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Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 is
- a)250 K
- b)300 K
- c)200 K
- d)100 K
Correct answer is option 'C'. Can you explain this answer?
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Two carnot engines are operated in succession. The first one, receives...
Given:
- Temperature of source for first engine (T1) = 400 K
- Temperature of sink for first engine (T2) = ?
- Temperature of sink for second engine (T3) = 100 K
- Efficiency of both engines = Equal
To find: Temperature of sink for first engine (T2)
Concepts used:
- Carnot engine: An ideal engine that operates between two heat reservoirs and has maximum possible efficiency
- Efficiency of Carnot engine: e = 1 - T2/T1 (where T1 is the temperature of the source and T2 is the temperature of the sink)
- Efficiency of two Carnot engines in succession: e = e1 x e2 (where e1 is the efficiency of first engine and e2 is the efficiency of second engine)
Solution:
1. Efficiency of both engines is equal:
- Let e be the efficiency of both engines
- Then, e = e1 x e2 (since the engines are operated in succession)
2. Efficiency of Carnot engine:
- For the first engine, efficiency (e1) is given by e1 = 1 - T2/T1
3. Efficiency of second engine:
- For the second engine, temperature of source is T2 and temperature of sink is T3
- Hence, efficiency (e2) is given by e2 = 1 - T3/T2
4. Substitute values and simplify:
- From step 1, e = e1 x e2
- Substituting the expressions for e1 and e2, we get:
e = (1 - T2/T1) x (1 - T3/T2)
- Since e is equal for both engines, we can equate the expressions:
(1 - T2/T1) x (1 - T3/T2) = e
- Simplifying the above expression, we get:
T2^2 - (T1 + T3) T2 + T1 T3 = 0
- Using the quadratic formula, we get:
T2 = (T1 + T3)/2 + sqrt[(T1 + T3)^2/4 - T1 T3]
5. Substitute values and evaluate:
- Substituting the given values of T1 and T3, we get:
T2 = (400 + 100)/2 + sqrt[(400 + 100)^2/4 - 400 x 100]
T2 = 250 K
Answer: The temperature of sink for the first engine (T2) is 250 K.
- Temperature of source for first engine (T1) = 400 K
- Temperature of sink for first engine (T2) = ?
- Temperature of sink for second engine (T3) = 100 K
- Efficiency of both engines = Equal
To find: Temperature of sink for first engine (T2)
Concepts used:
- Carnot engine: An ideal engine that operates between two heat reservoirs and has maximum possible efficiency
- Efficiency of Carnot engine: e = 1 - T2/T1 (where T1 is the temperature of the source and T2 is the temperature of the sink)
- Efficiency of two Carnot engines in succession: e = e1 x e2 (where e1 is the efficiency of first engine and e2 is the efficiency of second engine)
Solution:
1. Efficiency of both engines is equal:
- Let e be the efficiency of both engines
- Then, e = e1 x e2 (since the engines are operated in succession)
2. Efficiency of Carnot engine:
- For the first engine, efficiency (e1) is given by e1 = 1 - T2/T1
3. Efficiency of second engine:
- For the second engine, temperature of source is T2 and temperature of sink is T3
- Hence, efficiency (e2) is given by e2 = 1 - T3/T2
4. Substitute values and simplify:
- From step 1, e = e1 x e2
- Substituting the expressions for e1 and e2, we get:
e = (1 - T2/T1) x (1 - T3/T2)
- Since e is equal for both engines, we can equate the expressions:
(1 - T2/T1) x (1 - T3/T2) = e
- Simplifying the above expression, we get:
T2^2 - (T1 + T3) T2 + T1 T3 = 0
- Using the quadratic formula, we get:
T2 = (T1 + T3)/2 + sqrt[(T1 + T3)^2/4 - T1 T3]
5. Substitute values and evaluate:
- Substituting the given values of T1 and T3, we get:
T2 = (400 + 100)/2 + sqrt[(400 + 100)^2/4 - 400 x 100]
T2 = 250 K
Answer: The temperature of sink for the first engine (T2) is 250 K.
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Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer?
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Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer?.
Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer?.
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Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two carnot engines are operated in succession. The first one, receives heat from a source at T1 = 400 K and rejects to sink at T2 K. The second engine receives heat rejected by first engine and rejects to another sink at T3=100 K. If the efficiency of both the engines are equal then T2 isa)250 Kb)300 Kc)200 Kd)100 KCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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