Question

The magnitude of root mean square velocity of oxygen atoms in an oxygen cylinder kept at zero degrees centigrade is
a) Lesser than the average velocity of the atoms
b) Greater than the average velocity
c) Equal to the average velocity
d) There is no correlation between these two quantities.

Answer 1

There is no correlation here. The reason one does not calculate average velocity and instead chooses to calculate the root mean square velocity is because statistically, since the particles are going every which way with no particular preference, all of the velocities average to zero. So in general, the average velocity of such a system will be zero, while the rms velocity will be a function of the temperature.

Answer 2

Now, if you were to count up all the magnitudes of the velocities and average them, then this number would be larger than the RMS velocity.