A Volkswagen Passat has a six-cylinder Otto-cycle engine with compression ratio

Question

A Volkswagen Passat has a six-cylinder Otto-cycle engine with compression ratio r = 10.6. The diameter of each cylinder, called the bore of the engine, is 82.5 mm. The distance that the piston moves during the compression, called the stroke, is 86.4 mm. The initial pressure of the air-fuel mixture is 8.50 x 104 Pa, and the initial temperature is 300 K (the same as the outside air). Assume that 200 J of heat is added to each cylinder in each cycle by the burning gasoline, and that the gas has Cv = 20.5 J/mol K and y=1.40. Calculate the total work done in one cycle in each cylinder of the engine, and the heat released when the gas is cooled to the temperature of the outside air.

 

Explanation / Answer

Engine with compression ratio is r = 10.6 diameter of each cyllinder is d = 82.5 mm distance that the piston moves during compression is x = 86.4 mm initial pressure is P_0 = 8.50*10^4 Pa initial temperature is T _0 = 300K e = 1- 1 / (r^-1)       = 1- 1 / ( 10 .6^0.4 )       = 0.6111 Q_C = ( e - 1 )Q_H            = ( 0.6111-1) * 200 J            = - 78 J Work done W = Q_C + Q_H                              = -78 J + 200J                              = 122 J

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