Derive the entropy increase across a reaction wave in a perfect gas mixture for fixed initial stagnation state. Show that the entropy at the CJ detonation state is greater than the entropy at the CJ deflagration state, and that the minimum entropy increase occurs for a constant-pressure combustion process. The entropy increase can be used to evaluate propulsion efficiencies in steady engines using different modes of combustion; the penalties growing with entropy increase. For engines operating with stationary combustion waves, where the entropy increase throughout the steady flow of the engine occurs mainly across the combustion wave, evaluation of the entropy generation should be referenced to the upstream stagnation state. Hence, for this type of engines, the analysis indicates that constant pressure combustion is most beneficial. On the other hand, the static reference state (Problem 7.3) is more appropriate for engines operating unsteadily, such as a pulsed device where the gas is ignited intermittently. Consequently, for a given static initial state, detonations appear to be more efficient than deflagrations based on entropy generation across the combustion wave. (Foa 1960; Wintenberger & Shepherd 2006)