QJEEM22Phea6f: JEE Main 2022 Physics - Class 11 JEEM22Phea6f Solution: Sound travels in a mixture of two moles of helium and n moles…

Molar mass $M - {{2 \times 4 + n \times 1} \over {2 + n}}$ ..... (i)

Also, $\gamma = {{{n_1}{C_{{P_1}}} + {n_2}{C_{{P_2}}}} \over {{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}}} = {{2 \times 5R + n \times 7R} \over {2 \times 3R + n \times 5R}}$

$\Rightarrow \gamma = {{10 + 7n} \over {6 + 5n}}$ ...... (ii)

Given that ${V_{rms}} = \sqrt 2 \,{V_{sound}}$

$\Rightarrow \sqrt {{{3RT} \over M}} = \sqrt 2 \sqrt {{{\gamma RT} \over M}}$

$\Rightarrow \gamma = {3 \over 2}$

$\Rightarrow n = 2$