Question

Here we will use a simple example to demonstrate the difference between the rms speed and the average speed. Five ideal-gas molecules chosen at random are found to have speeds of 500, 600, 700, 800, and 900 m/s. Find the rms speed for this collection. Is it the same as the average speed of these molecules

Answer 1

Step-by-step explanation:

Given that,

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

The rms speed for this collection is as follows :

`v_(rms)=\sqrt{(v_1^2+v_2^2+v_3^2+v_4^2+v_5^2)/(5)} \\\\v_(rms)=\sqrt{(500^2+600^2+700^2+800^2+900^2)/(5)} \\\\v_(rms)=714.14`

The average speed of these molecules is :

`v_(a)=(v_1+v_2+v_3+v_4+v_5)/(5)} \\\\v_(a)={(500+600+700+800+900)/(5)} \\\\v_(a)=700\ m/s`

So, the rms speed is 714.14 m/s abd the average speed is 700 m/s.