A litre of dry air at STP expands adiabatically to a volume of 3 litres. If <math> <mi>γ</mi> <mo>=</mo> <mn>1.40</mn> </math> <math></math> , the work done by air is: <math> <mfenced separators="|"> <mrow> <mrow> <msup> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mn>1.4</mn> </mrow> </mrow> </msup> <mo>=</mo> <mn>4.6555</mn> </mrow> </mrow> </mfenced> </math> <math><mfenced separators="|"><mrow><mrow><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></mrow></mrow></mfenced></math> [Take air to be an ideal gas]

Δ l = 0.03 m m P 1 = 1 a t m , T 1 = 273 K Now work done P 1 V 1 γ = P 2 V 2 γ P 2 = P 1 V 1 V 2 γ = 1 a t m 1 3 1.4 Closes answer is = P 1 V 1 - P 2 V 2 γ - 1 = 88.7 J .

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If <math> <mi>γ</mi> <mo>=</mo> <mn>1.40</mn> </math> <math></math>&nbsp;, the work done by air is: <math> <mfenced separators="|"> <mrow> <mrow> <msup> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mn>1.4</mn> </mrow> </mrow> </msup> <mo>=</mo> <mn>4.6555</mn> </mrow> </mrow> </mfenced> </math> <math><mfenced separators="|"><mrow><mrow><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></mrow></mrow></mfenced></math>&nbsp;[Take air to be an ideal gas]

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Physics Thermodynamics Physics Class 11th Thermodynamics

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 -

$48 J$

Option 2 -

$90.5 J$

Option 3 -

$100.8 J$

Option 4 -

$60.7 J$

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Answered by

Vishal Baghel | Contributor-Level 10

a month 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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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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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]