JEE Main 2021 · 24 Feb · Shift 1 · Physics Q9

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PhysicsSingle correct+4 / -1Question 9 of 90

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 :

P-V diagram: A at (V1, P1), isothermal curve down to B at (2V1, P2), horizontal line back to C at (V1, P2), vertical line up to A.

nRT ln 2

nRT\left(\ln2+\dfrac12\right)

nRT\left(\ln2-\dfrac12\right)

Answer and worked solution

Official answer: D

Work. A → B: $nRT\ln2$ . B → C: $-P_2V_1=-\frac{nRT}2$ (since $P_2\cdot2V_1=nRT$ ). C → A: 0.

Total $nRT\left(\ln2-\frac12\right)$ .

(D)

Topics:Work done by a gas Thermodynamic processes

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JEE Main 2021 · 24 Feb · Shift 1, Physics question 9