Q 11-12-090JEE MainJEE Main 2022 (25 Jul, Shift 2)Medium
Sound travels in a mixture of two moles of helium and $n$ moles of hydrogen. If the rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of $n$ will be
Answer: (B) 2
$\dfrac{v_{\text{rms}}}{v_s} = \sqrt{\dfrac{3RT/M}{\gamma RT/M}} = \sqrt{\dfrac3\gamma} = \sqrt2\Rightarrow\gamma = \dfrac32$, i.e. $C_V = 2R$ for the mixture.
$$C_V = \frac{2\times\frac32R + n\times\frac52R}{2 + n} = 2R\ \Rightarrow\ 3 + 2.5n = 4 + 2n\ \Rightarrow\ n = 2$$
Solution by Sreeraj P, M.Sc Physics