4. Estimating D(E).
(a) Equation (2.16) gave the entropy of a monatomic classical ideal gas—that is, the dependence on T and V. Eliminate the temperature in terms of the system’s total energy E and then infer the dependence of the density of states D(E) on E and V. It would be reasonable to assume that the energy range δE is proportional to E.
The “constant” in equation (2.16) may depend on the number N of atoms, and so this route does not enable you to infer the entire dependence of D(E) an N.
(b) With sketches, compare the behavior of D(E) as a function of E for two cases : N >> 1 and N = 1.