Show that the thermal efficiency of an ideal Otto cycle is given by
Where the ratio r = V1/V2 is called either the compression ratio or the expansion ratio for a gasoline engine. In practice, r cannot be made greater than about 10, because if r is larger, then the rise in temperature upon compression of the mixture of gasoline and air is great enough to cause combustion before the discharge of the spark. This is called preignition. Take r equal to 9 and, ϒ equal to approximately 1.3 (because it is a mixture) and calculate the thermal efficiency.
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