A single Hugoniot curve determined from shock-wave experiments does not provide enough thermodynamic information to specify an equation of state. The assumptions which, along with shock-wave data, are sufficient to determine a complete equation of state are instructive to a serious student of thermodynamics, because they illustrate the significance of the state variables and the relations among them. This paper considers the specific problem of calculating the state variables of shock-induced states and discusses calculations based on the assumption of either constantCvor constantCpfrom a structural point of view. Methods of calculating the state variables are formulated to show how the assumptions make them possible. The assumption of constantCvspecifies implicitly the functional forms of the(E-p-v)and(p-v-T)equations of state. Similarly, the assumption of constantCpspecifies the functional forms of the(H-p-v)and(p-v-T)equations of state. The experimental Hugoniot curve is used as a boundary condition to determine arbitrary functions in these equations of state and to show how the assumptions and the experimental data lead to a complete thermodynamic description of shock-induced states.