The fuel cell electrochemical system is a function of multiple variables such as temperature, voltage, current, pressure, volume, and chemical potential. Currently this system is seen through simple mechanical equations of state (i.e. pressure, volume, temperature) developed for subsets of a more complex system. This provides a simplistic understanding of the electrochemical process and leads to several assumed ideal processes none of which really occur in a fuel cell. In the current research, an equation of state with 3 variables is proposed to arrive at the same relationships but in a more comprehensive way. Here, a superposition method is developed to resolve the limitation of obtaining Maxwell's equations from two variable systems. As a result of the 3 variable equations of state, 4 additional equations of convenience are gained to compliment enthalpy, Gibbs free energy and Helmholtz functions, providing additional relationships of thermodynamics properties such as voltage change with temperature. Also, the additional equations couple entropy to other thermodynamic properties. This leads to additional equations of state that lead to a more comprehensive understanding of the electrochemical processes in PEM fuel cell membranes.