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A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2 and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2 is
- a)680 K
- b)640 K
- c)600 K
- d)None
Correct answer is option 'C'. Can you explain this answer?
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A reversible heat engine A (based on carnot cycle) absorbs heat from a...
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A reversible heat engine A (based on carnot cycle) absorbs heat from a...
Explanation:
To solve this problem, we need to apply the principles of the Carnot cycle and the efficiency of a heat engine.
Carnot Cycle:
The Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. This cycle is used as a benchmark for the maximum efficiency that a heat engine can achieve.
Efficiency:
The efficiency of a heat engine is defined as the ratio of the useful work output to the heat energy input. For a reversible heat engine operating between two reservoirs at temperatures T1 and T2, the efficiency is given by the formula:
Efficiency = 1 - T2/T1
Solution:
Let's assume the amount of heat absorbed by engine A is Q. According to the problem statement, engine A absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. Therefore, the efficiency of engine A is given by:
Efficiency of A = 1 - T2/1000
Now, engine B absorbs the same amount of heat Q as rejected by engine A, from a reservoir at T2 and rejects energy to a reservoir at 360 K. Therefore, the efficiency of engine B is given by:
Efficiency of B = 1 - 360/T2
Since the efficiencies of engines A and B are the same, we can equate the two expressions:
1 - T2/1000 = 1 - 360/T2
Simplifying the equation:
T2/1000 = 360/T2
Cross-multiplying:
T2^2 = 360000
Taking the square root:
T2 = √360000
Calculating the value of T2:
T2 ≈ 600 K
Therefore, the temperature T2 is 600 K, which corresponds to option (c).
To solve this problem, we need to apply the principles of the Carnot cycle and the efficiency of a heat engine.
Carnot Cycle:
The Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. This cycle is used as a benchmark for the maximum efficiency that a heat engine can achieve.
Efficiency:
The efficiency of a heat engine is defined as the ratio of the useful work output to the heat energy input. For a reversible heat engine operating between two reservoirs at temperatures T1 and T2, the efficiency is given by the formula:
Efficiency = 1 - T2/T1
Solution:
Let's assume the amount of heat absorbed by engine A is Q. According to the problem statement, engine A absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. Therefore, the efficiency of engine A is given by:
Efficiency of A = 1 - T2/1000
Now, engine B absorbs the same amount of heat Q as rejected by engine A, from a reservoir at T2 and rejects energy to a reservoir at 360 K. Therefore, the efficiency of engine B is given by:
Efficiency of B = 1 - 360/T2
Since the efficiencies of engines A and B are the same, we can equate the two expressions:
1 - T2/1000 = 1 - 360/T2
Simplifying the equation:
T2/1000 = 360/T2
Cross-multiplying:
T2^2 = 360000
Taking the square root:
T2 = √360000
Calculating the value of T2:
T2 ≈ 600 K
Therefore, the temperature T2 is 600 K, which corresponds to option (c).
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A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer?
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A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer?.
A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A reversible heat engine A (based on carnot cycle) absorbs heat from a reservoir at 1000 K and rejects heat to a reservoir at T2. A second reversible engine B absorbs, the same amount of heat as rejected by the engine A, from the reservoir at T2and rejects energy to a reservoir at 360 K. If the efficiencies of engines A and B are the same then the temperautre T2isa)680 Kb)640 Kc)600 Kd)NoneCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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