A Velocity-Entropy invariance theorem for the Chapman-Jouguet detonation

The velocity and specific entropy of the Chapman–Jouguet (CJ) detonation are shown to remain invariant for initial-state families that each satisfy a common pressure–temperature dependence. Arbitrary reference states define distinct dependences and thereby distinct invariant values. The analysis yields additional properties that, in particular, allow the CJ state — including the adiabatic exponent — to be determined from the CJ velocity alone, without requiring an equation of state for the detonation products. For gaseous stoichiometric explosives with ideal detonation products, numerical calculations using detailed chemical equilibrium support the invariance to within O ( 1 0 − 2 ) % and the additional CJ properties to within O ( 1 0 − 1 ) %. For four organic liquid explosives, the predicted CJ pressures are approximately 20% higher than the available experimental values, highlighting both the difficulty of obtaining the experimental data required to calibrate empirical equations of state for detonation products from CJ properties and the physical limitations of the hydrodynamic modeling framework — namely, single-phase inviscid fluids. This invariance may represent a particular manifestation of a more general property of hyperbolic systems and their characteristic surfaces. Novelty and Significance Statement The novelty lies in an invariance property of the Chapman–Jouguet (CJ) detonation: both the detonation velocity and the specific entropy of the detonation products remain constant under the same appropriately chosen variations in initial temperature and pressure. In particular, this allows the CJ state — including the adiabatic exponent — to be determined from the CJ velocity alone, without requiring an equation of state for the detonation products. The significance lies, first, in a fundamental contribution to detonation physics that may extend to other hyperbolic phenomena; second, in highlighting the limitation ofthe inviscid homogeneous-fluid model when calibrating empirical equations of state for detonation products from measured detonation properties