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Operating temperature of a cold storage is –2°C From the surrounding at ambient temperature of 40°C heat leaked into the cold storage is 30 kW. If the actual COP of the plant is 1/10th of the maximum possible COP, then what will be the power required to pump out the heat to maintain the cold storage temperature at –2°C?
- a)1.90 kW
- b)3.70 k W
- c)20 .28 kW
- d)46.50 kW
Correct answer is option 'D'. Can you explain this answer?
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Given data:
Operating temperature of the cold storage = 2°C
Surrounding temperature (ambient temperature) = 40°C
Heat leaked into the cold storage = 30 kW
Actual COP of the plant = 1/10th of the maximum possible COP
To find:
Power required to pump out the heat to maintain the cold storage temperature at 2°C
Solution:
1. Calculation of Carnot COP:
The Carnot COP is given by the formula:
COP_carnot = Tc / (Th - Tc)
where Tc is the cold temperature (2°C) and Th is the hot temperature (40°C).
COP_carnot = 2 / (40 - 2)
COP_carnot = 0.057
2. Calculation of Actual COP:
The actual COP is given as 1/10th of the maximum possible COP. Therefore, the actual COP can be calculated as:
COP_actual = (1/10) * COP_carnot
COP_actual = (1/10) * 0.057
COP_actual = 0.0057
3. Calculation of Heat Pump Work:
The heat pump work can be calculated using the formula:
Power = Q / COP_actual
where Q is the heat leaked into the cold storage (30 kW).
Power = 30 / 0.0057
Power = 5263.1579 kW
4. Conversion of Power from kW to W:
Since the power is given in kW, we need to convert it to W by multiplying it by 1000.
Power = 5263.1579 * 1000
Power = 5263157.9 W
5. Conversion of Power to kW:
Finally, we convert the power back to kW by dividing it by 1000.
Power = 5263157.9 / 1000
Power = 5263.1579 kW
Therefore, the power required to pump out the heat to maintain the cold storage temperature at 2°C is approximately 5263.1579 kW, which is closest to option D (46.50 kW).
Operating temperature of the cold storage = 2°C
Surrounding temperature (ambient temperature) = 40°C
Heat leaked into the cold storage = 30 kW
Actual COP of the plant = 1/10th of the maximum possible COP
To find:
Power required to pump out the heat to maintain the cold storage temperature at 2°C
Solution:
1. Calculation of Carnot COP:
The Carnot COP is given by the formula:
COP_carnot = Tc / (Th - Tc)
where Tc is the cold temperature (2°C) and Th is the hot temperature (40°C).
COP_carnot = 2 / (40 - 2)
COP_carnot = 0.057
2. Calculation of Actual COP:
The actual COP is given as 1/10th of the maximum possible COP. Therefore, the actual COP can be calculated as:
COP_actual = (1/10) * COP_carnot
COP_actual = (1/10) * 0.057
COP_actual = 0.0057
3. Calculation of Heat Pump Work:
The heat pump work can be calculated using the formula:
Power = Q / COP_actual
where Q is the heat leaked into the cold storage (30 kW).
Power = 30 / 0.0057
Power = 5263.1579 kW
4. Conversion of Power from kW to W:
Since the power is given in kW, we need to convert it to W by multiplying it by 1000.
Power = 5263.1579 * 1000
Power = 5263157.9 W
5. Conversion of Power to kW:
Finally, we convert the power back to kW by dividing it by 1000.
Power = 5263157.9 / 1000
Power = 5263.1579 kW
Therefore, the power required to pump out the heat to maintain the cold storage temperature at 2°C is approximately 5263.1579 kW, which is closest to option D (46.50 kW).
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Operating temperature of a cold storage is –2°C From the surrounding at ambient temperature of 40°C heat leaked into the cold storage is 30 kW. If the actual COP of the plant is 1/10th of the maximum possible COP, then what will be the power required to pump out the heat to maintain the cold storage temperature at –2°C?a)1.90 kW b)3.70 k W c)20 .28 kW d)46.50 kWCorrect answer is option 'D'. Can you explain this answer?
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