The pressure and volume of an ideal gas are related as PV(3)/(2) = K (Constant). The work done when the gas is taken from state A( P _ 1 , V _ 1 , T _ 1 ) to state B( P _ 2 , V _ 2 , T _ 2 ) is :

Correct answer: A. 2 ( P _ 1 V _ 1 - P _ 2 V _ 2 ) For P V ^ x = constant, work done by the gas is given by, W = (nR )/(1 - x) = P _ 2 V _ 2 - P _ 1 V _ 1 1 - x . Here x = (3)/(2) , therefore we can write ∴ W = P _ 2 V _ 2 - P _ 1 V _ 1 - (1)/(2) = 2( P _ 1 V _ 1 - P _ 2 V _ 2 )

JEE Main 20241 FebruaryMorning Shift

Exam: JEE Main
Year: 2024
Date: 1 February
Shift: Morning Shift
Subject: Physics
Chapter: Thermodynamics

JEE Main 2024 · 1 February · Morning Shift · Physics · Thermodynamics

The pressure and volume of an ideal gas are related as PV(3)/(2) =...

The pressure and volume of an ideal gas are related as

PV\dfrac{3}{2} = K

(Constant). The work done when the gas is taken from state

A\left({P}_{1}, {V}_{1}, {T}_{1}\right)

to state

B\left({P}_{2}, {V}_{2}, {T}_{2}\right)

is :

Options

A $2 ( {P}_{1}{V}_{1} - {P}_{2}{V}_{2} )$
B $2 ( {P}_{2}{V}_{2} - {P}_{1}{V}_{1} )$
C $2\left(\sqrt{{P}_{1}}{V}_{1} - \sqrt{{P}_{2}}{V}_{2}\right)$
D $2\left({P}_{2}\sqrt{{V}_{2}} - {P}_{1}\sqrt{{V}_{1}}\right)$

Correct answer

A. $2 ( {P}_{1}{V}_{1} - {P}_{2}{V}_{2} )$

Step-by-step solution

For $P{V}^{x} =$ constant, work done by the gas is given by,

$W = \dfrac{nR\DeltaT}{1 - x} = \dfrac{{P}_{2}{V}_{2} - {P}_{1}{V}_{1}}{1 - x}$ .

Here $x = \dfrac{3}{2}$ , therefore we can write

$∴ W = \dfrac{{P}_{2}{V}_{2} - {P}_{1}{V}_{1}}{- \dfrac{1}{2}}$

$= 2\left({P}_{1}{V}_{1} - {P}_{2}{V}_{2}\right)$

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