Posted by Jen on .
The speed of propagation of a sound wave in air at 27 degrees Celsius is about 350 m/s. Calculate, for comparison, v_rms for nitrogen (N2) molecules at this temperature. The molar mass of nitrogen is 28.0 g/mol.
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.
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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