Linear relationship between Hugoniot temperature and shock Mach number

It is the purpose of this publication to discuss further the apparent validity of a linear relationship between the Hugoniot temperature and the shock Mach number, when used as an independent variable in the thermodynamics of very high pressures. Additional evidence for seventeen different materials is presented. Some of the materials discussed might present phase transitions within the ranges of pressure and temperature here studied. The case of molybdenum is discussed in particular because experimental data on phase transitions are available within the ranges of pressure and temperature considered. Equation of state results for a few materials, obtained using an exact analytical equation of state, are compared with those computed employing an approximate form of the equation, consequence of the linear relationship between the Hugoniot temperature and shock Mach number. The excellent agreement shows that this approximate and very simple equation of state can be very reliable and useful.