Consider a cell which operates revesibly at constant temperature and pressure. The electrical work done by the system per mole of reactant consumed (i.e electrical energy supplied by the cell) is nFE, where n is the number of electrons liberated at one electrode or valency of the metal, F is Faraday (i.e. 96500 coulombs) and E is the emf of the cell. At the same time free energy of the system decreases by an amount $∆$G Therefore
$-\mathrm{\Delta G}=\mathrm{nFE}$
$\text{ Also }\mathrm{\Delta G}=\mathrm{\Delta H}+\mathrm{T}{\left(\frac{\mathrm{\partial }\left(\mathrm{\Delta G}\right)}{\mathrm{\partial }\mathrm{T}}\right)}_{\mathrm{P}}\dots \text{ (Gibbs-Helmholtz equation.) }$
From the above two equations, we see
$\mathrm{nFE}=-\mathrm{\Delta H}+\mathrm{nFT}{\left(\frac{\mathrm{\partial }\mathrm{E}}{\mathrm{\partial }\mathrm{T}}\right)}_{\mathrm{P}}$
This equation gives heat of chemical reaction occurring within the cell as a function of EMF and temperature.
${\left(\frac{\mathrm{\partial }\mathrm{E}}{\mathrm{\partial }\mathrm{T}}\right)}_{\mathrm{P}}$ is known as temperature coefficient of the cell.