Is the root-mean-square velocity of gas particles always faster than the average velocity?
I’ve done a couple of calculations with both and that seems to be the case; however can you make a formal mathematical proof of it?
The classical analysis is known as the Maxwell-Boltzmann distribution.
The RMS velocity is about 108% of the average velocity.
Root-mean-square velocity is a scalar, average velocity is a vector. I am not sure how one can compare them. Maybe you meant the absolute value of average velocity?