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An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump is
- a)7.5
- b)6.5
- c)4.0
- d)3.0
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
An industrial heat pump operates between the temperatures of 27°C ...
It may not be a reversible heat pump. So we use only heat data to get COP
Hence, the correct option is (c).
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An industrial heat pump operates between the temperatures of 27°C ...
Understanding Coefficient of Performance (COP)
The Coefficient of Performance (COP) for a heat pump is defined as the ratio of heat delivered to the work input required to transfer that heat. It can be expressed mathematically as:
COP = Qh / W
where:
- Qh = Heat delivered to the hot reservoir (heat addition, in watts)
- W = Work input (in watts)
Given Values
- Heat addition (Qh) = 750 W
- Heat rejection (Qc) = 1000 W
To find the work input (W), we can use the relation:
W = Qc - Qh
Calculating Work Input
Now, substituting the given values:
- W = 1000 W - 750 W
- W = 250 W
Calculating COP
Now, we can compute the COP:
COP = Qh / W
Substituting the values:
- COP = 750 W / 250 W
- COP = 3.0
Conclusion
The calculated COP of the heat pump is 3.0, which matches option 'd'.
However, if the problem states that the correct answer is option 'c', which indicates a COP of 4.0, it’s essential to reevaluate the assumptions or constraints of the system or check for any additional information that might change the parameters of the problem.
In typical scenarios, a heat pump with these rates of heat addition and rejection would yield a COP of 3.0, based on the calculations shown.
The Coefficient of Performance (COP) for a heat pump is defined as the ratio of heat delivered to the work input required to transfer that heat. It can be expressed mathematically as:
COP = Qh / W
where:
- Qh = Heat delivered to the hot reservoir (heat addition, in watts)
- W = Work input (in watts)
Given Values
- Heat addition (Qh) = 750 W
- Heat rejection (Qc) = 1000 W
To find the work input (W), we can use the relation:
W = Qc - Qh
Calculating Work Input
Now, substituting the given values:
- W = 1000 W - 750 W
- W = 250 W
Calculating COP
Now, we can compute the COP:
COP = Qh / W
Substituting the values:
- COP = 750 W / 250 W
- COP = 3.0
Conclusion
The calculated COP of the heat pump is 3.0, which matches option 'd'.
However, if the problem states that the correct answer is option 'c', which indicates a COP of 4.0, it’s essential to reevaluate the assumptions or constraints of the system or check for any additional information that might change the parameters of the problem.
In typical scenarios, a heat pump with these rates of heat addition and rejection would yield a COP of 3.0, based on the calculations shown.
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An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct answer is option 'C'. Can you explain this answer?
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An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct 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 An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct 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 An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct answer is option 'C'. Can you explain this answer?.
An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct 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 An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct 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 An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump isa)7.5b)6.5c)4.0d)3.0Correct answer is option 'C'. Can you explain this answer?.
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