JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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 \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(v _{ s }=\sqrt{\frac{\gamma RT }{ M }}\) \(v _{ mms }=\sqrt{\frac{3 RT }{ M }}\) \(\frac{ v _{ s }}{ v _{ rms }}=\sqrt{\frac{\gamma}{3}}=\frac{1}{\sqrt{2}} \Rightarrow \frac{\gamma}{3}=\frac{1}{2} \Rightarrow \gamma=\frac{3}{2}\) \(\gamma=1+\frac{2}{ f _{\operatorname{mix}}}\)…
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