The amount of electrical work done on a system when
a charge Q flows across a potential difference 
is
(Recall the thermodynamic convention of defining work as being done on a system).
Standard thermodynamic arguments can now be used to determine the relationship between the Gibbs free energy and the electrical work output of a galvanic cell. Recall that the Gibbs free energy is defined to be
At constant pressure and temperature (usual conditions of a chemical reaction),
the change in the Gibbs free energy, 
is
From the first law of thermodynamics
assuming the cell is operated reversibly. Thus,
Again, assuming reversible operation of the cell,
Thus,
where the extra ``rev'' subscript reminds us that this relation is derived
assuming reversible thermodynamic transformations. Note, here, that
indicates a reversible process, rather than
as we derived in Chapter 8. The reason for this difference
is the presence of a new kind of work 
, which was
not present previously. If 
, then 
,
and the reaction occurs spontaneously. For an irreversible process,
Recalling the 
, the Gibbs free energy change can be written as
where the charge Q has been expressed in terms of the number n of
moles of electrons and the Faraday constant. Thus, there is a net output of
work from the cell only if or equivalently, 
.