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Two reversible heat engines operating between temperatures 2000 K and T K and T K and 500 K respectively. What is the intermediate temperature, if the efficiency of both the cycles is same?
- a)900 K
- b)1000 K
- c)1500 K
- d)1600 K
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two reversible heat engines operating between temperatures 2000 K and ...
Efficiency of first engine (E1), 
Efficiency of second engine 
As efficiency of both engine is same,
So, η1 = η2
⇒ T2 = 2000 × 50
Short Trick:
When efficiency of both engines are equal, then intermediate temperature
Most Upvoted Answer
Two reversible heat engines operating between temperatures 2000 K and ...
Explanation:
To find the intermediate temperature (T), we need to compare the efficiency of the two cycles.
Efficiency of a heat engine:
The efficiency of a heat engine is given by the formula:
η = 1 - (Tc/Th)
Where η is the efficiency, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.
Efficiency of the first cycle:
For the first cycle, the hot reservoir temperature (Th) is given as 2000 K and the cold reservoir temperature (Tc) is given as T K. Therefore, the efficiency of the first cycle is:
η1 = 1 - (T/T1)
Efficiency of the second cycle:
For the second cycle, the hot reservoir temperature (Th) is given as T K and the cold reservoir temperature (Tc) is given as 500 K. Therefore, the efficiency of the second cycle is:
η2 = 1 - (500/T)
Since both cycles have the same efficiency, η1 = η2. Therefore, we can equate the two expressions:
1 - (T/T1) = 1 - (500/T)
Simplifying this equation:
T/T1 = 500/T
Cross-multiplying:
T^2 = 500 * T1
T = √(500 * T1)
Since T1 is given as 2000 K, substituting this value:
T = √(500 * 2000) = √(1000000) = 1000 K
Therefore, the intermediate temperature is 1000 K.
Conclusion:
The intermediate temperature between the two heat engines is 1000 K. Therefore, the correct answer is option 'A'
To find the intermediate temperature (T), we need to compare the efficiency of the two cycles.
Efficiency of a heat engine:
The efficiency of a heat engine is given by the formula:
η = 1 - (Tc/Th)
Where η is the efficiency, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.
Efficiency of the first cycle:
For the first cycle, the hot reservoir temperature (Th) is given as 2000 K and the cold reservoir temperature (Tc) is given as T K. Therefore, the efficiency of the first cycle is:
η1 = 1 - (T/T1)
Efficiency of the second cycle:
For the second cycle, the hot reservoir temperature (Th) is given as T K and the cold reservoir temperature (Tc) is given as 500 K. Therefore, the efficiency of the second cycle is:
η2 = 1 - (500/T)
Since both cycles have the same efficiency, η1 = η2. Therefore, we can equate the two expressions:
1 - (T/T1) = 1 - (500/T)
Simplifying this equation:
T/T1 = 500/T
Cross-multiplying:
T^2 = 500 * T1
T = √(500 * T1)
Since T1 is given as 2000 K, substituting this value:
T = √(500 * 2000) = √(1000000) = 1000 K
Therefore, the intermediate temperature is 1000 K.
Conclusion:
The intermediate temperature between the two heat engines is 1000 K. Therefore, the correct answer is option 'A'
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Two reversible heat engines operating between temperatures 2000 K and T K and T K and 500 K respectively. What is the intermediate temperature, if the efficiency of both the cycles is same?a)900 Kb)1000 Kc)1500 Kd)1600 KCorrect answer is option 'A'. Can you explain this answer?
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Two reversible heat engines operating between temperatures 2000 K and T K and T K and 500 K respectively. What is the intermediate temperature, if the efficiency of both the cycles is same?a)900 Kb)1000 Kc)1500 Kd)1600 KCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two reversible heat engines operating between temperatures 2000 K and T K and T K and 500 K respectively. What is the intermediate temperature, if the efficiency of both the cycles is same?a)900 Kb)1000 Kc)1500 Kd)1600 KCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two reversible heat engines operating between temperatures 2000 K and T K and T K and 500 K respectively. What is the intermediate temperature, if the efficiency of both the cycles is same?a)900 Kb)1000 Kc)1500 Kd)1600 KCorrect answer is option 'A'. Can you explain this answer?.
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