Entropy in General

Entropy, introduced in Chap.  8 , is generalized here for all fluids. The generalization operates on new concepts—ordinary and thermodynamic points. The corresponding proof is rather complex, and an analysis of adiabatic processes precedes it. Adiabats of an ideal gas, a Van der Waals fluid, and water are examined. Then, a special type of cyclic processes, the Carnot cycle, and two additional related axioms are described. Finally, a general proof is developed in detail. Further, it is shown how entropy can alternatively be obtained from the integration factor of the basic heating model. It is also shown that the existence of the integration factor limits efficiency in the cycle: in a cyclic process, a body cannot absorb heat without also emitting heat. The chapter closes with a contemplation on the meaning of entropy.