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Sound travels in a mixture of two moles of helium and $\mathrm{n}$ moles of hydrogen. If rms speed of gas molecules in the mixture is $\mathrm{\sqrt{2}}$ times the speed of sound, then the value of $\mathrm{n}$ will be :
Option: 1
$1$

Option: 2
$2$

Option: 3
$3$

Option: 4
$4$

Answers (1)

For non-reacting gaseous mixture

$\mathrm{\frac{n_{\text {mix }}}{v_{\text {mix }}-1}=\frac{n_1}{v_1-1}+\frac{n_2}{r_2-1} }$

$\mathrm{\frac{2+n}{V_{\text {mix }}-1}=\frac{2}{\left(\frac{5}{3}-1\right)}+\frac{n}{\left(\frac{7}{5}-1\right)} }$

$\mathrm{\frac{2+n}{V_{\text {mix }}-1}=3+\frac{5}{2} n \rightarrow (1)}$

$\mathrm{R_{m s} \text { speed of gas molecules }=\sqrt{\frac{3 R T}{M}}}$

$\mathrm{\text { Speed of sound }=\sqrt{\frac{ VR T}{M}}}$

$\mathrm{\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{V R T}{M}} \times \sqrt{2}(\text { Given })}$

$\mathrm{2 V=3}$

$\mathrm{V_{\text {mix }}=V^2=\frac{3}{2} \rightarrow \text { (2) }}$

$\mathrm{\frac{2+n}{\frac{1}{2}}=3+\frac{5 n}{2}}$ (from eq 1 & 2)

$\mathrm{4+2 n=3+\frac{5}{2} n}$

$\mathrm{1=\frac{n}{2}}$

$\mathrm{n=2}$

Hence (2) is correct option.

Posted by

Sumit Saini

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