Motor Cycle Engine

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Main Question or Discussion Point

In a motor cycle engine, after combustion occurs in the top of the cylinder, the piston is forced down as the mixture of gaseous products undergo an adiabatic expansion. Find the average power involved in the expansion when the engine is running at 4000 rpm, assuming that the gauge pressure immediately after combustion is 15 atm, the initial volume is 50.0 cubic centimeters, and the volume of the mixture at the bottom of the stroke is 250 cubic centimeters. Assume that the gases are diatomic [tex](\gamma=1.4)[/tex]. In the 4000 times the piston goes up and down, half is the combustion and half is the exhaust.

Now i know one expression here:

[tex]W=\frac{P_{f}V_{f}-P_{i}V_{i}}{\gamma-1}[/tex]

now can i use the following equation for finding the final pressure

[tex]\frac{P_{f}V_{f}}{T_{f}}=\frac{P_{i}V_{i}}{T_{i}}[/tex]

and i found that the final pressure is 3 atm. now when i put it in the above equation for finding "W", i got zero as an answer. What does this mean?
Is it the wrong approach?

Moreover, how can i utilize the data of 4000rpm in solving this question. Please explain me the right scenario!!

Thanks
 

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