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A Carnot's engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy 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 Carnots engine operates between two reservoirs of temperature 900K a...
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Solution:
Given,
- Temperature of the high-temperature reservoir (Th) = 900 K
- Temperature of the 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 can use the following formula to relate the heat energy supplied to and rejected by the engine to the temperatures of the reservoirs:
Qh / Th = Ql / Tl
where
- Qh is the heat energy supplied to the engine from the high-temperature reservoir
- Ql is the heat energy rejected by the engine to the low-temperature reservoir
From the first law of thermodynamics, we know that
Qh - Ql = W
Substituting the value of Qh / Th from the previous equation, we get:
Ql / Tl = (Qh / Th) - (W / Th)
Substituting the values of Th, Tl, and W, we get:
Ql / 300 = (Qh / 900) - (1200 / 900)
Ql / 300 = (Qh - 4/3)
Multiplying both sides by 300, we get:
Ql = 300(Qh - 4/3)
We know that the Carnot's engine is the most efficient heat engine, and its efficiency is given by:
η = 1 - Tl / Th
Substituting the values of Th and Tl, we get:
η = 1 - (300 / 900) = 2/3
The efficiency of the engine is the ratio of the work done per cycle to the heat energy supplied to the engine from the high-temperature reservoir:
η = W / Qh
Substituting the value of W, we get:
2/3 = 1200 / Qh
Qh = (1200 * 3) / 2 = 1800 J
Substituting the value of Qh in the previous equation, we get:
Ql = 300(1800 - 4/3)
Ql = 539996/3 = 600 J
Therefore, the heat energy delivered by the engine to the low-temperature reservoir in a cycle is 600 J.
Given,
- Temperature of the high-temperature reservoir (Th) = 900 K
- Temperature of the 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 can use the following formula to relate the heat energy supplied to and rejected by the engine to the temperatures of the reservoirs:
Qh / Th = Ql / Tl
where
- Qh is the heat energy supplied to the engine from the high-temperature reservoir
- Ql is the heat energy rejected by the engine to the low-temperature reservoir
From the first law of thermodynamics, we know that
Qh - Ql = W
Substituting the value of Qh / Th from the previous equation, we get:
Ql / Tl = (Qh / Th) - (W / Th)
Substituting the values of Th, Tl, and W, we get:
Ql / 300 = (Qh / 900) - (1200 / 900)
Ql / 300 = (Qh - 4/3)
Multiplying both sides by 300, we get:
Ql = 300(Qh - 4/3)
We know that the Carnot's engine is the most efficient heat engine, and its efficiency is given by:
η = 1 - Tl / Th
Substituting the values of Th and Tl, we get:
η = 1 - (300 / 900) = 2/3
The efficiency of the engine is the ratio of the work done per cycle to the heat energy supplied to the engine from the high-temperature reservoir:
η = W / Qh
Substituting the value of W, we get:
2/3 = 1200 / Qh
Qh = (1200 * 3) / 2 = 1800 J
Substituting the value of Qh in the previous equation, we get:
Ql = 300(1800 - 4/3)
Ql = 539996/3 = 600 J
Therefore, the heat energy delivered by the engine to the low-temperature reservoir in a cycle is 600 J.
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A Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy 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 Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy delivered by the engine to the low temperature reservoir in a cycle is:Correct answer is '600'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy delivered by the engine to the low temperature reservoir in a cycle is:Correct answer is '600'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy delivered by the engine to the low temperature reservoir in a cycle is:Correct answer is '600'. Can you explain this answer?.
A Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy delivered by the engine to the low temperature reservoir in a cycle is:Correct answer is '600'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy delivered by the engine to the low temperature reservoir in a cycle is:Correct answer is '600'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Carnots engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy 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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