If at STP,the velocity of sound in a gas (gam | vedclass

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(C) The velocity of sound in a gas is given by $v_s = \sqrt{\frac{\gamma RT}{M}}$.The $r.m.s.$ velocity of gas molecules is given by $v_{rms} = \sqrt{

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$600\sqrt{2}$

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(C) The velocity of sound in a gas is given by $v_s = \sqrt{\frac{\gamma RT}{M}}$.The $r.m.s.$ velocity of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Taking the ratio of the two equations:$\frac{v_s}{v_{rms}} = \sqrt{\frac{\gamma RT / M}{3RT / M}} = \sqrt{\frac{\gamma}{3}}$.Given $\gamma = 1.5$ and $v_s = 600 \, m/s$,we substitute these values:$\frac{600}{v_{rms}} = \sqrt{\frac{1.5}{3}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.Solving for $v_{rms}$:$v_{rms} = 600\sqrt{2} \, m/s$.

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

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