Find the heat capacity of the system

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


thanks
 

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