Problem: Specific Heat of Metals and Insulators

      Sketch the temperature dependence of the specific heat contribution of a conduction electrons and lattice vibrations for temperatures ranging from 0 to 500 K. If possible, scale your plot in terms of these parameters: (Fermi energy), n (electron density), (Debye frequency), and N (number density of atoms). Also indicate the characteristic temperature dependence for the various regimes. Estimate the ratio of the two contributions to the specific heat at T=1K and at T=500 K, assuming typical values for the above parameters.