# Using Three Variable State Equations to Gain Insight into PEM Fuel Cell Membrane Thermodynamics

## TL;DR

This paper proposes using three-variable state equations to better understand the thermodynamics of PEM fuel cells.

## Contribution

The novelty lies in introducing three-variable equations of state to derive new thermodynamic relationships for PEM fuel cells.

## Key findings

- Three-variable equations of state yield four additional equations of convenience.
- These equations combine mechanical and electrical quantities for better thermodynamic modeling.
- The approach offers a more comprehensive understanding of PEM fuel cell thermodynamics.

## Abstract

A PEM fuel cell is
an electrochemical system dependent on multiple
variables such as temperature, voltage, current, pressure, volume,
and chemical potential. Thermodynamically, parts of this system are
seen through simpler mechanical equations of state developed for subsets
of the more complex system (a simple compressible substance, for instance),
providing a piecewise understanding of the whole. In this research,
a method using equations of state with three variables is proposed
to arrive at the thermodynamic relationships in a more comprehensive
way. As a result of three-variable equations of state, four additional
equations of convenience are gained to complement enthalpy, Gibbs,
and Helmholtz functions, providing additional relationships that contain
a mix of mechanical and electrical physical quantities. The proposed
approach is a more comprehensive path of gaining insight into a closer
thermodynamic representation of a functioning fuel cell to in turn
improve the understanding and modeling of this important electrochemical
system.