At very low temperatures the heat capacity of crystals os equal to `C = aT^3`, where `a` is a constant. Find the entropy of a crystal as a function of temperature in this temperature interval.

Explanation

We can take `S rarr 0 as T rarr 0` Then
`S = int_0^T C (dT)/(T) = int _0^T aT^2 dT = (1)/(3) aT^3`.