1983), the Helmholtz free energy is the thermodynamic potential of the system; however, in systems for which the pressure of one phase is controlled, such as in the case of bubble nucleation in a constant-pressure liquid, the appropriate free energy that acts as the thermodynamic potential for the multi-phase system must be determined (Ward and Levart, 1984).

The Helmholtz free energy [psi] is defined as [psi] = U - T[eta] (1) where U is the internal energy, T is the temperature, and [eta] is the entropy.

Assuming that the process is isothermal, gas in the bubble is ideal, and volume and temperature change of the system is negligible, Helmholtz free energy change, [Delta]F, is given as [Delta]F = [n.