  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.
