The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10 . The hot reservoi

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The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10 . The hot reservoir of the heat pump is at a temperature of 300 K . Which of the following statements is/are correct:

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Correct answer: C. Temperature of the cold reservoir of the heat pump is 270 K .

aligned & =0.4 \ & ( COP )_ HP =10 \ & ~W = Q _1=0.4 150=60 ~J \ & COP = Dissered Effect Work input \ & 10= Q _3 ~W \ & Q _3=600 ~J \ & Also \ & =0.4=1- T _2 ~T _1 \ & ~T _2=600 ~K \ & COP = T _3 ~T _3- T _4 =10 aligned aligned & = 300 300- T _4 =10 \ & ~T _4=270 ~K aligned

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