Question

At a given temperature if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ be the velocity of sound in it, then these are related as $\left(\gamma = \frac{C_p}{C_v}\right)$

• A. $V_{rms}=V_s$
• B. $V_{rms}=\sqrt{\frac{3}{\gamma}} \times V_s$
• C. $V_{rms}=\sqrt{\frac{\gamma}{3}} \times V_s$
• D. $V_{rms}=\left(\frac{3}{\gamma}\right) \times V_s$

Answer 1

Answer: (B)

$V_{rms}=\sqrt{\frac{3}{\gamma}} \times V_s$

Answer 2

We know that $\begin{array}{l} V_{\text {rms }}=\sqrt{\frac{3 R T}{M}}, V_{S}=\sqrt{\frac{Y R T}{M}} \\\ \Rightarrow \frac{V \text { rms }}{V_{S}}=\frac{\sqrt{3}}{\sqrt{y}} \end{array}$