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Q.

In the two vessels of same volume, hydrogen and helium at pressure 1atm and 2atm are filled. If temperature of both the sample is same then average speed of hydrogen $< C_{H} >$ will be related to that of helium $< C_{He} >$ as

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a

$< C_{H} > = \sqrt{2} < C_{He} >$

b

$< C_{H} > = < C_{He} >$

c

$< C_{H} > = \frac{< C_{He} >}{2}$

d

$< C_{H} > = 2 < C_{He} >$

answer is A.

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Detailed Solution

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Vessel-1:Hydrogen; Vessel-2: Helium
$\begin{array}{ll} P_{1} = 1 atm; P_{2} = 2 atm \\ V_{1} =; V_{2} = V_{1} \end{array}$ (average speed independent of pressure at constant temperature)
$\begin{array}{l} T_{1} =; T_{2} = T_{1} \\ ⟨ V ⟩_{1} = <Hydrogen speed >= \sqrt{\frac{8 RT}{{πM}_{1}}} \\ ⟨ V ⟩_{2} = ⟨ helium ⟩ = \sqrt{\frac{8 RT}{{πM}_{2}}} \\ \frac{<V_{1}>}{<V_{2}>} = \sqrt{\frac{M_{2}}{M_{1}}} = \sqrt{2} \end{array}$

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In the two vessels of same volume, hydrogen and helium at pressure 1atm and 2atm are filled. If temperature of both the sample is same then average speed of hydrogen<CH>will be related to that of helium <CHe> as