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A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?
- a)600 K
- b)625 K
- c)650 K
- d)675 K
Correct answer is option 'C'. Can you explain this answer?
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A reversible engine operates between temperatures 900 K & T2 (T2 &...
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A reversible engine operates between temperatures 900 K & T2 (T2 &...
Reversible engines operate between two temperature reservoirs and convert heat energy into work. The efficiency of a reversible engine is given by the Carnot efficiency formula, which is the ratio of the temperature difference between the two reservoirs to the higher temperature reservoir.
Let's consider the two reversible engines in series. The first engine operates between temperatures 900 K and T2, and the second engine operates between temperatures T2 and 400 K. We are given that the work outputs of both engines are equal.
To find the value of T2, we can equate the efficiencies of both engines.
Efficiency of the first engine:
η1 = 1 - (T2 / 900)
Efficiency of the second engine:
η2 = 1 - (400 / T2)
Since the work outputs of both engines are equal, we can equate their efficiencies:
η1 = η2
1 - (T2 / 900) = 1 - (400 / T2)
Simplifying the equation:
T2 - (T2^2 / 900) = 900 - (400 * T2 / T2)
T2 - (T2^2 / 900) = 900 - 400
T2 - (T2^2 / 900) = 500
Multiplying both sides by 900 to eliminate the fraction:
900 * T2 - T2^2 = 500 * 900
Rearranging the equation:
T2^2 - 900 * T2 + 500 * 900 = 0
This is a quadratic equation in T2. We can solve this equation using the quadratic formula:
T2 = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = -900, and c = 500 * 900
Calculating the values:
T2 = (-(-900) ± √((-900)^2 - 4 * 1 * (500 * 900))) / (2 * 1)
T2 = (900 ± √(810000 - 1800000)) / 2
T2 = (900 ± √(-990000)) / 2
Since the discriminant is negative, the equation has no real solutions. Therefore, the value of T2 cannot be determined.
Hence, the correct answer cannot be determined from the given information.
Let's consider the two reversible engines in series. The first engine operates between temperatures 900 K and T2, and the second engine operates between temperatures T2 and 400 K. We are given that the work outputs of both engines are equal.
To find the value of T2, we can equate the efficiencies of both engines.
Efficiency of the first engine:
η1 = 1 - (T2 / 900)
Efficiency of the second engine:
η2 = 1 - (400 / T2)
Since the work outputs of both engines are equal, we can equate their efficiencies:
η1 = η2
1 - (T2 / 900) = 1 - (400 / T2)
Simplifying the equation:
T2 - (T2^2 / 900) = 900 - (400 * T2 / T2)
T2 - (T2^2 / 900) = 900 - 400
T2 - (T2^2 / 900) = 500
Multiplying both sides by 900 to eliminate the fraction:
900 * T2 - T2^2 = 500 * 900
Rearranging the equation:
T2^2 - 900 * T2 + 500 * 900 = 0
This is a quadratic equation in T2. We can solve this equation using the quadratic formula:
T2 = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = -900, and c = 500 * 900
Calculating the values:
T2 = (-(-900) ± √((-900)^2 - 4 * 1 * (500 * 900))) / (2 * 1)
T2 = (900 ± √(810000 - 1800000)) / 2
T2 = (900 ± √(-990000)) / 2
Since the discriminant is negative, the equation has no real solutions. Therefore, the value of T2 cannot be determined.
Hence, the correct answer cannot be determined from the given information.
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A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. Can you explain this answer?
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A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. 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 A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. 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 A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. Can you explain this answer?.
A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. 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 A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. 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 A reversible engine operates between temperatures 900 K & T2 (T2 < 900 K), & another reversible engine between T2 & 400 K (T2 > 400 K) in series. What is the value of T2 if work outputs of both the engines are equal?a)600 Kb)625 Kc)650 Kd)675 KCorrect answer is option 'C'. Can you explain this answer?.
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