of state for a non-ideal classical gas using a microcanonical ensemble approach with a hard sphere potential, offering an alternative to the traditional canonical ensemble derivation.

Contribution

It presents a novel derivation of Van der Waal's equation in the microcanonical ensemble, expanding the theoretical framework for non-ideal gases.

Findings

Derivation of Van der Waal's equation in microcanonical ensemble

Use of hard sphere potential without short-range interactions

Provides an alternative theoretical approach

Abstract

The Van der Waal's equation of state for a (slightly) non-ideal classical gas is usually derived in the context of classical statistical mechanics by using the canonical ensemble. We use the hard sphere potential with no short range interaction and derive Van der Waal's equation of state in microcanonical ensemble formulation.