ThermodynamicsHard

Question

At very low temperature, the heat capacity of crystals is equal to C = aT3, where a is a constant. Find the entropy of a crystal as a function of temperature in this temperature interval.

Options

A.$S = \frac{aT^{3}}{3}$
B.S = aT3
C.$\frac{a.T^{2}}{2}$
D.$\frac{a.T}{3}$

Solution

$\int_{0}^{S}{dS} = \int_{0}^{T}{C.\frac{dT}{T}} = \int_{0}^{T}{T^{3}.\frac{dT}{T}} \Rightarrow S = \frac{aT^{3}}{3}$

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