Question

If the r.m.s. velocity of a gas at a given temperature (Kelvin scale) is 300 m/s, whathat will be the r.m.s. velocity of a gas having twice the molecular weight and half the temperature on Kelvin scale =

• A. 300 m/sec
• B. 600 m/sec
• C. 75 m/sec
• D. 150 m/sec

Answer 1

The correct option is D 150 m/sec

$v_{max}$ = $\sqrt{\frac{3RT}{M}}\Rightarrow V_{max}\infty \sqrt{\frac{T}{M}}$
$\frac{v_2}{v_1}$ = $\sqrt{\frac{M_1}{M_2}\times \frac{T_2}{T_1}}\sqrt{\frac{1}{2}\times \frac{1}{2}}$ $\Rightarrow v_2=\frac{v_1}{2}=\frac{300}{2}=150m/sec$