Continuum approach to phonon gas and shape changes of second sound via shock waves theory

Summary A continuum approach, based on the principles of modern extended thermodynamics, describing the model of a phonon gas is performed. The main difference with the ideal phonon gas theory consists in the presence of athermal inertia. We apply the shock wave theory and discuss the selection rules for physical shocks (theLax conditions and theentropy growth). In this way the existence of two new kinds of shocks (hot andcold shocks) in rigid heat conductors at low temperature is pointed out. In particular a critical temperature, characteristic of each material, changing the structure of the previous types of shocks is analytically deduced. This characteristic temperature permits also to explain the modification of the received second sound wave form with respect to the initial wave profile. Finally, the results are applied to the case of high-purity crystals (NaF, Bi,³He and⁴He) and compared with experimental results.