Final answer:
The Carnot engine performs 600 J of work per cycle, based on the calculated efficiency of the engine operating between 500 K and 300 K with a heat absorption of 1500 J from the high-temperature reservoir. The correct answer is not listed among the provided options.
Step-by-step explanation:
The student is asking how much work is performed by a Carnot engine per cycle when the engine operates between temperatures of 500 K and 300 K, with an absorption of 1500 J of heat from the high-temperature reservoir. To calculate the work done, we first need to determine the efficiency of the Carnot engine using the formula: efficiency (e) = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir (300 K) and Th is the temperature of the hot reservoir (500 K).
After calculating the efficiency, we can find the work done (W) using the formula: W = e × Qh, where Qh is the heat absorbed from the high-temperature reservoir. Therefore, the total work done by the engine is the product of the efficiency and the heat absorbed, i.e., W = (1 - 300/500) × 1500 J = 0.4 × 1500 J = 600 J.
Therefore, the correct answer to the student's question would be that the engine performs 600 J of work per cycle, which is not listed among the provided options (a, b, c, d).