Equation of state for all regimes of a fluid: from gas to liquid

TL;DR

This paper derives a general equation of state for fluids across all regimes, from gas to liquid, using Mayer's cluster expansion, addressing previous non-physical behaviors at condensed states.

Contribution

It introduces a new equation of state based on cluster integrals that works across all fluid regimes, including phase transition regions.

Findings

The equation qualitatively matches fluid behavior from gas to liquid.

Approximate solutions show potential for describing phase transitions.

Limitations due to data on cluster integrals affect accuracy.

Abstract

The study of Mayer's cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE non-physical behavior at condensed states of fluids. In particular, a general equation of state is derived for finite closed systems of interacting particles, where the pressure is expressed directly in terms of the density (or system volume) and temperature-volume dependent reducible cluster integrals. Although its accuracy is now greatly affected by the limited character of the existing data on the reducible cluster integrals and, especially, the absence of any information on their density dependence, a number of simple approximations indicate the qualitative adequacy of this equation in various regimes of a fluid: from gaseous to liquid states (including the transition region).