Thermodynamic relations along the principal Hugoniot

Some thermodynamic relations are derived along the principal Hugoniot of materials for which the Grüneisen relation is a function of volume only. Rather than being expressed in terms of traditional thermodynamic variables, such as volume and temperature, the relations are expressed in terms of the shock-Hugoniot behavior and of a term grouping that is related to the Grüneisen function. By so doing, a new perspective is gained on the interrelation of thermodynamic quantities along the Hugoniot, which may be of use in developing analytical equations of state.