On the Helmholtz Potential metric: The Isotherm Length-Work Theorem

TL;DR

This paper introduces the Isotherm Length-Work theorem using the Helmholtz potential metric and virial expansion, providing explicit solutions for thermodynamic length along isotherms up to third order.

Contribution

It presents a novel theorem linking thermodynamic length to virial expansion and provides explicit solutions for different orders of expansion.

Findings

Explicit solutions for thermodynamic length up to third order

Theoretical framework connecting Helmholtz potential metric and virial expansion

Insight into thermodynamic system behavior along isotherms

Abstract

In this paper we introduce the Isotherm Length-Work theorem using the Helmholtz potential metric and the virial expansion of pressure in inverse power of molar volume. The theorem tells us what length of a thermodynamical system described by equation of state through virial expansion along isotherms actually is with such a metric. We also give explicit solutions for thermodynamic length along isotherms in the case of first, second and third order expansion.