If a Carnot engine operates between Th = 600 K and Tc = 300 K and achieves 50% efficiency, how much work can it do at most if it absorbs 400 J of heat from the hot reservoir?

• A. 100 J
• B. 200 J
• C. 0 J
• D. 400 J

Answer: (B)

The amount of work a heat engine can do from a given heat input is limited by its efficiency. For a Carnot engine, the maximum efficiency between two reservoirs is η = 1 − Tc/Th. With Th = 600 K and Tc = 300 K, η_max = 1 − 300/600 = 0.5 (50%). Since the engine is at this limit, the work it produces from 400 J of heat absorbed is W = η Qh = 0.5 × 400 J = 200 J. The remaining energy, 200 J, is expelled to the cold reservoir (Qc = Qh − W). Therefore, the maximum work is 200 J. The other numbers would require different efficiencies (e.g., 25%, 0%, or 100%), which don’t match the Carnot limit for these temperatures.