Thermodynamic length in a 2-D thermodynamic state space

TL;DR

This paper derives explicit formulas for thermodynamic length in a two-dimensional state space, exploring its relation to work, sound speed, and metric determinants, providing new insights into thermodynamic geometry.

Contribution

It offers an explicit formulation of thermodynamic length in 2D state space and analyzes its relation with work, sound speed, and metric determinants.

Findings

Explicit thermodynamic length formulas along isotherms

Relation between thermodynamic length and work

Difference in determinants of energy and entropy metrics by a factor of T^4

Abstract

The main goal of this paper is to reach an explicit formulation and possible interpretation of thermodynamic length in a thermodynamic state space with two degrees of freedom. Using the energy and entropy metric in a general form, we get explicit results about thermodynamic length along isotherms, its relation with work and with speed of sound. We also look at the relation between the determinants of the energy and entropy metrics and find that they differ by a factor of $T^{4}$.