Calculating Average Power in Motorcycle Engine at 4000 RPM

[shaiqbashir]

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 $$(\gamma=1.4)$$. 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:

$$W=\frac{P_{f}V_{f}-P_{i}V_{i}}{\gamma-1}$$

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

$$\frac{P_{f}V_{f}}{T_{f}}=\frac{P_{i}V_{i}}{T_{i}}$$

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

 

[Illmatic1]

. The correct equation to use here is the Ideal Gas Law: PV = nRT where n is the number of moles of gas and R is the ideal gas constant. Using this equation you can calculate the final pressure based on the initial pressure, initial temperature, volume of the mixture at the bottom of the stroke, and the molar mass of the diatomic gas. Once you have the final pressure, you can use the equation you provided W=\frac{P_{f}V_{f}-P_{i}V_{i}}{\gamma-1} to calculate the average power involved in the expansion. To utilize the data of 4000 rpm, you must first calculate the time for one cycle using the formula t=60/rpm. For 4000rpm, this is 0.015 seconds. This is the time it takes for the piston to go up and down once. The power is then calculated by multiplying the average power by the number of cycles per second. In this case, it would be 4000*W, where W is the average power as calculated from the equation above.

 

[ravenprp]

for your help

To calculate the average power involved in the expansion of the motorcycle engine at 4000 rpm, we need to use the following equation:

P = \frac{W}{t}

where P is the power, W is the work done, and t is the time.

To find the work done, we can use the expression:

W = \frac{P_fV_f - P_iV_i}{\gamma - 1}

where P_f and P_i are the final and initial pressures, V_f and V_i are the final and initial volumes, and \gamma is the ratio of specific heats (1.4 for diatomic gases).

Using the given values: P_i = 15 atm, V_i = 50.0 cc, V_f = 250 cc, and \gamma = 1.4, we can calculate the work done as:

W = \frac{(3 atm)(250 cc) - (15 atm)(50.0 cc)}{1.4 - 1} = 535.7 J

Now, to find the time t, we need to convert the engine speed (4000 rpm) to revolutions per second (rps):

t = \frac{1}{4000/60} = 0.015 s

Finally, we can calculate the average power as:

P = \frac{535.7 J}{0.015 s} = 35713.3 W or 35.7 kW

Therefore, the average power involved in the expansion of the motorcycle engine at 4000 rpm is 35.7 kW. This means that the engine is capable of producing this amount of power every second.

As for your approach, it seems like you have used the correct equations, but there may have been a calculation error in finding the final pressure or work done. It is also important to note that the given data does not specify the time period for which the engine is running at 4000 rpm. So, in this calculation, we have assumed that the engine is running at this speed for one second. If the time period is different, the power output would also be different.

Overall, to utilize the data of 4000 rpm, we need to convert it to rps and use it in our calculations to find the time period. I hope this explanation helps.