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Sep 26, 2014 at 11:13 comment added ProfRob @Jan Hirschner It is the energy density that has the additional quadratic term. I suppose you could think of this as a fraction $\sim kT/E_F$ electrons are above the "roll-off" region in the distribution and each of these has $\sim kT$ of energy above $E_F$. Differentiating this gives a heat capacity that is linearly dependent on $T$.
Sep 26, 2014 at 10:56 comment added Jan Hirschner Thank you very much, after a short calculation the Sommerfeld expansion adds temperature dependent term to the electron density approximation, which I was looking for. Interesting point is, that I have always thought, that the thermal dependence would turn out linear rather than quadratic.
Sep 26, 2014 at 10:50 vote accept Jan Hirschner
Sep 26, 2014 at 0:04 history edited ProfRob CC BY-SA 3.0
put in a clearer reference
Sep 25, 2014 at 22:07 history answered ProfRob CC BY-SA 3.0