During the power stroke in a four-stroke auto- mobile engine, the piston is forc

Question

During the power stroke in a four-stroke auto-
mobile engine, the piston is forced down as the
mixture of gas and air undergoes a reversible
adiabatic expansion.
Find the average power generated during
the expansion by assuming the engine is run-
ning at v = 2400 rpm, the gauge pressure
right before the expansion is Pgauge = 19 atm,
the volumes of the mixture right before and
after the expansion are Vi = 52 cm3 and
Vf = 500 cm3, respectively, the time involved
in the expansion is one-fourth that of the total
cycle, and the mixture behaves like an ideal
diatomic gas.
Answer in units of kW.

Explanation / Answer

average power = work / time . time for one cycle is 1 minute / 2400 cycles =   0.000416667 minutes / cycle =   0.025seconds . time for this process = 1/4 * 0.025 =   0.00625 sec . Final pressure of the gas =    initialpressure ( initial volume / final volume)1.4 = .                      = (19 + 1) (52 / 500)1.4 =   0.841156 atm . Work done for adiabatic process = - (5/2) (pV final - pV initial) = .         = - (5/2) *(0.841156 * 0.500 L - 20 * 0.052 L) =  1.54855 atm-L =   156.87 Joules . Finally    average power = 156.87 J/ 0.00625 s =   25099 Watts =   25.1 kW

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