Heating Due to Electrochemical Reactions
For an electrochemical reaction process one can write the total heat balance as:
•
Heat generated = Total reaction enthalpy – Electrical energy leaving the system
Using Faraday’s law for an electrode reaction, m, at the interface between the electron and ion conducting phase this corresponds to
(3-5)
where ΔHm is the enthalpy change of the reaction, and ΔGm is the Gibbs free energy of the reaction, ΔGm, defined as
where ΔSm is the net entropy change. Equation 3-5 may now be rearranged into
(3-6)
where the first term represents the irreversible activation losses, and the second term is the reversible heat change due to the net change of entropy in the conversion process.
In Equation 3-5 we have used the total overpotential, ηm,tot,(including potential effects from film resistances and similar), defined as
The equilibrium potential is related to ΔGm in the following way:
 
By the relation between the temperature derivative of the equilibrium potential and the entropy:
the local heat source due to the electrochemical conversion process becomes
Alternatively, by defining the thermoneutral voltage of the reaction as
one may also define the heat source as
The total heat source due to the electrochemical reactions, QEC, for an electrode surface is the sum of all individual heat sources of the electrode reactions according to
For a porous electrode joule heating and electrochemical sources are summed up for a total heat source in the domain according to