# Experimentally Determining Entropy

gsingh2011
Out of curiosity, how would one experimentally determine the entropy of a substance at standard state?

## Answers and Replies

Gold Member
Starting with the Third Law of Thermodynamics, you take the entropy of the pure crystalline form of the substance to be 0 at absolute 0. The definition of entropy is
$$\Delta S = \int\frac{dQ_{rev}}{T}$$
You need to integrate this to get the entropy in the standard state by choosing a path that leads from absolute 0 and any pressure to the standard state. You can do this, for instance by heating at constant pressure, then the expression for the entropy would be
$$S = \int_{0}^{T}\frac{c_{P}dT}{T}$$
So the problem reduces to measuring the heat capacity as a function of T. The main experimental difficulty would be measuring cp near absolute 0. In practice, you measure as close as you can and then use the Debye approximation (http://en.wikipedia.org/wiki/Debye_model) to get the best approximation you can of the heat capacity near absolute 0.