Three Carnot engines operate between temperature reservoirs as follows: Engine A: T_h = 1,100 K,T_c = 1,000 K;Engine B: T_h = 1,100 K,T_c = 500 K;Engine C: T_h = 550 K,T_c = 500 K.Which two engines have the same thermal efficiency?

Question

Quizplus · Accepted Answer

The thermal efficiency of a Carnot engine depends only on the temperature of the hot and cold reservoirs, and can be calculated as:

efficiency = 1 - (Tc/Th)

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

Comparing the engines, we see that engine A has Th = 1100 K and Tc = 1000 K, giving it an efficiency of:

efficiency A = 1 - (1000/1100) = 0.091 (rounded to three decimal places)

Engine B has Th = 1100 K and Tc = 500 K, giving it an efficiency of:

efficiency B = 1 - (500/1100) = 0.545 (rounded to three decimal places)

Engine C has Th = 550 K and Tc = 500 K, giving it an efficiency of:

efficiency C = 1 - (500/550) = 0.091 (rounded to three decimal places)

Therefore, engines A and C have the same thermal efficiency of 0.091, making choice C the correct answer.

Three Carnot Engines Operate Between Temperature Reservoirs as Follows: Engine