The Helmholtz free energy is defined by
where E is the energy, T is the temperature, and S is the entropy. When a system changes its thermodynamic state, the change in Helmholtz free energy is therefore given by
If T and V are constant, the (2) reduces to
But the combined law of thermodynamics states that
and, since we have stipulated dV = 0, this becomes
Therefore
The Helmholtz free energy is intimately related to the equilibrium constant at constant volume via
where k is Boltzmann's constant.
A system with fixed external parameters in thermal contact with a heat reservoir at equilibrium has a minimum
Helmholtz free energy, commonly denoted
Free Energy, Gibbs Free Energy, Heat Reservoir
