IIT-JEE 2009 · Paper 2 · Physics Q45

PhysicsMultiple correct+4 / -1Question 45 of 57

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,

the process during the path A → B is isothermal

heat flows out of the gas during the path B → C → D

work done during the path A → B → C is zero

positive work is done by the gas in the cycle ABCDA

Answer and worked solution

Official answer: B, D

Points. A(2, 3), B(3, 2), C(2, 1), D at the left end of the ellipse, traversed clockwise.

(A) A circular arc is not an isotherm $PV=$ const (at its midpoint $PV=(2+\frac{\sqrt2}2)(2+\frac{\sqrt2}2)>6$ ). False.
(B) From B to D the volume decreases (work done on the gas) and $PV$ falls from 6 to about 1, so the internal energy drops: $Q=\Delta U+W<0$ , heat flows out. True.
(C) A → B → C encloses the right half-disc with the line $V=2$ ; the work equals the area under the arc, not zero. False.
(D) The cycle runs clockwise in the P-V plane, so the net work by the gas is positive. True.

(B), (D)

IIT-JEE 2009 · Paper 2, Physics question 45