Resolving the entropy minimum paradox of the Chapman-Jouguet Theory of Detonation*

The Chapman-Jouguet (CJ) theory of detonation, developed in 1899, predicts the velocity of detonation wave by the tangency point of the Rayleigh line and the Hugoniot, expressions relating initial-and final-state thermodynamic variables through the basic conservation laws for mass, momentum, and energy. The CJ theory has been an enormous success, as it has been found to be consistent with experimental results, predicting the measured detonation wave velocity and final state density, temperature, and pressure with great accuracy for a vast number of unstable gas mixtures. In 1935, however, R.L. Scorah published a scathing criticism of the CJ theory, showing that the tangency point represents an entropy minimum. This arises as an obvious flaw in the thermodynamic analysis of the closed shock wave system, violating the second law of thermodynamics. That the CJ theory obviously gives the right answer for the wrong reason presents a paradox that has remained unresolved after 89 years of experimental investigation and increasing sophistication of computer modeling. This work focuses on attempting to resolve the paradox by the inclusion coordinates for the chemical reactions involved in detonation. We will also investigate the CJ paradox in real gas mixtures and solids.