The figure shows the P−V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then,
(A)the process during the path A→B is isothermal
(B)heat flows out of the gas during the path B→C→D✓ Correct
(C)work done during the path A→B→C is zero
(D)positive work is done by the gas in the cycle ABCDA✓ Correct
Answer: (B), (D)
Solution
From the first law, ΔQ=ΔU+W. For path B→C→D, both volume and pressure decrease, so temperature decreases (ΔU<0). Also, work done by the gas is negative (W<0). Therefore, ΔQ<0, meaning heat flows out (option B). For the complete cycle ABCDA, the area enclosed is positive, indicating net positive work done by the gas (option D). Path A→B is not isothermal (it's part of a semicircle, not a hyperbola), and work done during A→B→C is not zero (the area under the curve is non-zero).
JEE Advanced · 2009 · 12 Apr 2009 · Paper 2 · One or more correct options