Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 28

28 At very low temperatures, the molar specific heat \(C_V\) of many solids is approximately \(C_V = AT^3\), where \(A\) depends on the particular substance. For aluminum, \(A = 3.15 \times 10^{-5} \text{ J/mol} \cdot \text{K}^4\). Find the entropy change for 4.00 mol of aluminum when its temperature is decreased from 8.00 K to 5.00 K.