A multicylinder gasoline engine in an airplane, operating at 2500 rev/min, takes in 7800 J of energy and exhausts 4600 J for each revolution of its crankshaft. What is the mechanical power output of the engine in kilowatts.
To determine the mechanical power output of the engine, we need to calculate the amount of energy transferred per unit of time. The formula for power is:
Power = Energy / Time
In this case, we'll use 1 revolution as our unit of time.
Step 1: Convert the given values to the same units.
The energy values are already in joules (J). The engine operates at 2500 rev/min, so we need to convert it to revolutions per second:
Revolutions per second = 2500 rev/min * (1 min / 60 s) = 41.67 rev/s
Step 2: Calculate the energy transferred per revolution.
Energy per revolution = Energy taken in - Energy exhausted
Energy per revolution = 7800 J - 4600 J = 3200 J
Step 3: Calculate the power output in watts.
Power = Energy per revolution / Time per revolution
Power = 3200 J / 1 rev
Power = 3200 J/rev
Step 4: Convert the power to kilowatts.
1 kilowatt (kW) = 1000 watts (W)
Power (kW) = Power (W) / 1000
Let's put the values together and calculate the power output:
Power (kW) = (3200 J/rev) / 1000 = 3.2 kW
Therefore, the mechanical power output of the engine is 3.2 kilowatts.