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 ??=1.40.
a. 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.
b. Calculate the volume of the air-fuel mixture at point a in the cycle.
c. Calculate the pressure, volume and temperature of the gases at points b, c and d in the cycle.
d. Compare the efficiency of this engine with the efficiency of a Carnot-cycle engine operating between the same maximum and minimum temperatures.

Explanation / Answer

a. 122J , 77.8J

b. 5.10*10^-4

c. Temp at a = 300K

Temp at b = 771K

Temp at c = 1330K

Temp at d = 518K

Pres at a = 8.50*10^4 Pa

Pres at b = 2.32*10^6 Pa

Pres at c = 4.00*10^6 Pa

Pres at d = 1.47*10^5 Pa

Vol at a = 5.10*10^-4 m^3

Vol at b = 4.81*10^-5 m^3

Vol at c = 4.81*10^-5 m^3

Vol at d = 5.10*10^-4 m^3

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