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A refrigerator based on reversed Carnot cycle works between two such temperatures that the ratio between the low and high temperature is 0.8. If a heat pump is operated between same temperature range, then what would be its COP?
  • a)
    2    
  • b)
    3  
  • c)
    4    
  • d)
Correct answer is option 'D'. Can you explain this answer?
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Refrigerator based on reversed Carnot cycle and Heat Pump:

Reversed Carnot cycle is a cycle that can be used to describe the functioning of a refrigerator or a heat pump. In this cycle, the working substance is made to go through a series of processes that involves compression, cooling, expansion, and heating. The cycle is reversed because it involves the transfer of heat from a low-temperature reservoir to a high-temperature reservoir, which is opposite to the natural flow of heat.

Refrigerator based on reversed Carnot cycle:

A refrigerator based on the reversed Carnot cycle operates between two temperatures, T1 and T2. The ratio of the low and high temperatures is given by T2/T1 = 0.8. The coefficient of performance (COP) of the refrigerator is given by COP = T1/(T2 - T1). Substituting the given values, we get COP = T1/(0.2T1) = 5.

Heat pump based on reversed Carnot cycle:

A heat pump based on the reversed Carnot cycle also operates between the same two temperatures, T1 and T2. The COP of the heat pump is given by COP = T2/(T2 - T1). Substituting the given values, we get COP = T2/(0.2T2) = 5.

Thus, the correct answer is option D, which is 5.
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