Difficulty: Hard
Correct Answer: COP = (T3/(T2 − T3)) × ((T1 − T2)/T1)
Explanation:
Concept/Approach
An 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 sketch
Carnot 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 check
B matches the ideal expression.
Other options either omit the driving-temperature factor or misplace temperatures.
Final Answer
COP = (T3/(T2 − T3)) × ((T1 − T2)/T1).
Discussion & Comments