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A Carnot refrigerator works between the temperatures of 200 K and 300 K. If the refrigerator receives 1 kW of heat the work requirement will be: 
  • a)
    0.5 kW  
  • b)
    0.67 kW  
  • c)
    1.5 kW  
  • d)
    3 kW 
Correct answer is option 'A'. Can you explain this answer?
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Carnot Refrigerator Efficiency:
The efficiency of a Carnot refrigerator is given by the equation:
Efficiency = (Tc - Th) / Tc
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. In this case, Tc = 200 K and Th = 300 K, so the efficiency is:
Efficiency = (200 - 300) / 200 = -0.5

Work Requirement:
The work requirement for a refrigerator is given by the equation:
Work = Qh - Qc
where Qh is the amount of heat absorbed from the hot reservoir and Qc is the amount of heat rejected to the cold reservoir. In this case, the refrigerator receives 1 kW of heat, so Qh = 1 kW. Using the efficiency equation, we can calculate Qc:
Efficiency = (Qh - Qc) / Qh
-0.5 = (1 - Qc) / 1
-0.5 = 1 - Qc
Qc = 1 - (-0.5) = 1.5 kW

Therefore, the work requirement is:
Work = Qh - Qc
Work = 1 kW - 1.5 kW = -0.5 kW

Since work cannot be negative in this context, we can conclude that the work requirement is 0.5 kW (option A).
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A Carnot refrigerator works between the temperatures of 200 K and 300 K. If the refrigerator receives 1 kW of heat the work requirement will be:a)0.5 kW b)0.67 kW c)1.5 kW d)3 kWCorrect answer is option 'A'. Can you explain this answer?
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