Question

The temperature, at which the rms velocity of hydrogen is four times of its value at NTP is:

• A. $819$
• B. $1090$
• C. $4368$
• D. $4095$

Answer 1

The correct option is D $4095$

Root mean square velocity is defined as the square root of the mean of the squares of the random velocities of the individual molecules of a gas. Maxwellian speed distribution law states that
$c_{rms}=\sqrt{\left(\frac{3kT}{m}\right)}$
$\Rightarrow c_{rms}\propto \sqrt{T}$
$\therefore \frac{c_{{\left(rms\right)}_1}}{c_{{\left(rms\right)}_2}}=\sqrt{\frac{T_1}{T_2}}$
or $\frac{4}{1}=\sqrt{\frac{T^{\prime }}{273}}$
or $T^{\prime }=4368K$
$=4095$
Note: At absolute zero, rms velocity of the gs molecules becomes zero, so mean KE molecule of the gas becomes zero at absolute zero.