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A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP is
- a)1.108
- b)1.2
- c)2.2
- d)9.26
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A Carnot heat pump works between temperature limits of 277º C and...
[We may put T1 and T2 in ºC or in K but T1 – T2 will be same]
Most Upvoted Answer
A Carnot heat pump works between temperature limits of 277º C and...
Explanation:
The Carnot cycle is a theoretical thermodynamic cycle that is the most efficient cycle for converting heat into work. The COP (Coefficient of Performance) of a heat pump is defined as the ratio of heat delivered to the heat absorbed from the source.
The COP of a Carnot heat pump can be calculated using the following formula:
COP = (Th - Tc) / Th
Where Th is the temperature of the hot reservoir (in Kelvin) and Tc is the temperature of the cold reservoir (in Kelvin).
Given:
Th = 277 C = 550 K
Tc = 27 C = 300 K
Using the above formula, the COP of the Carnot heat pump can be calculated as:
COP = (550 - 300) / 550 = 0.4545
However, this is the COP of the heat pump when expressed in terms of the temperature difference. To express the COP in terms of the efficiency, we need to use the following formula:
Efficiency = 1 - (Tc / Th)
Where Tc and Th are the temperatures of the cold and hot reservoirs respectively.
Using the above formula, the efficiency of the Carnot heat pump can be calculated as:
Efficiency = 1 - (300 / 550) = 0.4545
Therefore, the COP of the Carnot heat pump is equal to the efficiency, which is 0.4545 or 45.45%. To convert this into a COP value, we need to use the following formula:
COP = 1 / Efficiency
COP = 1 / 0.4545 = 2.2
Therefore, the correct answer is option C, which is 2.2.
The Carnot cycle is a theoretical thermodynamic cycle that is the most efficient cycle for converting heat into work. The COP (Coefficient of Performance) of a heat pump is defined as the ratio of heat delivered to the heat absorbed from the source.
The COP of a Carnot heat pump can be calculated using the following formula:
COP = (Th - Tc) / Th
Where Th is the temperature of the hot reservoir (in Kelvin) and Tc is the temperature of the cold reservoir (in Kelvin).
Given:
Th = 277 C = 550 K
Tc = 27 C = 300 K
Using the above formula, the COP of the Carnot heat pump can be calculated as:
COP = (550 - 300) / 550 = 0.4545
However, this is the COP of the heat pump when expressed in terms of the temperature difference. To express the COP in terms of the efficiency, we need to use the following formula:
Efficiency = 1 - (Tc / Th)
Where Tc and Th are the temperatures of the cold and hot reservoirs respectively.
Using the above formula, the efficiency of the Carnot heat pump can be calculated as:
Efficiency = 1 - (300 / 550) = 0.4545
Therefore, the COP of the Carnot heat pump is equal to the efficiency, which is 0.4545 or 45.45%. To convert this into a COP value, we need to use the following formula:
COP = 1 / Efficiency
COP = 1 / 0.4545 = 2.2
Therefore, the correct answer is option C, which is 2.2.
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A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP isa)1.108 b)1.2 c)2.2 d)9.26Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP isa)1.108 b)1.2 c)2.2 d)9.26Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP isa)1.108 b)1.2 c)2.2 d)9.26Correct answer is option 'C'. Can you explain this answer?.
A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP isa)1.108 b)1.2 c)2.2 d)9.26Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP isa)1.108 b)1.2 c)2.2 d)9.26Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Carnot heat pump works between temperature limits of 277º C and 27º C. Its COP isa)1.108 b)1.2 c)2.2 d)9.26Correct answer is option 'C'. Can you explain this answer?.
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