Thermodynamic identities and thermodynamic consistency of Equation of States

TL;DR

This paper introduces a systematic method to construct and verify thermodynamically consistent equations of state (EOSs) for pure materials, ensuring they adhere to fundamental thermodynamic identities and constraints.

Contribution

It provides a minimal set of relations to check and enforce thermodynamic consistency in both complete and incomplete EOSs, addressing common issues in classical models.

Findings

Applied approach to classical EOSs for pure materials

Identified hidden properties necessary for thermodynamic consistency

Highlighted risks of inconsistent parameter fitting

Abstract

We present a systematic approach to construct complete equations of state (EOSs), or to ensure thermodynamic consistency of complete and incomplete forms of EOSs using a minimal and sufficient set of relations. We apply the proposed approach to some common classical equations of state for pure materials. In fact, classical equations of state come generally in an incomplete form that hides essencial properties necessary for thermodynamic consistency. If not aware of such constraints one may generalize the EOS, or fit its thermodynamic parameters from emprirical data in an inconsistent way.