In Example 18.7 (Section 18.3) we saw that Urms, > Vav. It is not difficult to show that this is always the case. (The only exception is when the particles have the same speed, in which case Urms = Vav.)
(a) For two particles with speeds UI and U2, show that Urms≥ Uav. Regardless of the numerical values of UI and U2. Then show that Urms > Uav. If U1≠ U2.
(b) Suppose that for a collection of N particles you know that Urms > Uav.
Another particle, with speed u, is added to the collection of particles. If the new rms and average
Speeds are denoted as U€™rms and U€™av show that



(c) Use the expressions in part (b) to show that U€™rms > U€™av regardless of the numerical alue of u. (d) Explain why your results for (a) and (c) together show that Urms > Uav for any collec1ion of particles if the particles do not all have the same speed.

Nu2+ u? N+1 Nu + u N+1 and