Find the heat capacity of the system

[senan]

Homework Statement

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.

Homework Equations

Z=e^-βε+e^-2βε+e^-3βε

d²lnZ/dβ²=kT²C

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

 

[Avodyne]

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

 

[senan]

thanks