# Find the heat capacity of the system

1. Jun 25, 2009

### senan

1. The problem statement, all variables and given/known data

A system posesses three energy levels E1=ε, E2=2ε, E3=3ε with degeneracies g(E1)=g(E3)=1 , g(E2)=2
Find the heat capacity of the system.

2. Relevant equations

Z=e-βε+e-2βε+e-3βε

d2lnZ/dβ2=kT2C

3. The attempt at a solution

i got the partition function and then differenciated it twice which gives me an expression for C however its not correct and i can't see how to bring it the degeneracites i presume they are needed

2. Jun 25, 2009

### Avodyne

Re: Degeneracies

$$Z=\sum_i g_i e^{-\beta E_i}$$

3. Jun 26, 2009

### senan

Re: Degeneracies

thanks