In order for the engine to operate at 21% efficiency, approximately 101.27 J of energy must be added to the engine during one cycle.
The efficiency of an engine is defined as the ratio of useful work output to the energy input. In this case, the engine operates at 21% efficiency.
To determine the energy added to the engine during one cycle, we can use the formula for efficiency:
Efficiency = Useful work output / Energy input
Given that the efficiency is 21%, we can express this as 0.21. Let's denote the energy input as E.
0.21 = Useful work output / E
To find the energy added to the engine, we need to find the useful work output. The useful work output is the difference between the energy input and the energy removed from the engine as heat.
Energy removed from the engine as heat = 80 J
Therefore, the useful work output can be calculated as:
Useful work output = Energy input - Energy removed from the engine as heat
= E - 80 J
Now, we can substitute the values into the efficiency formula:
0.21 = (E - 80 J) / E
To solve for E, we can cross-multiply and rearrange the equation:
0.21E = E - 80 J
0.21E - E = -80 J
-0.79E = -80 J
Dividing both sides of the equation by -0.79 gives:
E = -80 J / -0.79
E ≈ 101.27 J
Therefore, in order for the engine to operate at 21% efficiency, approximately 101.27 J of energy must be added to the engine during one cycle.