Compare the work that a 22-kW car engine does in 60 seconds if its efficiency changes from 100% to 75%.
1 kW = 1 kJ/s
Work done
= 22 kW * 60 s
= 22*60 kJ
= 1320 kJ
If the efficiency changes to 75% from 100%, the work done is reduced in the same ratio.
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To compare the work done by a 22-kW car engine with an efficiency change from 100% to 75%, we need to calculate the work done in both scenarios.
1. Calculating the work done when the efficiency is 100%:
The power output of the car engine is given as 22 kW, which means it can deliver 22,000 J of energy per second (since 1 kW = 1000 J/s).
Work done = Power output x Time
= 22,000 J/s x 60 s
= 1,320,000 J
2. Calculating the work done when the efficiency is 75%:
The efficiency of 75% means that the engine can convert 75% of the input energy into useful work. Thus, the power output in this case would be 75% of the total power output at 100% efficiency.
Power output (at 75% efficiency) = 0.75 x 22,000 J/s
= 16,500 J/s
Work done = Power output x Time
= 16,500 J/s x 60 s
= 990,000 J
Therefore, when the efficiency changes from 100% to 75%, the work done by the 22-kW car engine in 60 seconds decreases from 1,320,000 J to 990,000 J.
To compare the work done by a 22-kW car engine at two different efficiency levels, we need to calculate the work done in both cases.
First, let's calculate the work done by the engine at 100% efficiency in 60 seconds. The work done by an engine can be calculated using the formula:
Work = Power × Time
Given:
Power (P1) = 22 kW
Time (t) = 60 seconds
Using the formula, we can find the work done at 100% efficiency:
Work1 = P1 × t
Work1 = 22 kW × 60 seconds
Next, let's calculate the work done by the engine at 75% efficiency in 60 seconds. The efficiency of an engine is defined as the ratio of the useful work it produces to the total energy input. Given that the efficiency changes from 100% to 75%, this means that the engine is only producing 75% of the work it would produce at 100% efficiency.
To find the work done at 75% efficiency, we first need to calculate the power at 75% efficiency. We can use the formula:
Power2 = Efficiency × Power1
Given:
Efficiency (E2) = 75% = 0.75
Power1 = 22 kW (as given)
Using the formula, we can find the power at 75% efficiency:
Power2 = 0.75 × 22 kW
Now, we can calculate the work done at 75% efficiency using the power at 75% efficiency:
Work2 = Power2 × t
Work2 = (0.75 × 22 kW) × 60 seconds
After calculating both Work1 and Work2, you can compare the work done by the engine at 100% efficiency and 75% efficiency to see the difference.