# Why only the electrons around the Fermi energy gain energy when a material is heated?

I am reading Introduction to Solid State Physics (by Kittel).

When studying the heat capacity of a metal, conformed by $$N$$ atoms (each providing one valence electron, which is mobile and capable of electrical conduction), it says that classical statistical mechanics predict that the heat capacity should be $$\frac{3}{2}N k_B$$. However, it says that experimental results give around 1% of this value.

Then he says that this can by explained as follows:

"When we heat the specimen from absolute zero, not every electron gains an energy $$~k_BT$$ as expected classically, but only those electrons in orbitals within an energy range $$k_BT$$ of the Fermi level are excited thermally"

My question is: why only these electrons are excited?

• You should google Pauli blocking May 16 '20 at 22:21

• No, it makes sense. Yes there will be some free energy states that now those electrons at a lower energy than kT from the Fermi energy can jump up to. What Kittel says is more of an approximation because of what you've said. Look at the graph he provides, after a change in temperature the occupied levels don't go down in a straight diagonal line starting from $E_f-kT$, it curves down (the curve starting from before $E_f-kT$) May 17 '20 at 12:36