A velocity-entropy invariance theorem for the Chapman-Jouguet detonation

The velocity and specific entropy of the Chapman-Jouguet (CJ) equilibrium detonation are shown to be invariant under the same variations of initial temperature with initial pressure. This leads to additional CJ relations, for example, for calculating the CJ state -- including the adiabatic exponent -- from the only CJ velocity, without using an equation of state for the detonation products. For gaseous stoichiometric explosives with ideal products, numerical calculations with detailed chemical equilibrium confirm the invariance theorem to $\mathcal{O}(10^{-2}$\% and the additional CJ properties to $\mathcal{O}(10^{-1}$\%. However, for four liquid carbon explosives, the predicted CJ pressures are about 20\% higher than the measurements. The analysis emphasizes the limited physical representativeness of the hydrodynamic framework of the modelling, i.e. single-phase inviscid fluids at equilibrium for the initial and final states of the explosive. This invariance may illustrate a general feature of hyperbolic systems and their characteristic surfaces.