In Example 18.7 (Section 18.3) we saw that It is not

Chapter 18, Problem 18.93

(choose chapter or problem)

In Example 18.7 (Section 18.3) we saw that 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 (a) For two particles with speeds and show that regardless of the numerical values of and Then show that if (b) Suppose that for a collection of N particles you know that Another particle, with speed u, is added to the collection of particles. If the new rms and average speeds are denoted as and show that (c) Use the expressions in part (b) to show that regardless of the numerical value of u. (d) Explain why your results for (a) and (c) together show that for any collection of particles if the particles do not all have the same speed.