The temperature T_L 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)3, 4, 1, 2 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 is given by (Th - Tc)/Th, where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir. The higher the difference between Th and Tc, the higher the efficiency.

Ranking the engines by their hot reservoir temperatures, we get:
Engine 2: Th = 400 K
Engine 1: Th = 500 K
Engine 4: Th = 600 K
Engine 3: Th = 700 K

Now we can calculate the efficiency for each engine using the formula above:

Engine 1: (500-100)/500 = 80%
Engine 2: (400-100)/400 = 75%
Engine 3: (700-300)/700 = 57%
Engine 4: (600-300)/600 = 50%

Therefore, the engines ranked in order from greatest to least efficiency are 1, 2, 4, 3, and the correct choice is E.

The Temperature TL of the Cold Reservoirs and the Temperatures

The Temperature T_L of the Cold Reservoirs and the Temperatures