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 = 2 V _ 1 and

Correct answer: A. nRT( 2 - (1)/(2)) W _ isothermal = nRT ( V _ 2 V _ 1 ) \ W _ isobaric = P = nR W _ isochoric = 0 W _ 1 = nRTln((2V)/(V)) = nRTln2 W _ 2 = nR((T)/(2) - T) = - nR(T)/(2) W _ 3 = 0 ⇒ W _ net = W _ 1 + W _ 2 + W _ 3 W _ net = nRT( 2 - (1)/(2))

JEE Main 202124 FebruaryMorning Shift

Exam: JEE Main
Year: 2021
Date: 24 February
Shift: Morning Shift
Subject: Physics
Chapter: Thermodynamics

JEE Main 2021 · 24 February · Morning Shift · Physics · Thermodynamics

n mole of a perfect gas undergoes a cyclic process ABCA (see...

$n$ mole of a perfect gas undergoes a cyclic process $ABCA$ (see figure) consisting of the following processes.

$A \to B:$ Isothermal expansion at temperature $T$ so that the volume is doubled from ${V}_{1}$ to ${V}_{2} = 2{V}_{1}$ and pressure changes from ${P}_{1}$ to ${P}_{2}$
$B \to C:$ Isobaric compression at pressure ${P}_{2}$ to initial volume ${V}_{1} .$

$C \to A:$ Isochoric change leading to change of pressure from ${P}_{2}$ to ${P}_{1}$

Total work done in the complete cycle $ABCA$ is:

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A → B:

Options

A $nRT\left(\ln 2 - \dfrac{1}{2}\right)$
B $nRTln2$
C $nRT\left(\ln 2 + \dfrac{1}{2}\right)$
D $0$

Correct answer

A. $nRT\left(\ln 2 - \dfrac{1}{2}\right)$

Step-by-step solution

${W}_{isothermal} = nRT \ln \left(\dfrac{{V}_{2}}{{V}_{1}}\right)$ \

${W}_{isobaric} = P\DeltaV = nR\DeltaT$

${W}_{isochoric} = 0$

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A → B:

${W}_{1} = nRTln\left(\dfrac{2V}{V}\right) = nRTln2$

${W}_{2} = nR\left(\dfrac{T}{2} - T\right) = - nR\dfrac{T}{2}$

${W}_{3} = 0$

$⇒ {W}_{net} = {W}_{1} + {W}_{2} + {W}_{3}$

${W}_{net} = nRT\left(\ln 2 - \dfrac{1}{2}\right)$

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