During the power stroke in a four-stroke automobile engine, the piston is forced

Question

During the power stroke in a four-stroke automobile 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 running at v = 1500 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 = 47 cm3 and Vf = 550 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

Assuming idealised cycle Power P is rate of change of energy E with respect tochange in time t P =E/t t = 1/4 T where T is time of the total cycle T= 1 /(rpm/ 60 ) = 60/rpm = 60/1500 = 1/25 s then t = 1/100 s Now let's find E or work done W W=E= P(V2-V1) don't frogetto use proper units 1 atm = 101,325 Pascals 1cm3 = 1x10-6 m3 E= 19 x 101,325  [(550 - 47 ) x 1x10-6 ] E= 968J finally P= 968/ (1/100) = 96,800 W or P=96.8 kW

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