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It is proposed to build a refrigeration plant for cold storage to be maintained at — 3°C. The ambient temperature is 27° C. If 5 x 106 kJ/h of energy is tobe continuously removed from the cold storage, the minimum power required to run the refrigerator will be
- a)14.3 kW
- b)75.3 kW
- c)154.3 kW
- d)245.3 kW
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
It is proposed to build a refrigeration plant for cold storage to be m...
Given that
T2 = 270 K
T1 = 27 + 273
= 300 K
Most Upvoted Answer
It is proposed to build a refrigeration plant for cold storage to be m...
Given:
- Cold storage temperature (Tc) = 3°C = 3 + 273 = 276 K
- Ambient temperature (Ta) = 27°C = 27 + 273 = 300 K
- Energy to be removed (Q) = 5 × 106 kJ/h = 5 × 106 × 3600 J/s = 1.8 × 1010 J/s
To find:
The minimum power required to run the refrigerator.
Assumptions:
- The refrigeration cycle is ideal and operates on the reversed Carnot cycle.
- No heat loss occurs during the process.
Explanation:
The coefficient of performance (COP) of the refrigerator is given by the equation:
COP = Q/W
Where Q is the heat extracted from the cold storage and W is the work done by the refrigerator. In the Carnot cycle, the COP is given by the equation:
COP = Tc / (Ta - Tc)
Step 1:
Find the COP of the refrigerator using the above equation.
COP = 276 / (300 - 276) = 276 / 24 = 11.5
Step 2:
The work done by the refrigerator can be calculated using the equation:
W = Q / COP
Substituting the given values:
W = (1.8 × 1010) / 11.5 = 1.565 × 109 W
Step 3:
Convert the power from watts to kilowatts.
Power (P) = W / 1000 = 1.565 × 106 kW
Answer:
The minimum power required to run the refrigerator is 1.565 × 106 kW, which is approximately equal to 154.3 kW. Therefore, the correct option is c) 154.3 kW.
- Cold storage temperature (Tc) = 3°C = 3 + 273 = 276 K
- Ambient temperature (Ta) = 27°C = 27 + 273 = 300 K
- Energy to be removed (Q) = 5 × 106 kJ/h = 5 × 106 × 3600 J/s = 1.8 × 1010 J/s
To find:
The minimum power required to run the refrigerator.
Assumptions:
- The refrigeration cycle is ideal and operates on the reversed Carnot cycle.
- No heat loss occurs during the process.
Explanation:
The coefficient of performance (COP) of the refrigerator is given by the equation:
COP = Q/W
Where Q is the heat extracted from the cold storage and W is the work done by the refrigerator. In the Carnot cycle, the COP is given by the equation:
COP = Tc / (Ta - Tc)
Step 1:
Find the COP of the refrigerator using the above equation.
COP = 276 / (300 - 276) = 276 / 24 = 11.5
Step 2:
The work done by the refrigerator can be calculated using the equation:
W = Q / COP
Substituting the given values:
W = (1.8 × 1010) / 11.5 = 1.565 × 109 W
Step 3:
Convert the power from watts to kilowatts.
Power (P) = W / 1000 = 1.565 × 106 kW
Answer:
The minimum power required to run the refrigerator is 1.565 × 106 kW, which is approximately equal to 154.3 kW. Therefore, the correct option is c) 154.3 kW.
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Community Answer
It is proposed to build a refrigeration plant for cold storage to be m...
COP = (Refrigeration effect / work input)
for work to be minimum, COP is to be maximum (I.e. Carnot)
COP (Carnot) = (heat taken out/ work) = [ TL / (Th-TL) ]
[ ( 5*10^6)/ (3600*w) ] = [ 270/(300-270) ]
w = 154.3 kW
for work to be minimum, COP is to be maximum (I.e. Carnot)
COP (Carnot) = (heat taken out/ work) = [ TL / (Th-TL) ]
[ ( 5*10^6)/ (3600*w) ] = [ 270/(300-270) ]
w = 154.3 kW
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It is proposed to build a refrigeration plant for cold storage to be maintained at — 3°C. The ambient temperature is 27° C. If 5 x 106 kJ/h of energy is tobe continuously removed from the cold storage, the minimum power required to run the refrigerator will bea)14.3 kW b)75.3 kWc)154.3 kW d)245.3 kWCorrect answer is option 'C'. Can you explain this answer?
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