Grüneisen equation of state for solids and solution of the Riemann problem

Abstract

Equation of state for solids in terms of the specific internal energy, entropy, and specific volume has been discussed starting from the Gruneisen assumption. Thermal variables, like specific heat or temperature can be expressed by specific volume and entropy. The square of the acoustic impedance along an isentrope is expressed as a polynomial of a function X, which is the solution of the differential equation for isentropic pressure. In this case, the form of the Riemann integral has been obtained explicitly. The solution of the Riemann problem has been calculated for the case of aluminum.