Physics - Heat & Thermo Question with Solution | TestHub

RMS speed is given by, $v_{rms}=\sqrt{\frac{3RT}{M}}$ and average speed is given by, $v_{avg}=\sqrt{\frac{8}{\mathrm{\pi }}\frac{RT}{M}}$.

As per question,

$v_{rms}=\sqrt{\frac{\alpha +5}{\alpha }}{v}_{avg}$

$\Rightarrow \sqrt{\frac{3RT}{M}}=\sqrt{\frac{\alpha +5}{\alpha }}\sqrt{\frac{8}{\mathrm{\pi }}\frac{RT}{M}}$

$\Rightarrow 3=\frac{\alpha +5}{\alpha }\times \frac{8}{{\displaystyle \frac{22}{7}}}$

$\Rightarrow \alpha =28$