MCQ
Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of $n$ will be
- A$1$
- ✓$2$
- C$3$
- D$4$
✓
Answer
Correct option: B.
$2$
b
$v _{ s }=\sqrt{\frac{\gamma RT }{ M }}$
$v _{ s }=\sqrt{\frac{\gamma RT }{ M }}$
$v _{ mms }=\sqrt{\frac{3 RT }{ M }}$
$\frac{ v _{ s }}{ v _{ rms }}=\sqrt{\frac{\gamma}{3}}=\frac{1}{\sqrt{2}} \Rightarrow \frac{\gamma}{3}=\frac{1}{2} \Rightarrow \gamma=\frac{3}{2}$
$\gamma=1+\frac{2}{ f _{\operatorname{mix}}}$
$f _{\operatorname{mix}}=\frac{2 \times 3+ n \times 5}{ n +2}=\frac{6+ n \times 5}{( n +2)}$
$\gamma=1+\frac{2( n +2)}{6+ n \times 5}=\frac{6+5 n +2 n +4}{6+5 n }$
$\gamma=\frac{7 n +10}{6+5 n }=\frac{3}{2}$
$14 n +20=18+15 n$
$n =2$
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