I’m reading a 40-year old book, Methods of Thermodynamics by Howard Reiss. I think I bought it after reading a recommendation on Amazon.com, describing this book as one of the few that takes the idea of axiomatic thermodynamics seriously, and treats it without mixing in concepts from statistical physics or quantum mechanics.
It is a very good book. Not only does it deliver on its promise, it also raises some issues that would not have occurred to me otherwise. For instance, the idea that a so-called equation of state does not fully describe the state of a material, even an ideal gas. You cannot derive U = CvT from the equation of state. You cannot that the internal energy U is a linear function of the temperature T, it has to be postulated.
One thing you can derive from the ideal gas equation of state alone is that an adiabatic expansion must be isothermal. As an ideal gas expands and its volume increases while its pressure decreases, its temperature remains constant. It also made me think again about the cosmological equation of state… cosmologists often play with idealized cases (e.g., dust-filled universe, radiation-filled universe) but until now, I never considered the possibility that even in these idealized cases, the equations of state do not full describe the stuff that they supposedly represent.