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:
- Work extracted from the Carnot engine in one cycle is 60 J.
- Temperature of the cold reservoir of the Carnot engine is 600 K.
- Temperature of the cold reservoir of the heat pump is 270 K.
- Heat supplied to the hot reservoir of the heat pump in one cycle is 540 J.
Answer
(1) Work extracted from the Carnot engine in one cycle is 60 J., (2) Temperature of the cold reservoir of the Carnot engine is 600 K., (3) Temperature of the cold reservoir of the heat pump is 270 K.
Solution
Engine: W= QH=0.4 150=60 J. (A) correct.
=1- TCTH TC=0.6 1000=600 K. (B) correct.
Heat pump: COP= THTH-TC=10 300-TC=30 TC=270 K. (C) correct.
Heat delivered to hot reservoir =COP W=10 60=600 J, not 540 J. (D) wrong.
Answer: (A), (B), (C)