Chapter 18, Problem 93E

(a)

To determine

To show: The rms velocity and the average velocity are related as $v_{\text{rms}}\ge v_{\text{av}}$ for two particles and $v_{\text{rms}}>v_{\text{av}}$ only if the two particles do not have the same velocity.

(b)

To determine

To show: The new rms and average values of velocity are given by ${v^{\prime }}_{\text{rms}}=\sqrt{\frac{N{v}_{\text{rms}}^2+u^2}{N+1}}$ and ${v^{\prime }}_{\text{av}}=\frac{N{v}_{\text{av}}+u}{N+1}$.

(c)

To determine

To show: The new rms velocity and the average velocity are related as ${v^{\prime }}_{\text{rms}}>{v^{\prime }}_{\text{av}}$.

(d)

To determine

The reason for the results obtained in part (a) and (c) if the particles do not all have the same speed.