Question

The velocity of sound in a diatomic gas is 300 m/s. What is the Root-mean-square velocity of its molecules?

• A. 400 m/s
• B. 40 m/s
• C. 439 m/s
• D. 300 m/s

Answer 1

Answer: (C)

439 m/s

$\begin{array}{c}PM=\rho RT\\ \frac{P}{\rho }=\frac{RT}{M}\\ \Rightarrow v=\sqrt{\frac{\gamma RT}{M}}\\ \Rightarrow \frac{RT}{M}=\frac{v^2}{\gamma }\\ V_{rms}=\sqrt{\frac{3RT}{M}}\\ \Rightarrow V_{rms}=\sqrt{\frac{3v^2}{\gamma }}\\ Hence,\\ V_{rms}=439m/s\end{array}$

So, option $C$ s correct answer.