Reference: Daniel V. Schroeder, *An Introduction to Thermal Physics*, (Addison-Wesley, 2000) – Problem 3.14.

A curve fit to experimental measurements of the heat capacity of one mole of alumin(i)um at low temperatures is

where and .

We can use this to work out the entropy from the formula

If we take , we can evaluate the formula at a few temperatures.

At we have

In dimensionless form, we have

At