Discussions on the temperature wave equation

The purpose of this paper is to discuss some extensions of classical and continuum thermodynamics. At first the first law in continuum thermodynamics is approximately or exactly extended to the case where the temperature is varied with time. Secondly an inertial entropy concept is introduced to the second law of the thermodynamics. The temperature wave equation with finite phase velocity is derived by the inertial entropy theory (IET) in a very simple fashion. Comparison of the inertial entropy theory and the Cattaneo-Vernotte's equation is given. Some other problems to illustrate the rationality of IET are also discussed shortly.