A litre of dry air at STP expands adiabatically to a volume of 3 litres. If γ = 1.40, the work done by air is: ( 3 ^ 1.4 = 4.6555) [Take air to be an ideal gas]

Correct answer: B. 90.5J P _ 1 = 1atm, T _ 1 = 273K P _ 1 V _ 1 ^ γ = P _ 2 V _ 2 ^ γ P _ 2 = P _ 1 [ V _ 1 V _ 2 ] ^ γ = 1atm ((1)/(3)) ^ 1.4 Now work done = P _ 1 V _ 1 - P _ 2 V _ 2 γ - 1 = 90.5J

JEE Main 20207 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 7 January
Shift: Morning Shift
Subject: Physics
Chapter: Thermodynamics

JEE Main 2020 · 7 January · Morning Shift · Physics · Thermodynamics

A litre of dry air at STP expands adiabatically to a volume of 3...

A litre of dry air at STP expands adiabatically to a volume of

3

litres. If

\gamma = 1.40,

the work done by air is:

\left({3}^{1.4} = 4.6555\right)

[Take air to be an ideal gas]

Options

A $60.7J$
B $90.5J$
C $100.8J$
D $48J$

Correct answer

B. $90.5J$

Step-by-step solution

{P}_{1} = 1atm, {T}_{1} = 273K

{P}_{1}{V}_{1}^{\gamma} = {P}_{2}{V}_{2}^{\gamma}

{P}_{2} = {P}_{1}{\left[\dfrac{{V}_{1}}{{V}_{2}}\right]}^{\gamma}

= 1atm{\left(\dfrac{1}{3}\right)}^{1.4}

Now work done

= \dfrac{{P}_{1}{V}_{1} - {P}_{2}{V}_{2}}{\gamma - 1} =

90.5J

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