I’m trying to get a grasp of thermodynamics as advance preparation for taking statistical mechanics this fall. It is turning out to be more challenging than I expected – there are these little points in derivations which do not seem at all obvious to me. For example, it was interesting to see that the zeroth law establishes thermodynamic equilibrium as an equivalence relation over the set of thermodynamic states, but going from this to the existence of empirical temperature seemed to pull some things out of thin air, or at least make some assumptions that didn’t seem to be rigorously justified. But I guess there will always be some of this, since classical thermodynamics is essentially phenomenological.
Always remember: “Heat is not a type of energy. It is a process – a mode of transfer of energy. There is no sense in which we can divide up the energy of a system into heat and work.” (David Tong).