(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

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

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Entropy of N particle system

**Physics Forums | Science Articles, Homework Help, Discussion**