At very low temperature, the heat capacity of crystals is equal to , where is a constant. Find the e — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Entropy is determined by integrating $\frac{C}{T} dT$ from absolute zero. $\Delta S = \int_0^T \frac{aT^3}{T} dT = \int_0^T aT^2 dT = \left[ \frac{aT^3}{3} \right]_0^T$. According to the Third Law of Thermodynamics, $S(0) = 0$, so absolute entropy evaluates precisely to $S = \frac{aT^3}{3}$.