At low temperatures, the heat capacity of some metals has been found to follow a modified version of the Debye T³ law, varying with temperature according to the relationship
C_p.m=aT³+bT
With the additional, linear term arising from the electrons. Derive an expression for the molar entropy of such a metal at a low temperature T.

Question

Quizplus · Accepted Answer

The molar entropy, S(T), can be derived from the heat capacity, C(T), by integrating C(T)/T with respect to T. Given C(T) = aT^3 + bT, integrating this expression with respect to T gives S(T) = (1/3)aT^3 + bT, which matches option C.

At Low Temperatures, the Heat Capacity of Some Metals Has