Question

For a given gas at $1atm$ pressure, rms speed of the molecules is $200m/s$ at $127^{\circ }C$. At $2$ atm pressure and at $227^{\circ }C$, the rms speed (in $m/s$ ) of the molecules will be: ___
$(100\sqrt{5})$

Answer 1

Answer: 100

$V_{rms}=\sqrt{\frac{3RT}{M}}$
$\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{(273+127)}{(273+227)}}$
$=\sqrt{\frac{400}{500}}=\sqrt{\frac{4}{5}}=\frac{2}{\sqrt{5}}$
$\therefore v_2=\frac{\sqrt{5}}{2}{v}_1=\frac{\sqrt{5}}{2}\times 200=100\sqrt{5}m/s$