An ideal Carnot engine extracts 529 J of energy from a high-temperature reservoir during each cycle,and rejects $225 \mathrm {~J}$ of energy to a low-temperature reservoir during the same cycle.What is the efficiency of the engine?

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by the formula:
Efficiency = (1 - (T_L/T_H)) * 100%
where T_L is the temperature of the low-temperature reservoir and T_H is the temperature of the high-temperature reservoir.

Now, we know that the engine extracts 529 J of energy from the high-temperature reservoir and rejects 225 J of energy to the low-temperature reservoir. Therefore, the net work done by the engine in one cycle is:
W = Q_H - Q_L
where Q_H is the heat absorbed from the high-temperature reservoir and Q_L is the heat rejected to the low-temperature reservoir.
W = 529 J - 225 J = 304 J

Since this is an ideal Carnot engine, the net work done is equal to the maximum work that can be obtained from the engine, which is given by:
W_max = Q_H * Efficiency
Therefore, we can write:
Efficiency = W_max / Q_H

Substituting the values given in the problem, we get:
Efficiency = (304 J / 529 J) * 100% = 57.4%
Rounding off to two decimal places, we get the answer as 57%, which is option A.

An Ideal Carnot Engine Extracts 529 J of Energy from a High-Temperature