Question

What is the physical reason for the fact that the chemical potential of a pure substance decreases as temperature is raised?

Answer 1

From the energy equation the temperature dependance of chemical potential is equal to the negative molar entropy.

From the energy equation the temperature dependance of chemical potential is equal to the negative molar entropy.

So now it gets easy, in order to explain why the chemical potential decreases with increasing temperature for various substances, we only have to understand their entropies. We can ignore the second order effect of entropy dependence on temperature and note that gases have higher entropies than liquids, so their chemical potential will reduce faster than liquids. Similarly solids.