Homework Help: Heat capacity in 3-level systems

1. Dec 2, 2014

Kjkus

1. The problem statement, all variables and given/known data
I uploaded a picture of the problem here: http://imgur.com/kD35ROl
Sorry about the norwegian text, the problem is this:
The three figures with red lines indicate three different energy levels of a system in thermal equilibrium with a reservoir of temperature T. The three plots are the corresponding heat capacities, the problem is assigning the graphs to the correct energy structure. The plots are all with the same reference temperature Theta, but different reference heat capacities C*

2. Relevant equations

3. The attempt at a solution
I tried calculating the partition function, and working from there. I got Z=exp(-B.E_0)+exp(-B.E_1)+exp(-B.E_2). From there I tried calculating the average internal energy by taking the logarithm of Z and differentiating with respect to beta (B). The heat capacity should then be the derivative of the average internal energy with respect to temperature, but this doesn't really help me solve the problem at all. I think I may be attacking this all wrong

2. Dec 3, 2014

Staff: Mentor

I guess it is possible to solve it with the partition function, but I would simply do it by looking at the plots. Just one graph has a non-zero heat capacity at very low temperature. There is just one energy level system that can correspond to that.
The other two can be found in the same way.