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## Homework Statement

A system of particles is in equilibrium at temperature T. Each particle may have energy 0, epsilon, or 2 epsilon. Find the entropy of the system.

## Homework Equations

[tex]F=-\tau log(Z)[/tex]

[tex]\sigma=-(\frac{\partial\sigma}{\partial\tau})|_{V}[/tex]

## The Attempt at a Solution

[tex]

Z = 1+exp(\frac{-\epsilon}{\tau})+exp(\frac{-2\epsilon}{\tau})

[/tex]

[tex]F=-\tau log(1+exp(\frac{-\epsilon}{\tau})+exp(\frac{-2\epsilon}{\tau}))[/tex]

[tex]\sigma=-log(1+exp(\frac{-\epsilon}{\tau})+exp(\frac{-2\epsilon}{\tau}))-\tau\frac{[\epsilon\tau^{-2}exp(-\epsilon/\tau)+2\epsilon\tau^{-2}exp(-2\epsilon/\tau)]}{1+exp(\frac{-\epsilon}{\tau})+exp(\frac{-2\epsilon}{\tau})}[/tex]

Hows that look? I'm really rusty with my thermal physics so even though this is not very complicated, I just have no confidence. One thing I was worried about was my partition function. When is the function I used applicable, and when do I need to use

[tex]Z_{N}=\frac{Z^{N}_{1}}{N!}?[/tex]

As I type this I am becoming increasing doubtful that I used the right partition function. Thanks for reading!

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