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

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

Answer 2

Answer:

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

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 :

$v_{avg}=\dfrac{sum\ of\ speeds}{no\ of\ molecules}$

$v_{avg}=\dfrac{15+16+17+18+19+20+21+22+23+24+25}{11}$

$v_{avg}=20\ m/s$

Root mean square velocity is given by :

$v_{rms}=\sqrt{\dfrac{sum\ of\ squares\ of\ speeds}{no\ of\ molecules}$

$v_{rms}=\sqrt{\dfrac{15^2+16^2+17^2+18^2+19^2+20^2+21^2+22^2+23^2+24^2+25^2}{11}}$

$v_{rms}=20.24\ m/s$

Hence, this is the required solution.