Q. A Carnot engine used first ideal monoatomic gas and then an ideal diatomic gas, if the source and sink temperatures are $411℃$ and $69℃$, respectively and the engine extract 1000 J of heat from the source in each cycle, then
A) Area enclosed by the $p - V$ diagram is 10 J
B) Heat energy rejected by engine is 1st case is 600 J while that in 2nd case in 113 J
C) Area enclosed by the $p - V$ diagram is 500 J
D) Efficiencies of the engine in both the cases are in ratio 21:25
Explanation
(c) Here, $T_{1} = 411℃ = (411 + 273)K = 684\ K$
$T_{2} = 69℃ = (69 + 273)K = 342\ K$
$Q_{1} = 1000\ J$
$\eta = \frac{W}{Q_{1}} = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{342}{684} = \frac{1}{2}$
$W = \frac{Q_{1}}{Q_{2}} = \frac{1000}{2} = 500\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.