Application of the Fourth-Order Anharmonic Theory to Shock Waves and the Derivation of the Temperature along the Hugoniot Curves

The fourth-order anharmonic equation of state combined with the Hugoniot relation is used to describe the thermodynamic response of a solid subject to shock-wave compression. There is a quasiabsolute agreement in volume-ratio range $1\ge \frac{V_H}{V_0}\ge 0.8$ for the five materials considered: aluminum, copper, silver, sodium, and periclase. This agreement seems to be independent of the nature and the compressibility of the species. It is possible, therefore, to calculate the temperature along the obtained curves using the fourth-order anharmonic theory. There is a discrepancy of less than 1% between our results and the other published results.