# Enthelpy of Reaction and Efficiency of Galvanic Cells

Dario56
TL;DR Summary
Why is Enthalpy of Reaction Used as Energy Input in Galvanic Cells When Defining its Efficiency?
For electrochemical energy devices such as batteries or fuel cells working reversibly, efficiency is defined as:

η=ΔrG⦵/ΔrH⦵

Since cell operates reversibly Gibbs energy change of the system is equal to electrical work done by the cell, so we can instead just use standard Gibbs energy of reaction as energy output. What I am not clear about is why is enthalpy of reaction used as energy input? Since electrochemical energy devices transform chemical energy of electroactive materials to electrical energy, energy input should be chemical energy, but I am not sure why enthalpy of reaction represents chemical energy? Enthalpy of reaction is given by this equation:

ΔrH⦵=ΔrG⦵+TΔrS⦵

Since cell operates reversibly, ΔrG⦵ represents reversible electrical work (maximum non-PV work done by the cell) and TΔrS⦵represents heat exchanged with surroundings to keep cell at constant T in reversible operation since change in Gibbs energy as measure of non-PV work is only applicable for closed systems at constant p and T.

Mentor
Summary:: Why is Enthalpy of Reaction Used as Energy Input in Galvanic Cells When Defining its Efficiency?

For electrochemical energy devices such as batteries or fuel cells working reversibly, efficiency is defined as:

η=ΔrG⦵/ΔrH⦵

Since cell operates reversibly Gibbs energy change of the system is equal to electrical work done by the cell, so we can instead just use standard Gibbs energy of reaction as energy output. What I am not clear about is why is enthalpy of reaction used as energy input? Since electrochemical energy devices transform chemical energy of electroactive materials to electrical energy, energy input should be chemical energy, but I am not sure why enthalpy of reaction represents chemical energy? Enthalpy of reaction is given by this equation:

ΔrH⦵=ΔrG⦵+TΔrS⦵

Since cell operates reversibly, ΔrG⦵ represents reversible electrical work (maximum non-PV work done by the cell) and TΔrS⦵represents heat exchanged with surroundings to keep cell at constant T in reversible operation since change in Gibbs energy as measure of non-PV work is only applicable for closed systems at constant p and T.
Can you please provide a reference for that efficiency equation?

Dario56
Can you please provide a reference for that efficiency equation?
This equation isn't correct, my mistake. It should be ratio of Gibbs energy change of system divided by enthalpy change of system for reversible cell. There should be no standard reaction Gibbs energy in equation.
Can you please provide a reference for that efficiency equation?
Basically, I am not sure why is enthalpy change of system taken as energy input since I don't know what is physical interpretation of enthalpy change in electrochemical cell. When there is no non-PV work, it is equal to heat exchanged with surroundings at constant p and T. But, in electrochemicall cells we have electrical work, so interpretation of enthalpy change of system isn't as straightforward, so I am not sure why is it taken as energy input?