Question

The root mean square velocity of a gas is double when temperature is?

• A. Increased four times
• B. Increased two times
• C. Reduced to half
• D. Reduced to one-fourth

Answer 1

The correct option is A Increased four times

$v_{rms}=\sqrt{\frac{3RT}{M}}$
$v_{rms}\propto \sqrt{T}$
Thus, the root mean square velocity of a gas is directly proportional to the square root of temperature.
$\frac{v_{rms}}{v_{rms}^{\prime }}=\sqrt{\frac{T}{T^{\prime }}}$
The root mean square velocity of a gas is doubled.
$v_{rms}^{\prime }=2v_{rms}$
$\frac{1}{2}=\sqrt{\frac{T}{T^{\prime }}}$
$\frac{1}{4}=\frac{T}{T^{\prime }}$
$T^{\prime }=4T$.
The root mean square velocity of a gas is double when temperature is increased four times.