On the impossibility of isothermal heat transfer and its implications for thermal physics

Abstract

The physical impossibility of heat transfer under isothermal conditions implies that the classical expression for the entropy of the ideal gas may not be compatible with the internal energy of the gas itself. A corrected expression of the ideal gas entropy is derived here. It is independent on volume. This result is shown to be at a variance with the statistical interpretations of entropy as a quantity that is related to the number of microstates compatible with the macroscopic state of the system. It also offers a better understanding of the thermodynamic notion of entropy. The present analysis also establishes a general equation that links the entropy of a system to its internal energy.