# Statistical mechanics: Heat capacity

#### espen180

I am trying to work out the heat capacity of a body-centered cubic iron lattice using stat.mech., but am having some trouble.

Firstly, I assumed that the iron atoms behaved as harmonic occilators, not taking electronic or nuclear spin into account. Is this a good or bad approximation?

Then, when I compute the partition function and calculate the heat capacity $$C_V=\frac{dU}{dT}|_V$$, I get

$$C_V=\frac{N\hbar^2\omega^2}{kT^2}\left(\frac{e^{\frac{\hbar\omega}{kT}}}{\left(1-e^{\frac{\hbar\omega}{kT}}\right)}+\frac{e^{\frac{2\hbar\omega}{kT}}}{\left(1-e^{\frac{\hbar\omega}{kT}}\right)^2}\right)$$.

I can provide intermediate steps if neccesary.

For large T, the value of this expression is $$C_V=Nk$$. I find this an indication that either my model isn't working or I have messed up, since I think the heat capacity should be dependent on the bond strength and packing density of the lattice.

If I want to make a better approximation, how do take the influence the different iron atoms have on each other into account?

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