# Partition function, particular energy for microstate

## 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

$$Z_{total} = \frac{1}{N!} Z_{1}^{N}$$
$$Z_{1} = e^{-\beta E_{j}}$$

## 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 $$E_{j} = \frac{3}{2} k T$$. Somehow I feel that is way too simple, since that means my partition function reduces to $$Z_{total} = \frac{1}{N!} e^{-\frac{3}{2}}$$.

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