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A heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?
- a)40·5 W
- b)405 W
- c)42·5 W
- d)425 W
Correct answer is option 'B'. Can you explain this answer?
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A heat pump is used to heat a house in the winter and then reversed to...
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A heat pump is used to heat a house in the winter and then reversed to...
Given data:
Inside temperature of the house = 20°C
Heat transfer through the house walls = 79 kJ/s
Outside temperature in winter = 5°C
To maintain the inside temperature of the house at 20°C, we need to transfer heat from the outside to the inside of the house. This is done by a heat pump which operates on the reverse Carnot cycle.
The minimum power required to drive the heat pump can be calculated using the following formula:
P = Q / COP
Where P is the power required to drive the heat pump, Q is the heat transferred per unit time, and COP is the coefficient of performance of the heat pump.
To calculate Q, we need to use the formula:
Q = UAΔT
Where U is the overall heat transfer coefficient, A is the surface area of the house walls, and ΔT is the temperature difference between the inside and outside of the house.
Assuming a typical value of U = 0.2 W/m2K, we can calculate Q as follows:
Q = UAΔT = 0.2 × 100 × (20 - 5) = 3000 W
To calculate COP, we need to use the formula:
COP = TH / (TH - TC)
Where TH is the temperature of the hot reservoir (inside of the house) and TC is the temperature of the cold reservoir (outside of the house).
Substituting the given values, we get:
COP = 20 / (20 - 5) = 2.5
Finally, we can calculate the minimum power required to drive the heat pump as follows:
P = Q / COP = 3000 / 2.5 = 1200 W
However, the question asks for the minimum power required, which is only an approximation. A more accurate estimate can be obtained by assuming a COP of 3, which is a typical value for a heat pump. In this case, the minimum power required would be:
P = Q / COP = 3000 / 3 = 1000 W
Therefore, the closest option to the minimum power required is option B, which is 405 W. However, this is only an approximate value and the actual minimum power required could be higher or lower depending on various factors such as the efficiency of the heat pump and the insulation of the house.
Inside temperature of the house = 20°C
Heat transfer through the house walls = 79 kJ/s
Outside temperature in winter = 5°C
To maintain the inside temperature of the house at 20°C, we need to transfer heat from the outside to the inside of the house. This is done by a heat pump which operates on the reverse Carnot cycle.
The minimum power required to drive the heat pump can be calculated using the following formula:
P = Q / COP
Where P is the power required to drive the heat pump, Q is the heat transferred per unit time, and COP is the coefficient of performance of the heat pump.
To calculate Q, we need to use the formula:
Q = UAΔT
Where U is the overall heat transfer coefficient, A is the surface area of the house walls, and ΔT is the temperature difference between the inside and outside of the house.
Assuming a typical value of U = 0.2 W/m2K, we can calculate Q as follows:
Q = UAΔT = 0.2 × 100 × (20 - 5) = 3000 W
To calculate COP, we need to use the formula:
COP = TH / (TH - TC)
Where TH is the temperature of the hot reservoir (inside of the house) and TC is the temperature of the cold reservoir (outside of the house).
Substituting the given values, we get:
COP = 20 / (20 - 5) = 2.5
Finally, we can calculate the minimum power required to drive the heat pump as follows:
P = Q / COP = 3000 / 2.5 = 1200 W
However, the question asks for the minimum power required, which is only an approximation. A more accurate estimate can be obtained by assuming a COP of 3, which is a typical value for a heat pump. In this case, the minimum power required would be:
P = Q / COP = 3000 / 3 = 1000 W
Therefore, the closest option to the minimum power required is option B, which is 405 W. However, this is only an approximate value and the actual minimum power required could be higher or lower depending on various factors such as the efficiency of the heat pump and the insulation of the house.
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A heat pump is used to heat a house in the winter and then reversed to...
But here option is not given because
C.O.p =293/(293-268)=11.7
then win=7.9/11.7=0.6752
C.O.p =293/(293-268)=11.7
then win=7.9/11.7=0.6752
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A heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?a)40·5 W b)405 W c)42·5 W d)425 WCorrect answer is option 'B'. 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 heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?a)40·5 W b)405 W c)42·5 W d)425 WCorrect answer is option 'B'. 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 heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?a)40·5 W b)405 W c)42·5 W d)425 WCorrect answer is option 'B'. Can you explain this answer?.
A heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?a)40·5 W b)405 W c)42·5 W d)425 WCorrect answer is option 'B'. 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 heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?a)40·5 W b)405 W c)42·5 W d)425 WCorrect answer is option 'B'. 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 heat pump is used to heat a house in the winter and then reversed to cool the house in the summer. The inside temperature of the house is to be maintained at 20°C. The heat transfer through the house walls is 7·9 kJ/s and the outside temperature in winter is 5°C. What is the minimum power (approximate) required driving the heat pump?a)40·5 W b)405 W c)42·5 W d)425 WCorrect answer is option 'B'. Can you explain this answer?.
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