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