Free energy

In thermodynamics, free energy is a measure of the amount of work that can be extracted from a system. In this sense, it measures not the energy content of the system, but the "useful energy" content.

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In different situations, free energy is related to internal energy in different ways. If one is measuring the internal energy of a system at constant pressure and constant temperature, Gibbs free energy is the most useful (hence its utility to solution-phase chemists). Otherwise, Helmholtz free energy is useful, since it is related to the partition function of a canonical ensemble in statistical mechanics (hence its utility to gas-phase chemists, and physicists).

Related Topics:
Internal energy - Gibbs free energy - Helmholtz free energy - Partition function - Canonical ensemble - Statistical mechanics

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Helmholtz free energy is A = U - TS, where U is the internal energy, T is the temperature, and S is the entropy.

Related Topics:
Helmholtz free energy - Entropy

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Gibbs free energy is G = H - TS, where H is the enthalpy, T is the temperature, and S is the entropy. This takes into account work to "make space for molecules" (as H is U + PV, where P is pressure and V is volume).

Related Topics:
Gibbs free energy - Enthalpy

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The historical notation in physics and chemistry is confusing and as follows:

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• In physics, free energy by default refers to Helmholtz free energy, and is notated F.
• In chemistry, free energy by default refers to Gibbs free energy, and is also notated F.

However, both fields do often require use of the 'other' free energy. Recently a compromise notation has become common, using A for the Helmholtz function, G for the Gibbs function, and avoiding F entirely.

Related Topics:
Compromise - Helmholtz function - Gibbs function

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