Thermodynamic potential

Helmholtz free energy

The Helmholtz free energy is the Thermodynamic potential minimized by a system held at constant temperature and volume. It may be thought of as measuring the useful work obtainable from a closed thermodynamic system in an isothermal process.

Applying ^Quasistatic

whence the equations of state

Proof of minimization

Consider a system of constant volume in thermal contact with a heat reservoir. Then

Noting that since the volume and chemical makeup are fixed by the First law of thermodynamics, it follows from the entropy maximum principle that

hence is minimized.

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