What is the point of the four different thermodynamic potentials?

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Steinherrjm · Accepted Answer

An an example, imagine that you have an insulated cylinder with a locked piston which is partially filled with liquid H_2OO. Some amount of the liquid will evaporate and form an H_2OO vapor atmosphere which fills the remainder of the container. In equilibrium, how much of the H_2OO will be in the vapor phase?
The principle of maximum entropy states that if we obtain a functional relation

S = S (U, x)

(where x is e.g. the number of moles of H_2OO in the vapor phase), then the equilibrium value for x is obtained by holding U fixed and maximizing S with respect to x.
This principle can be inverted to yield the principle of minimum energy, which states that if we obtain an equation of state

U = U (S, x)

, then the equilibrium value x is obtained by holding S fixed and minimizing U with respect to x.
These approaches turn out to be equivalent, so which one you use depends on which equation of state is more convenient to model.

What is the point of the four different thermodynamic potentials?

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