Electromotive Force in Thermodynamics
When multiplied by an amount of charge dZ the emf ℰ yields a thermodynamic work term ℰdZ that is used in the formalism for the change in Gibbs free energy when charge is passed in a battery:
where G is the Gibb's free energy, S is the entropy, V is the system volume, P is its pressure and T is its absolute temperature.
The combination ( ℰ, Z ) is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature T (a measurable quantity) to the change in entropy S when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is:
If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is:
where n0 is the number of electrons/ion, and F0 is the Faraday constant and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:
where ΔH is the heat of reaction. The quantities on the right all are directly measurable.
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