The front of a shock wave in an ideal fluid is characterized by a discontinuous transition from the undisturbed state to a highly compressed state in which the entropy of the fluid has increased. The relations between pressure, density, propagation velocity, and particle velocity behind the shock front are represented by the equations for conservation of mass, momentum, and energy and by the equation of state of the fluid. The entropy change produced by the transition is third order in the compression for weak shocks. The propagation of shock waves through metals can be described by a hydrodynamic theory which assumes that the metal is an ideal fluid behind the shock front, and that the hydrostatic equation of state is applicable there. Three hydrostatic equations of state for Al, Cu, Fe, and Pb are compared with experimental data at low pressures and quantum mechanical calculations pressures up to several hundred megabars. With these equations of state the hydrodynamic theory is used to calculate explicitly the entropy increase across the shock front, the amount by which the pressure exceeds the adiabatic pressure for a given compression, and the temperature rise after the shock pressure has been relieved for the metals mentioned above.
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Duvall et al. (1955) studied this question.