**Helmholtz free energy (work function) and its significance**

In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature and volume.

**(a) Helmholtz free energy and maximum work**

Like Gibbs free energy the Helmholtz free energy A is a state function. For change in A,

∆A = ∆U – T∆S

If we consider an isothermal change at T, it can be shown, as in the case of Gibbs energy, by combining the first and second law of thermodynamics that,

– ∆A = W_{max}

Thus the decrease in Helmholtz Free Energy is equal to the maximum work done by the system in an isothermal process at constant volume. The Helmholtz free energy function is called a ‘work function’, because of the relationship between A and w.

**(b) Helmholtz free energy, spontaneity and equilibrium**

For constant volume processes the relations of ∆A to spontaneity and equilibrium may be summarized as follows:

∆A < 0 (negative); the process is spontaneous

∆A > 0 (positive); the process is non-spontaneous

∆A = 0; the system is at equilibrium.