Thermodynamic Formulation of Wu-Jing Equation of State for Condensed Substances

Thermodynamic formulation has been made for the enthalpy-pressure-volume equation of state for condensed substances based on the assumptions proposed by Wu and Jing in the reference. [Q. Wu, and F. Jing, J. Appl. Phys., \textbf{80} (1996)4343-4349.] These state variables seem attractive for the numerical simulation of propagation of shock or detonation waves containing chemical reaction. We found a unique thermodynamic identity containing Wu-Jing parameter, i.e., the non-dimensional material parameter defined by them and the specific heat at constant pressure. This equation gives a constraint for these two parameters. Behavior of Wu-Jing parameter and constant pressure specific heat upon compression has been evaluated based on the calculation of the Gr\"{u}neisen parameter by using three theoretical models. Comparison of Wu-Jing parameter along shock Hugoniot curve and along an isentrope centering uncompressed initial state revealed that Wu-Jing parameter does depend on entropy as well as pressure, but its entropy dependence is very small. This result strongly suggests that Wu-Jing parameter as a function of only pressure will give sufficient description of high-pressure behavior of solid materials within appropriate range of pressure.