Question

The temperatures TC of the cold reservoirs and the temperatures TH of the hot reservoirs for four Carnot heat engines are:

engine 1: TC = 400K and TH = 500K
engine 2: TC = 500K and TH = 600K
engine 3: TC = 400K and TH = 600K
engine 4: TC = 600K and TH = 800K

Rank these engines according to their efficiencies, least to greatest

A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 1, 3, 2, 4
D) 2, 1, 3, 4

Answer 1

The efficiencies of the four Carnot heat engines provided are calculated and ranked from least to greatest. Answer: B) 4, 3, 2, 1

Step-by-step explanation:

The efficiency of a Carnot heat engine is given by the formula:

efficiency = 1 - (TC/TH)

where TC is the temperature of the cold reservoir and TH is the temperature of the hot reservoir. The higher the efficiency, the better the engine can convert heat into work.

Now, let's calculate the efficiency for each engine:

1. Engine 1: TC = 400K, TH = 500K, efficiency = 1 - (400/500) = 0.2
2. Engine 2: TC = 500K, TH = 600K, efficiency = 1 - (500/600) = 0.167
3. Engine 3: TC = 400K, TH = 600K, efficiency = 1 - (400/600) = 0.333
4. Engine 4: TC = 600K, TH = 800K, efficiency = 1 - (600/800) = 0.25
   

Ranking the engines according to their efficiencies from least to greatest:

Answer: B) 4, 3, 2, 1