On linear dynamical equations of state for isotropic media. II. Some cases of special interest

In a previous paper we have investigated the relation (dynamical equation of state) among the hydrostatic pressure P, the volume v and the temperature T of an isotropic medium with an arbitrary number, say n, of scalar internal degress of freedom. It has been shown that linearization of the theory leads to a dynamical equation of state which has the form of a linear relation among P, v, T, the first n derivatives with respect to time of P and T and the first n+1 derivatives with respect to time of v. In this paper we give a more detailed investigation of the coefficients of P, v and T in the linear dynamical equation of state. Furthermore, we consider the case of media without volume viscosity. It is shown that for these media the derivative with respect to time of order n+1 of the volume does not occur in the dynamical equation of state. Finally, we pay special attention to media with one and with two scalar internal variables