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Helmholtz free energy problem

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The Helmholtz free energy is given by

F = U - TS

(a) What is the natural (independent) variables of the Helmholtz free energy F?
(b) Show that the differential of the Helmholtz free energy F is a function of its natural variable only.
(c) Show that for fixed mole numbers, fixed temperature and fixed volume, the Helmholtz free energy F of a system will evolve to a minimum.

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