Under what conditions is the Helmholtz free energy F a minimum for a system in equilibrium?

Under what conditions is the Helmholtz free energy F a minimum for a system in equilibrium? The work corresponding to an increase in the surface area of a liquid is dW = Γ dA, where Γ is the surface tension, and A is the area of the surface. Consider a bubble of air in a large container of liquid in equilibrium. Write the total Helmholtz free energy of the system as the sum of contributions from the air in the bubble, Fa, the surface of the bubble, Fs, and the surrounding liquid, Fl. Show that the pressure of the air inside the bubble is equal to pl + 2Γ /r, where pl is the pressure of the liquid.

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