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## Homework Statement

The problem is simple: two compartments, allowed to exchange heat with environment (canonical ensemble) are allowed to mix. Show change in U,P and S.

## Homework Equations

[tex]Z_{total} = \frac{1}{N!} Z_{1}^{N} [/tex]

[tex]Z_{1} = e^{-\beta E_{j}}[/tex]

## The Attempt at a Solution

I know how to derive all the required thermodynamic quantities from the partition theorem. I am however stuck at assigning a particular energy to the state my system is in. I am inclined to simply use the equipartition theorem and say [tex]E_{j} = \frac{3}{2} k T[/tex]. Somehow I feel that is way too simple, since that means my partition function reduces to [tex] Z_{total} = \frac{1}{N!} e^{-\frac{3}{2}}[/tex].

Am I right in doing this, or how should I proceed?