Debye specific-heat theory — UPSC CSE 1998 Physics PYQ

State the basic assumptions of Debye theory of specific heat of solids and write the expression for C_V derived from this theory. Show that this expression yields the famous T^3 law of specific heat at low temperature. Discuss the extent to which the theory agrees (or disagrees) with observation on specific heat through the variation of the Debye characteristic temperature \Theta_D with temperature, in general.