# Heat capacity (statistical physics)

1. Feb 6, 2006

### broegger

Hi. I've just started a course on statistical physics and the first assignment is this:

A system possesses 3 energy levels, $$E_1 = \epsilon,$$ $$E_2 = 2\epsilon$$ and $$E_3 = 3\epsilon$$. The degeneracy of the levels are g(E1) = g(E3) = 1, g(E2) = 2. Find the heat capacity of the system.

I've forgotten all this thermodynamics stuff, so I would appreciate some hints :-)

2. Feb 8, 2006

3. Feb 8, 2006

### Gokul43201

Staff Emeritus
If you are given a description of a system, what quantity do you first compute, from which you can determine other thermodynamic quantities ?

4. Feb 20, 2006

### broegger

Yes, yes, the partition function, I know :-)

5. May 4, 2009

### marblepony

sum over states to get Q

Q= exp{-B.E) + 2exp{-B.2E} + exp{-B.3E}

B=kT Q=partition E=energy (two in front of second term beacuse of degenercy)

U= - Diff (lnQ) w.r.t (B)

U= internal energy prof can be found ( http://www.chem.arizona.edu/~salzmanr/480b/statt01/statt01.html)..... if you are interested

gives U= E.exp(-B.E) + 4E.exp(-B.2E) + 3E.exp(-B.3E)

makes sense highest energy has least probabilty of being populated but contributes three times as much to internal enrgy when it is. same would apply to the middle state but there is two of them so it is four instead of two.