In short, free energy is that portion
of any First-Law energy that is available for doing thermodynamic
work; i.e., work mediated by thermal energy. Since free
energy is subject to irreversible loss in the course of
such work and First-Law energy is always conserved, it
is evident that free energy is an expendable, Second-Law
kind of energy that can make things happen within finite
amounts of time.
In solution chemistry and biochemistry,
the Gibbs free energy change (denoted by ?G) is commonly
used merely as a surrogate for (-T times) the entropy
produced by spontaneous chemical reactions in situations
where there is no work done; or at least no "useful"
work; i.e., other than PdV. As such, it serves as a particularization
of the second law of thermodynamics, giving it the physical
dimensions of energy, even though the inherent meaning
in terms of entropy would be more to the point.
The free energy functions are Legendre
transforms of the internal energy. For processes involving
a system at constant pressure P and temperature T, the
Gibbs free energy is the most useful because, in addition
to subsuming any entropy change due merely to heat flux,
it does the same for the PdV work needed to "make
space for additional molecules" produced by various
processes. (Hence its utility to solution-phase chemists,
including biochemists.) The Helmholtz free energy has
a special theoretical importance since it is proportional
to the logarithm of the partition function for the canonical
ensemble in statistical mechanics.
