# A universal equation-of-state model based on single variable functions

## TL;DR

This paper introduces a simple and universal equation of state model that captures thermodynamic properties without relying on material-specific assumptions.

## Contribution

A new universal equation-of-state model is proposed using single-variable thermodynamic functions with physically meaningful coefficients.

## Key findings

- The model derives two simple equations of state (P–V–T and P–S–T) similar in form to the ideal gas law.
- Coefficients in the model have clear thermodynamic significance and can be calculated directly without fitting.
- The model performs well in characterizing thermodynamic properties and is applicable to high-density and supercritical conditions.

## Abstract

Since the ideal gas equation of state (EOS) was established in 1840, a wide variety of EOS theories have been developed. However, due to the diversity of material structures and the complexity of intermolecular interactions, numerous EOS either have complex forms or have empirical coefficients without physical meaning, which severely limits their applications. This paper builds a simple and universal EOS model by means of a fully macroscopic thermodynamic approach. Firstly, two single variable thermodynamic functions as a function of pressure only and as a function of temperature only, respectively, are constructed. On this basis, two EOS in the forms of P–V–T and P–S–T are obtained by thermodynamic derivation, which are almost as simple as the ideal gas EOS. There are no assumptions about material structures and intermolecular interactions involved here. Therefore, the model is universal. Moreover, the coefficients in these two EOS have clear thermodynamic significance and thus can be calculated directly without fitting. The model is shown to characterize the thermodynamic properties of substances well and may play an important role in high-density and supercritical applications. This work may provide a new way of developing EOS theory and enrich the fundamentals of thermodynamics.