Thermodynamics of the low density excluded volume hadron gas

TL;DR

This paper develops a general and simplified thermodynamic framework for low-density excluded volume hadron gases, accounting for particle size and shape variations, and discusses its applicability to hard sphere models.

Contribution

It introduces a general method to derive thermodynamic functions for multi-component excluded volume gases without transcendental equations, applicable to particles with variable sizes and shapes.

Findings

Derived thermodynamic functions using Maxwell identities

Applicable to multi-component gases with different particle sizes

Discussed validity limits for hard sphere models

Abstract

We consider thermodynamics of the excluded volume particles at finite temperature and chemical potential, in the low density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas thermodynamics at the same temperature, pressure and numbers of particles. We show, that considering the change of the free enthalpy due to the excluded volume, and using the Maxwell identities, one can derive relevant thermodynamic functions and parameters of multi-component gases. The derivation is quite general as particles may have different sizes and shapes which can also depend on their momenta. Besides it's simplicity and generality, our approach has the advantage of eliminating the transcendental equations occurring in earlier studies. A representative example of the excluded volume thermodynamics is the single-component gas of hard spheres. For this case, using the viral expansion, the validity limits of the low-density approximation are also discussed.