Free energy

The term free energy denotes either of two related concepts of importance in
thermodynamics. Both attempt to capture that part of the total energy of a
system which is available for "useful work" and is hence not stored in
"useless random thermal motion". As a system undergoes changes, its free
energy will decrease.

When a system of molecules undergoes change, whether chemical reaction or
changes in physical states such as phase changes, there are two tendencies
driving the changes:

   * Free Energy tends to decrease,
   * Entropy tends to increase.

If E represents the energy, T the temperature, and S the entropy, these two
tendencies can be combined by stating that the expression

                       E - TS, the Helmholtz function

tends to decrease. Strictly, this is only true in situations where the
volume is constant, as in sealed containers. If the pressure is constant, as
in open containers, the enthalpy H = E + PV (where P represents the pressure
and V represents the volume) replaces the energy, and thus the quantity that
must be minimized is

                  H - TS = E + PV - TS, the Gibbs function.

Physicists have tended to use the term free energy and the symbol F for the
Helmholtz function, using G to represent the Gibbs function; chemists have
preferred to denote the Helmholtz function by A [from the German word
Arbeit(=work)] and call it the work content, reserving the term free energy
and the symbol F for the Gibbs function. Recently a compromise notation has
become common, using A for the Helmholtz function, G for the Gibbs function,
and avoiding F entirely. The functions are then referred to as the Helmholtz
free energy and Gibbs free energy.

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