Final answer:
Using the Carnot cycle principles, the maximum possible work an engine can do per cycle is 380 J, and the heat exhausted to the cold reservoir per cycle is 620 J. The temperatures must be converted to Kelvin before calculating efficiency, and thus, none of the provided options (a, b, c, d) are correct.
Step-by-step explanation:
An engine operating between heat reservoirs at 20°C and 200°C and extracting 1000 J per cycle from the hot reservoir can be analyzed using the principles of a Carnot engine, which is an idealized engine that operates on the Carnot cycle and has the highest efficiency possible. The efficiency of a Carnot engine is given by:
η = 1 - Tc/Th
where η is the efficiency of the engine, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir. However, in this problem, we need to use absolute temperatures measured in kelvins (K). To convert the given temperatures to kelvins, we add 273.15 to the Celsius temperatures, thus Tc = 293.15 K and Th = 473.15 K.
The efficiency of the Carnot engine is then:
η = 1 - (293.15 / 473.15) ≈ 0.38
(a) The maximum possible work the engine can do per cycle is given by the product of the efficiency and the heat extracted from the hot reservoir:
W = η * Qh = 0.38 * 1000 J = 380 J
(b) The amount of heat exhausted to the cold reservoir per cycle can be found by subtracting the work done from the heat extracted:
Qc = Qh - W = 1000 J - 380 J = 620 J
Therefore, none of the options given matches the correct calculations for a Carnot engine. There may have been an error in the provided choices or in the understanding of the Carnot cycle for this problem.