Today, we derive the electronic heat capacity in metals. This gives a contribution to the heat capacity that is linear in temperature. Phonons gave a T^3 dependence, and so this can distinguish the 2 contributions to the specific heat. We also discuss how to measure the occupied density of states through X-ray measurements, as well as the effective mass of an electron inside of a solid. (The effective mass is one important way that we correct the free electron picture for use in a real solid.) We derive the electrical conductivity (the response to an electric potential gradient), and the thermal conductivity (the response to a thermal gradient) for the free electron picture. The famous Wiedemann-Franz ratio relates the two, and remarkably can be expressed in terms of fundamental constants. That's right -- measure 2 things about a metal, divide them, and you'll get an answer only dependent on fundamental constants. Solids are amazing. Lecture Audio

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