Applications of statistical physics to selected solid-state physics phenomena for metals
“similar” models for thermal and electrical conductivity for metals, on basis of free electron gas, treated with Maxwell-Boltzmann statistics – i.e. as if it were an ideal gas
Lorenz numbers, a fortuitous result, don’t be fooled, the physics (Maxwell-Boltzmann statistics) behind it is not applicable as we estimated earlier
But Fermi-Dirac statistics gets us the right physics Metals have high conductivities for both electricity and heat. To explain both the high conductivities and the trend in this table we need to have a model for both thermal and electrical conductivity, that model should be able to explain empirical observations, i.e. Ohm’s law, thermal conductivity, Wiedemann- Franz law, Wiedemann and Franz Law, 1853, ratio K/σT = Lorenz number = constant 2.4 10-8 W Ω K -2
independent of the metal considered !! So both phenomena should be based on similar physical idea !!!
Classical from Drude (early 1900s) theory of free electron gasToo small by factor 2, seems not too bad ???2.22.552.3300K ...