Problem 7.3. A lattice contains N normal lattice sites and N interstitial lattice sites. The lattice sites are all distinguishable. N identical atoms sit on the lattice, M on the interstitial sites, and NM on the normal sites (N > M >1). If an atom occupies a normal site, it has energy E = 0. If an atom occupies an interstitial site, it has energy E=E. Compute the internal energy and heat capacity as a function of temperature for this lattice.