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The term free energy is used to denote two related concepts that are 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:
If E represents the energy, T the temperature, and S the entropy, these two tendencies can be combined by stating that the expression
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
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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