Question

For a given gas at $1 \,atm$ pressure, rms speed of the molecules is $200 \,m / s$ 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

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