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 14m/s higher than the average speed.
• C. the root mean square speed is 14m/s lower than the average speed.
• D. the root mean square speed is √(14)m/s higher than the average speed.

Hint:

For any distribution of speeds: vᵣms ≥ vₐvg

Answer 1

The Correct Option is B

Step 1: Average speed: vₐvg=(500+600+700+800+900)/(5)=700m/s 

Step 2: Root mean square speed: vᵣms=√((500²+600²+700²+800²+900²)/(5)) =√((250000+360000+490000+640000+810000)/(5)) =√(510000)≈714m/s 

Step 3: Difference: vᵣms-vₐvg≈ 14m/s