From kinetic theory of gases, the rms speed of molecules of a gas is given by,
where P is the pressure of the gas and ρ is the density. From ideal gas law
Where R is the universal gas constant, T is temperature and M is the molecular mass of the gas.
The speed of sound on the other hand is given by
where γ is the ratio of specific heat at constant pressure to specific heat at constant volume for air, R is the universal gas constant, T is temperature and M is the molecular mass of the gas.
For a diatomic gas γ = 1.4, and hence
And is independent of temperature.
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