Question

In given gas, sound travels at a speed of $300metres/sec$. Find the order of the root-mean-square velocity of the molecules of this gas:

• A. $41m/sec$
• B. $410m/sec$
• C. $4100m/sec$
• D. $4m/sec$

Answer 1

The correct option is B $410m/sec$

As we know relation between speed of sound in gas and roof mean square speed of molecules of this gas $C_{rms}$

$\Rightarrow \frac{V_{sound}}{C_{rms}}=\sqrt{\frac{r}{3}}$

$\Rightarrow r\cong 1.6;V_{sound}=300m/s;$

$So,C_{rms}=300\sqrt{\frac{3}{1.6}}$

$\Rightarrow C_{rms}=410$

Hence the answer is $410m/sec.$