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Simobartz

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For example on the book

*Herbert B. Callen - Thermodynamics and an Introduction to Thermostatistics*it is written:

**Helmholtz Potential Minimum Principle.**The equilibrium value of any unconstrained internal parameter in a system in diathermal contact with a heat reservoir minimizes the Helmholtz potential over the manifold of states for which ##T = T^r##.

I tired to figure out an example of this using an ideal gas but I'm not sure i have understood. If i consider a closed system with a pure gas the thermodynamic variables are ##P,V,T##. If i put the system in thermal contact with a reservoir at ##T^r## then at equilibrium ##T=T^r##. But since the degree of freedom of a pure gas are two, then it is impossible to determine ##P## and ##V##. My guess is that if I fix also another external parameter like the volume ##V## then the last degree of freedom, the pressure, will be found by the minimization of the Helmoltz free energy ##(dF/dP)_{T,V}##. In this case the minimization of the thermodynamic potential would give me an equation equivalent to the equation of state and this is weird to me.So, can you please give me an example about a pure gas in which

**Helmholtz Potential Minimum Principle**can be used to determine the equilibrium state?