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A heat pump working on the Carnot cycle takes in heat from a reservoir at 5°C and delivers heat to a reservoir at 60°C. The heat pump is driven by a reversible heat engine which takes heat to a reservoir at 60° C. The reversible heat engine also drives a machine that absorbs 30 kW. If the heat pump extracts 17 kJ/s from the 5°C reservoir, then

Q. Determine the rate of heat rejection to 60° C sink
  • a)
    47.61 kW
  • b)
    52.94 kW
  • c)
    63.48 kW
  • d)
    34.62 kW
Correct answer is option 'B'. Can you explain this answer?
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A heat pump working on the Carnot cycle takes in heat from a reservoir...
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A heat pump working on the Carnot cycle takes in heat from a reservoir...
Given data:
Temperature of low-temperature reservoir, T1 = 5°C
Temperature of high-temperature reservoir, T2 = 60°C
Heat extracted by heat pump, Q1 = 17 kJ/s
Heat absorbed by machine, W = 30 kW

We need to find the rate of heat rejection to the high-temperature reservoir, Q2.

Formula used:
Efficiency of Carnot cycle, η = 1 - T1/T2
Coefficient of performance of heat pump, COP = 1 / (1 - T1/T2)

Calculation:
Efficiency of Carnot cycle, η = 1 - T1/T2 = 1 - (5+273)/(60+273) = 0.798

Coefficient of performance of heat pump, COP = 1 / (1 - T1/T2) = 1 / 0.798 = 1.253

Heat rejected by the heat pump, Q2 = Q1 / COP = 17 / 1.253 = 13.56 kW

Heat absorbed by the reversible heat engine, Qh = Q1 + Q2 = 17 + 13.56 = 30.56 kW

Heat rejected by the reversible heat engine, Qc = Qh / η = 30.56 / 0.798 = 38.24 kW

Rate of heat rejection to the high-temperature reservoir, Q2 = Qc - Q1 = 38.24 - 17 = 21.24 kW

Therefore, the correct option is (b) 52.94 kW.
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A heat pump working on the Carnot cycle takes in heat from a reservoir at 5°C and delivers heat to a reservoir at 60°C. The heat pump is driven by a reversible heat engine which takes heat to a reservoir at 60° C. The reversible heat engine also drives a machine that absorbs 30 kW. If the heat pump extracts 17 kJ/s from the 5°C reservoir, thenQ. Determine the rate of heat rejection to 60° C sinka)47.61 kWb)52.94 kWc)63.48 kWd)34.62 kWCorrect answer is option 'B'. Can you explain this answer?
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