Question

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

• 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)

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