The efficiency of a fuel cell is defined as the ratio of the useful electrical work obtained to the total energy released by the combustion of the fuel. The maximum useful work a system can do is given by the change in its Gibbs free energy ($\Delta G$), while the total heat energy available from the reaction is given by its enthalpy change ($\Delta H$). Therefore, the thermodynamic efficiency of a fuel cell ($\eta$) is mathematically expressed as $\frac{\Delta G}{\Delta H}$.