(i) we showed in class that in the classical limit λ = eμ/r-n/nq 《 1 the grand potential of a fermion gas is approximately (setting 1 for simplicity) derive from this expression the helmholtz free energy of an ideal gas (ii) we also showed that the density of a degenerate fermion gas can be expressed as use this expression to compute the exact fermi energy ef as a function of density. (iii) beginning with the warm-phonon formula derived in class, f-3ntlog(1-e/) derive the internal energy formula u-3nt. (iv) explain in a few sentences why you would expect the cold-phonon heat capacity to have the same temperature dependence as that of photons.