Equation is the definition of specific heat given in terms of the fermi-dirac distribution function and the density of states equation
The first consideration that I make is that the fermi level is a function of temperature, so I use the following conservation equation to solve for the fermi level
where is the number of free electrons. For example in Copper it would be 1 electron/atom.
My question is around how to determine the number of free electrons in a metal as a function of temperature. All the analysis that I have seen just assumes a static amount of free electrons for a material, but we know as the number of free electrons goes towards the atomic number of the metal.
My question is how can I solve for if I know ?