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An industrial heat pump operates between the temperature 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 ____.
Correct answer is '4'. Can you explain this answer?
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An industrial heat pump operates between the temperature of 27°C ...
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An industrial heat pump operates between the temperature of 27°C ...
Explanation:
Given data:
- Temperature at the evaporator (low temperature) = 13°C
- Temperature at the condenser (high temperature) = 27°C
- Heat addition rate = 750 W
- Heat rejection rate = 1000 W
Coefficient of Performance (COP)
The Coefficient of Performance (COP) is defined as the ratio of heat output to the work input of a heat pump. It is given by:
COP = Heat output / Work input
Calculation of COP
The heat input to the heat pump is equal to the heat rejected plus the heat output. Therefore,
Heat input = Heat output + Heat rejected
750 W = Heat output + 1000 W
Heat output = 750 W – 1000 W = -250 W (negative sign indicates heat is being removed)
Now, the COP can be calculated as:
COP = Heat output / Work input = -250 W / 750 W = -1/3
The negative value of COP indicates that the heat pump is not operating in the desired mode. This is because the heat pump is rejecting more heat than it is absorbing. Therefore, the COP cannot be determined from the given data.
However, if we assume that the heat rejection rate is the same as the heat addition rate, then the heat output would be zero, and the COP can be calculated as:
Heat input = Heat output + Heat rejected = 750 W + 750 W = 1500 W
COP = Heat output / Work input = 0 / 750 W = 0
This is not a realistic scenario, but it shows that the COP can be zero if the heat output is zero.
Therefore, the given answer of 4 for COP is incorrect, and the COP cannot be determined from the given data without making assumptions.
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An industrial heat pump operates between the temperature 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 ____.Correct answer is '4'. Can you explain this answer?
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