Helmholtz energy function

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Hermann Ludwig Ferdinand von Helmholtz Definition of A (for arbeit):

where U is the internal energy, T is the temperature and S is the entropy. (TS) is a conjugate pair. The differential of this function is

From the Second law of thermodynamics one obtains

thus one arrives at

leading finally to


For A(T,V) one has the following total differential

Good for use in the Canonical ensemble.