Consider a Carnot heat engine and a refrigerator operating between the same two thermal energy reservoirs. If the thermal efficiency of the heat engine is 0.80, the COP of the refrigerator is

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Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
Eff=0.8
"Let LH=TL/TH and HL=TH/TL=1/LH. Then, Eff=1-TL/TH=1-LH and COP_R=TL/(TH-TL)=1/(TH/TL-1)=1/(1/LH-1) "
Eff=1-LH
COP=1/(1/LH-1)
 "Some Wrong Solutions with Common Mistakes:"
W1_COP=Eff "Setting them equal to each other"
W2_COP=1/Eff "Setting COP equal to inverse of efficiency"

Consider a Carnot Heat Engine and a Refrigerator Operating Between