Question

Eleven molecules have speeds 15, 16, 17, . . . , 25 m/s. Calculate (a) vavg, and (b) vrms. Part a express your answer with the appropriate units.

Answer 1

Average velocity of molecules is 20 m/s and root mean square velocity of molecules is 20.24 m/s

Step-by-step explanation:

It is given that, eleven molecules have speeds 15,16,17,18,19,20,21,22,23,24,25 m/s. We have to calculate (1) average velocity (2) root mean square velocity of molecules.

Average velocity can be calculated as :

`v_(avg)=(sum\ of\ speeds)/(no\ of\ molecules)`

`v_(avg)=(15+16+17+18+19+20+21+22+23+24+25)/(11)`

`v_(avg)=20\ m/s`

Root mean square velocity is given by :

`v_(rms)=\sqrt{(sum\ of\ squares\ of\ speeds)/(no\ of\ molecules)`

`v_(rms)=\sqrt{(15^2+16^2+17^2+18^2+19^2+20^2+21^2+22^2+23^2+24^2+25^2)/(11)}`

`v_(rms)=20.24\ m/s`

Hence, this is the required solution.

Answer 2

The speeds are

15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 m/s.

Vavg = 15 + 16 + 17 + 18 + 19 + 20 +21 +22+ 23+24+ 25 / total molecules = 20 m/s

Vrms = ((sum of square of speed of molecules ) / total molecules )^1/2

Vrms = ( (15^2 + 16^2 + 17^2 + ....25^2) / 11 )^1/2

= (225+ 256 + 289 + 324 + 361+ 400 + 441 + 484 + 529 +576 +625 / 11)^1/2

= (4510 / 11 )^1/2 = 20.25 m /s