Question

If at STP, velocity of sound in a gas $(\gamma =1.5)$ is $600m/s$, the r.m.s. velocity of the gas molecules at STP will be :

• A. $400m/s$
• B. $600m/s$
• C. $600\sqrt{2}m/s$
• D. $300\sqrt{2}m/s$

Answer 1

Answer: (C)

$600\sqrt{2}m/s$

As velocity of sound in gas is given by $v=\sqrt{\frac{\gamma RT}{m}}$

$\gamma =\frac{3}{2}$ given

$R=$ gas constant, $T=$Temp,

$m=$ molecular weight

and

$v_{rms}=\sqrt{\frac{3RT}{m}}$

Now given

$v=600$

$600=\sqrt{\frac{3}{2}\frac{RT}{m}}$

$\sqrt{\frac{RT}{m}}=600\sqrt{\frac{2}{3}}$

$v_{rms}=\sqrt{\frac{3RT}{m}}=\sqrt{3}\times 600\sqrt{\frac{2}{3}}$

$v_{rms}=600\sqrt{2}$.