Absorption refrigeration (ideal/Carnot): expression for C.O.P. Let T1 = generator (heat source) temperature, T2 = condenser/absorber (heat sink) temperature, T3 = evaporator (refrigerated space) temperature, all in absolute units (K). Select the correct ideal C.O.P. formula for an absorption refrigerator.
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ACOP = T3 / (T2 − T3)
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BCOP = (T3/(T2 − T3)) × ((T1 − T2)/T1)
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CCOP = (T3/(T1 − T3)) × ((T1 − T2)/T2)
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DCOP = (T2/(T1 − T2)) × ((T3 − T2)/T3)
Answer
Correct Answer: COP = (T3/(T2 − T3)) × ((T1 − T2)/T1)
Explanation
Concept/ApproachAn ideal absorption refrigerator can be modeled as a combination of a heat-driven heat pump (generator/absorber loop operating between T1 and T2) powering a refrigeration cycle (evaporator/condenser between T3 and T2). The maximum (Carnot) C.O.P. is the product of the Carnot C.O.P. of the refrigerator and the efficiency of the heat-to-work conversion analogue.
Derivation sketchCarnot refrigerator between T3 (cold) and T2 (sink): COPref = T3/(T2 − T3).Carnot heat engine analogue between T1 (source) and T2 (sink): ηCarnot = (T1 − T2)/T1.For a heat-driven refrigerator, the effective COP (per unit heat at T1) = COPref × ηCarnot = (T3/(T2 − T3)) × ((T1 − T2)/T1).
Option checkB matches the ideal expression.Other options either omit the driving-temperature factor or misplace temperatures.
Final AnswerCOP = (T3/(T2 − T3)) × ((T1 − T2)/T1).