The gasoline engine in your car can be modeled as the Otto

Chapter 21, Problem 21.102

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The gasoline engine in your car can be modeled as the Otto cycle shown in FIGURE CP21.73. A fuel-air mixture is sprayed into the cylinder at point 1, where the piston is at its farthest distance from the spark plug. This mixture is compressed as the piston moves toward the spark plug during the adiabatic compression stroke. The spark plug fires at point 2, releasing heat energy that had been stored in the gasoline. The fuel burns so quickly that the piston doesnt have time to move, so the heating is an isochoric process. The hot, high-pressure gas then pushes the piston outward during the power stroke. Finally, an exhaust value opens to allow the gas temperature and pressure to drop back to their initial values before starting the cycle over again.a. Analyze the Otto cycle and show that the work done per cycle is Wout = nR 1 - g 1T2 - T1 + T4 - T32b. Use the adiabatic connection between T1 and T2 and also between T3 and T4 to show that the thermal efficiency of the Otto cycle is h = 1 - 1 r 1g-12 where r = Vmax/Vmin is the engines compression ratio. c. Graph h versus r out to r = 30 for a diatomic gas.