First slide

Rms speed

Question

The root mean square velocity of the molecules of a gas is 1260 m/s. The average speed of the molecules is

Easy

A

1029 m/s
B

1161 m/s
C

1671 m/s
D

917 m/s

Solution

$\bar{v} = \sqrt{(\frac{8 kT}{πm})} and v_{rms} = \sqrt{(\frac{3 kT}{m})} ∴ \frac{\bar{V}}{V_{rms}} = \frac{\sqrt{(8 / π)}}{\sqrt{3}} = \sqrt{(\frac{8}{3 π})} \bar{V} = v_{rms} \times \sqrt{(8 / 3 π)} = 1260 \sqrt{(8 / 3 π)} = 1161 m / s$

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