n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A → B : Isothermal expansion at temperature T so that the volume is doubled from $V_1$ to $V_2=2V_1$ and pressure changes from $P_1$ to $P_2$. B → C : Isobaric compression at pressure $P_2$ to initial volume $V_1$. C → A : Isochoric change leading to change of pressure from $P_2$ to $P_1$. Total workdone in the complete cycle ABCA is :

Option 4: $nRT\left(\ln 2-\frac{1}{2}\right)$

$nRT\left(\ln 2+\frac{1}{2}\right)$

$nRT\left(\ln 2-\frac{1}{2}\right)$

JEE Main 2021 · PhysicsMultiple choiceDiagram basedMediumCalculation

JEE Main 24 February 2021, Shift 1, Physics Q9

Question 9 of 90 in this shift, Physics question 9 of 30, Section A.

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A → B : Isothermal expansion at temperature T so that the volume is doubled from

V_1

V_2=2V_1

and pressure changes from

P_1

P_2

. B → C : Isobaric compression at pressure

P_2

to initial volume

V_1

. C → A : Isochoric change leading to change of pressure from

P_2

P_1

. Total workdone in the complete cycle ABCA is :

The figure, in words

P-V graph with P on the vertical axis and V on the horizontal axis. P1 and P2 are marked on the P-axis (dashed horizontal lines), V1 and V2=2V1 marked on the V-axis (dashed vertical lines). A is at (V1, P1), B at (V2, P2), C at (V1, P2). A curve with an arrow goes from A down to B; a horizontal line with an arrow points from B to C (leftwards); a vertical line with an arrow goes from C up to A.

(1) $0$
(2) $nRT\ln 2$
(3) $nRT\left(\ln 2+\frac{1}{2}\right)$
(4) $nRT\left(\ln 2-\frac{1}{2}\right)$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Thermodynamics
Topic: Thermodynamic Processes
Idea tested: Cyclic Process Work

Same idea in other shifts

Asked 7× in all

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.