A mathematical model of ionized gases: thermodynamic properties

The aim of this note is to give a brief account of a paper of Asakura-Corli, showing the thermodynamic property of a particular mathematical model of ionized gases. Thermal ionization occurs in a high temperature region behind a single shock wave passing through the gas. By assuming the local state attains the thermal equilibrium, the thermodynamic quantities: temperature, particle density and degree of ionization are computed by the Rankine-Hugoniot condition and the Saha ionization formula for given initial state and the speed of the shock wave. The mathematical model is proposed by Fukuda, Okasaka and Fujimoto. We also propose a rigorous deduction of Saha's law.