The Otto cycle in Figure P18.64 models the operation of the internal combustion engine in an automobile. A mixture of gasoline vapor and air is drawn into a cylinder as the piston moves down during the intake stroke O → A. The piston moves up toward the closed end of the cylinder to compress the mixture adiabatically in process A → B. The ratio r = V1/V2 is the compression ratio of the engine. At B, the gasoline is ignited by the spark plug and the pressure rises rapidly as it burns in process B → C. In the power stroke C → D, the combustion products expand adiabatically as they drive the piston down. The combustion products cool further in an isovolumetric process D → A and in the exhaust stroke A → O, when the exhaust gases are pushed out of the cylinder. Assume that a single value of the specific heat ratio characterizes both the fuel-air mixture and the exhaust gases after combustion. Prove that the efficiency of the engine is .
