Question

The root mean square velocity of a gas is doubled when the temperature is

• A. increased four times
• B. increased two times
• C. reduced to half
• D. reduced to one fourth

Answer 1

Answer: (A)

$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\therefore v_{rms}\propto \sqrt{T}$
$\therefore$ At two different temperatures,
$\frac{v_{rms}}{v_{rms}^{\prime }}=\sqrt{\frac{T}{T^{\prime }}}$
Given $v_{rms}^{\prime }=2v_{rms}$
$\frac{1}{2}=\sqrt{\frac{T}{T^{\prime }}}$
or $\frac{1}{4}=\frac{T}{T^{\prime }}$
$\therefore T^{\prime }=4T$
$\therefore v_{rms}$ gets doubled, when the temperature is increased four times.