Gibbs free energy

The Gibbs free energy is the Thermodynamic potential minimized by a system held at constant temperature and pressure. It may be thought of as measuring the work other than pressure-volume work obtainable from a closed thermodynamic system in an isothermal, isobaric process.

Applying ^Quasistatic

whence the equations of state

Proof of minimization

Consider a system whose volume is free in contact with a heat and pressure reservoir. Then

Noting that since the chemical makeup is fixed by the First law of thermodynamics, it follows form the entropy maximum principle that

hence is minimized.

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