Question

Five gas molecules chosen at random are found to have speeds of $500, 600, 700, 800$ and $900 \,m/s$:

• A. The root mean square speed and the average speed are the same.
• B. The root mean square speed is 14 m/s higher than the average speed.
• C. The root mean square speed is 14 m/s lower than the average speed.
• D. The root mean square speed is Ö14 m/s higher than the average speed.

Answer 1

Answer: (B)

$v_{a v}=\left[\frac{500+600+700+800+900}{5}\right]=700 \,m / s$ and
$=\sqrt{\frac{500^{2}+600^{2}+700^{2}+800^{2}+900^{2}}{5}}=714 \,m / s$
Thus $v_{r m s}$ is greater than average speed by $14 m / s$.