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THE thermodynamic analysis of an internal-combustion engine, even in the idealized case, is in general more complex than a similar analysis of an engine cycle in which the fluid undergoes no chemical change. It is the purpose of this paper to show that, despite the inherent complexity of the problem, an exact solution by graphical methods is possible, and the method is very similar in nature to those used in connection with the Mollier diagram for steam. Two types of charts are presented, one descriptive of the thermodynamic properties of the airfuel mixture (and residual products of combustion) before combustion, the other descriptive of the properties of the equilibrium mixture after combustion. Full allowance is made for the variation of specific heats with temperature and for the complex dissociation at the high temperatures attained after combustion. All calculations are based on the most recent basic thermodynamic data available in the literature.