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]

Option 1 - <math> <mn>48</mn> <mtext> </mtext> <mi mathvariant="normal">J</mi> </math>

Option 2 - <math> <mn>90.5</mn> <mtext> </mtext> <mi mathvariant="normal">J</mi> </math>

Option 3 - <math> <mn>100.8</mn> <mtext> </mtext> <mi mathvariant="normal">J</mi> </math>

Option 4 - <math> <mn>60.7</mn> <mtext> </mtext> <mi mathvariant="normal">J</mi> </math>

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 2

Detailed Solution:

$Δ l = 0.03 m m$

$P_{1} = 1 a t m, T_{1} = 273 K$

Now work done $\begin{array}{r} _{}_{}^{}_{}_{}^{} \end{array}$ $\begin{array}{r} P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \\ P_{2} = P_{1} {[\frac{V_{1}}{V_{2}}]}^{γ} \\ = 1 a t m {(\frac{1}{3})}^{1.4} \end{array}$

Closes answer is $\frac{_{}_{}_{}_{}}{}$ $= \frac{P_{1} V_{1} - P_{2} V_{2}}{γ - 1} = 88.7 J$ .

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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]

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