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A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1,200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is
Correct answer is '600'. Can you explain this answer?
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A Carnot engine operates between two reservoirs of temperatures 900 K ...
Solution:
Given:
Temperature of high-temperature reservoir, Th = 900 K
Temperature of low-temperature reservoir, Tl = 300 K
Work done per cycle, W = 1200 J
We need to find the heat energy delivered by the engine to the low-temperature reservoir in a cycle.
We know that the efficiency of a Carnot engine is given by:
η = (Th - Tl)/Th
We can rearrange this expression to get:
Th/Tl = (Th-Tl)/W + 1
Substituting the given values, we get:
Th/Tl = (900-300)/1200 + 1 = 1.5
Solving for Tl, we get:
Tl = Th/1.5 = 900/1.5 = 600 K
Therefore, the heat energy delivered by the engine to the low-temperature reservoir in a cycle is given by:
Ql = W(1 - 1/Th/Tl) = 1200(1 - 1/1.5) = 600 J
Hence, the correct answer is 600 J.
Summary:
- Efficiency of a Carnot engine: η = (Th - Tl)/Th
- Th/Tl = (Th-Tl)/W + 1
- Tl = Th/1.5
- Ql = W(1 - 1/Th/Tl) = 1200(1 - 1/1.5) = 600 J
Given:
Temperature of high-temperature reservoir, Th = 900 K
Temperature of low-temperature reservoir, Tl = 300 K
Work done per cycle, W = 1200 J
We need to find the heat energy delivered by the engine to the low-temperature reservoir in a cycle.
We know that the efficiency of a Carnot engine is given by:
η = (Th - Tl)/Th
We can rearrange this expression to get:
Th/Tl = (Th-Tl)/W + 1
Substituting the given values, we get:
Th/Tl = (900-300)/1200 + 1 = 1.5
Solving for Tl, we get:
Tl = Th/1.5 = 900/1.5 = 600 K
Therefore, the heat energy delivered by the engine to the low-temperature reservoir in a cycle is given by:
Ql = W(1 - 1/Th/Tl) = 1200(1 - 1/1.5) = 600 J
Hence, the correct answer is 600 J.
Summary:
- Efficiency of a Carnot engine: η = (Th - Tl)/Th
- Th/Tl = (Th-Tl)/W + 1
- Tl = Th/1.5
- Ql = W(1 - 1/Th/Tl) = 1200(1 - 1/1.5) = 600 J
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A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1,200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, isCorrect answer is '600'. Can you explain this answer?
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