n mole of 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 V1 to V2 and Pressure changes from P1 to P2. B->C : Isobaric compression at pressure P2 to initial volume V1. C->A : Isobaric change leading to change of pressure from P2 to P1. Total work done in the complete cycle ABCA is:

W A B = n R T l n 2 V 1 V 1 = n R T l n 2 . W B C = P 2 ( V 1 − 2 V 1 ) = − P 2 V 1 = − 1 2 n R T [At B, 2P2 V1 = nRT] W C A = 0 [CA is isochoric process]. W A B C A = W A B + W B C + W C A = n R T ( l n ( 2 ) − 1 2 )

n mole of 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 V₁ to V₂ and Pressure changes from P₁ to P₂.

B->C : Isobaric compression at pressure P₂ to initial volume V₁.

C->A : Isobaric change leading to change of pressure from P₂ to P₁.

Total work done in the complete cycle ABCA is:

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Option 2 - <math> <mrow> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mrow> <mo>(</mo> <mrow> <mi>I</mi> <mi>n</mi> <mn>2</mn> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math>

Option 3 - 0

Option 4 - nRTIn2

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Alok Kumar Singh | Contributor-Level 10

5 months ago

Correct Option - 3

Detailed Solution:

$W_{A B} = n R T l n \frac{2 V_{1}}{V_{1}} = n R T l n 2 .$