Confused by some aspects of thermodynamics

AI Thread Summary
In thermodynamics, when discussing equilibrium conditions with constraints of temperature, volume, and particle number, it implies that these variables are fixed for the subsystem, excluding the reservoir. The free energy must decrease at non-equilibrium under these fixed conditions, highlighting the importance of temperature, volume, and particle number as "natural" arguments for free energy. If the partition function Z is known, it allows for the calculation of free energy, which can then be used to derive other thermodynamic properties such as pressure, entropy, and various potentials through established thermodynamic identities. Understanding these relationships is crucial for analyzing thermodynamic systems effectively. Mastery of these concepts is essential for navigating the complexities of thermodynamics.
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I am quite confused by some aspects of thermodynamics. First of all, I just wonder, when the textbook says that "when the constraints are temperature, volume and particle number, minimise F for equilibrium" (and similar statements for G and H), does it mean that the temperature, volume and particle number of the sub-system (i.e. excluding the reservoir) is fixed?

And also, if Z, the partition function, is given, how should I proceed to find the equation of state?

Thank you. :-p
 
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Because
dF \leq -SdT -PdV + \mu dN
then at fixed volume , temperature, and particle number, the free energy can only decrease, if we are at non-equilibrium. Thus temperature, volume, and particle number called "natural" arguments for the free energy.

If you know a partition function, you can calculate free energy. After that you can find pressure, enthropy, and thermodynamic potential using the thermodynamic identities
 

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