JEE Advanced2025PhysicsThermodynamicsActual
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:
Options
- AWork extracted from the Carnot engine in one cycle is 60 J .
- BTemperature of the cold reservoir of the Carnot engine is 600 K .
- CTemperature of the cold reservoir of the heat pump is 270 K .
- DHeat supplied to the hot reservoir of the heat pump in one cycle is 540 J .
Correct answer
A. Work extracted from the Carnot engine in one cycle is 60 J .
Step-by-step solution
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