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A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300K. The Coefficient of Performance (COP) of the heat pump is ___________.
Correct answer is between '1.66,1.70'. Can you explain this answer?
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Calculation of Coefficient of Performance (COP) of the heat pump:
To find the Coefficient of Performance (COP) of the heat pump, we need to use the formula:
COP = Qh / W
where Qh is the amount of heat delivered to the room and W is the amount of work done by the heat pump.
Step 1: Find the amount of heat delivered to the room (Qh):
The amount of heat delivered to the room can be calculated using the formula:
Qh = Qc + W
where Qc is the amount of heat absorbed from the outside environment.
Given that the heat pump absorbs 10 kW of heat from the outside environment, we have:
Qc = 10 kW
Therefore, the amount of heat delivered to the room is:
Qh = 10 kW + W
Step 2: Find the amount of work done by the heat pump (W):
Given that the heat pump absorbs 15 kW of work, we have:
W = 15 kW
Step 3: Calculate the Coefficient of Performance (COP):
Substituting the values of Qh and W into the formula for COP, we get:
COP = (10 kW + 15 kW) / 15 kW
COP = 25 kW / 15 kW
COP ≈ 1.67
Therefore, the Coefficient of Performance (COP) of the heat pump is approximately 1.67.
Explanation:
The Coefficient of Performance (COP) of a heat pump represents the ratio of the amount of heat delivered to the room to the amount of work done by the heat pump. In this case, the heat pump absorbs 10 kW of heat from the outside environment and delivers it to the room while absorbing 15 kW of work.
The COP of the heat pump is a measure of its efficiency. A higher COP indicates a more efficient heat pump. In this case, the COP is approximately 1.67, which means that for every unit of work done by the heat pump, it delivers approximately 1.67 units of heat to the room.
This high COP value indicates that the heat pump is able to effectively transfer heat from the outside environment to the room, providing an efficient heating solution.
To find the Coefficient of Performance (COP) of the heat pump, we need to use the formula:
COP = Qh / W
where Qh is the amount of heat delivered to the room and W is the amount of work done by the heat pump.
Step 1: Find the amount of heat delivered to the room (Qh):
The amount of heat delivered to the room can be calculated using the formula:
Qh = Qc + W
where Qc is the amount of heat absorbed from the outside environment.
Given that the heat pump absorbs 10 kW of heat from the outside environment, we have:
Qc = 10 kW
Therefore, the amount of heat delivered to the room is:
Qh = 10 kW + W
Step 2: Find the amount of work done by the heat pump (W):
Given that the heat pump absorbs 15 kW of work, we have:
W = 15 kW
Step 3: Calculate the Coefficient of Performance (COP):
Substituting the values of Qh and W into the formula for COP, we get:
COP = (10 kW + 15 kW) / 15 kW
COP = 25 kW / 15 kW
COP ≈ 1.67
Therefore, the Coefficient of Performance (COP) of the heat pump is approximately 1.67.
Explanation:
The Coefficient of Performance (COP) of a heat pump represents the ratio of the amount of heat delivered to the room to the amount of work done by the heat pump. In this case, the heat pump absorbs 10 kW of heat from the outside environment and delivers it to the room while absorbing 15 kW of work.
The COP of the heat pump is a measure of its efficiency. A higher COP indicates a more efficient heat pump. In this case, the COP is approximately 1.67, which means that for every unit of work done by the heat pump, it delivers approximately 1.67 units of heat to the room.
This high COP value indicates that the heat pump is able to effectively transfer heat from the outside environment to the room, providing an efficient heating solution.
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A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300K. The Coefficient of Performance (COP) of the heat pump is ___________.Correct answer is between '1.66,1.70'. Can you explain this answer?
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