Final answer:
The Carnot engine operating between a hot reservoir at 417K and a cold reservoir at 287K performs approximately 748.2024 J of work per cycle when it absorbs 2400 J of heat.
Step-by-step explanation:
The student is asking about the work done by a Carnot engine operating between two temperature reservoirs. The efficiency (e) of a Carnot engine is given by the formula e = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. The work (W) performed by the engine per cycle is equal to the product of the efficiency and the heat absorbed from the hot reservoir (Qh). Given the temperatures: Th = 417K and Tc = 287K, and the heat absorbed Qh = 2400 J, we can calculate the efficiency e: e = 1 - (Tc/Th) = 1 - (287K/417K) = 1 - 0.688249 = 0.311751 Now, the work done per cycle W can be found using: W = e × Qh = 0.311751 × 2400 J = 748.2024 J The Carnot engine performs approximately 748.2024 J of work per cycle.