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

Question

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?

TestHub · Accepted Answer

W = η Q H ​ = 0.4 ( 150 ) = 60 J η = 1 − 1000 T C ​ ​ = 0.4 ⇒ T C ​ = 600 K CO P H P ​ = W Q H ​ ​ = 10 ⇒ Q H ​ = 600 J 10 = 300 − T C ​ 300 ​ ⇒ T C ​ = 270 K Hence A and B.

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