Posted by Jen on Thursday, November 15, 2007 at 7:30pm.
You will find the two velocites to be roughly the same.
The mean kinetic energy of the molecules is
Eav = (3/2) kT = 6.21*10^-21 J
That equals (1/2) M V^2 (where V is the rms average).
M = (28.0 g/mole)/[(6.02*10^23 molecules/mole)* 1 kg/1000 g]
= 4.65*10^-26 kg/molecule
V^2 = 2 Eav/M = 2.67*10^5 m^2/s^2
Vrms = sqrt V^2 = 517 m/s
Check my reasoning and numbers.
See http://teacher.pas.rochester.edu/phy121/LectureNotes/Chapter21/Chapter21.html
for more about this
The speed of sound is always less than the rms speed, by a factor
sqrt(gamma/3). Gamma, the specific heat ratio Cp/Cv, equals 1.4 for diatonic gases
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