Why Is RMS Speed Used to Represent Average Speed in Gases?

[artwork]

obviously the root-means-square speed value is greater than the average value.

Question is to why the root-mean-square speed is taken as a kind of average speed for gases but formula used in statistic in getting average number ?

As when the number is squared, the final average value is always greater than the statistic average !

 

[vin300]

While deriving the pressure equation, the mean square velocity comes into picture.Obviously, the velocity to be considered is the RMS velocity and we know it is drastically different from mean velocity in case of opposite velocities.

 

[cipher42]

Any time the values that you want to average over can be both positive and negative, you run the risk of them canceling each other out, in these cases, the RMS is a more effective tool.

For example, with the velocities of particles in a gas, if we look in any given direction, the average velocity will be approximately zero since just as many will be moving in the positive direction as will be moving in the negative direction. This doesn't help us if we are interested in finding a representative speed of a particle. But if we compute the RMS velocity, now we will have a positive number much more indicative of velocity with which any given particle will be traveling.

In the special case that all of the sample values are positive, it is true that the RMS and the arithmetic average will not give the same number (the geometric average will also be different!), but the important thing is to understand what each of these statistical tools measures and when it is appropriate/necessary to use each one.