A heat engine operates between a cold reservoir at 10 degrees Celcius and a hot

Question

A heat engine operates between a cold reservoir at 10 degrees Celcius and a hot reservoir at 200 degrees Celcius. If the engine performs near maximum efficiency and produces 1000J of work, how much heat must be exhausted as waste? The answer is 1.5kJ. Please show me how to do this problem

Explanation / Answer

? = 1 - Tc/Th => Th = Tc / (1 - ?) at 30% efficiency Th = 283K / ( 1 - 0.3) = 404K at 70% efficiency Th = 283K / ( 1 - 0.7) = 943K => ? T = 943K - 404K = 539K You have to increase hot reservoir temperature by about 540°C to raise efficiency to the desired level. Second question Maximum possible efficiency is the efficiency of an ideal Carnot engine: ?_c = 1 - Tc/Th = 1 - 293K / 873K = 0.6644 So the actual efficiency of the engine is: ? = 0.3·?_c = 0.1993 Efficiency is the ratio of (useful) work done divided by heat extracted from hot reservoir ? = W/Qh

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