The temperature T_C of the cold reservoirs and the temperatures T_H of the hot reservoirs for four Carnot heat engines are Rank these engines according to their efficiencies, least to greatest A) 1, 2, 3, 4 B) 1 and 2 tie, then 3 and 4 tie C) 2, 1, 3, 4 D) 1, 2, 4, 3 E) 2, 1, 4, 3

Question

Quizplus · Accepted Answer

The efficiency of a Carnot heat engine depends only on the temperatures of the reservoirs between which it operates. The efficiency is given by:

η = 1 - (TC/TH)

where TC is the temperature of the cold reservoir and TH is the temperature of the hot reservoir.

For the four Carnot heat engines in this problem, we list their efficiencies in decreasing order:

Engine 2: η = 1 - (11/100) = 0.89
Engine 1: η = 1 - (11/200) = 0.945
Engine 4: η = 1 - (22/100) = 0.78
Engine 3: η = 1 - (22/200) = 0.89

Engines 2 and 3 tie for efficiency since they have the same hot and cold reservoir temperatures. Engines 1 and 4 also tie for efficiency since they have the same temperature ratio between the hot and cold reservoirs. Therefore, the rank of efficiencies from least to greatest is: Engine 4, Engine 2 (tie), Engine 3 (tie), Engine 1 (tie). Thus, the correct answer is E.

The Temperature TC of the Cold Reservoirs and the Temperatures

The Temperature T_C of the Cold Reservoirs and the Temperatures