B Can we use molecular speed of gas formula also for the air?

[Lotto]

TL;DR

Can we use molecular speed of gas formula also for the air? I mean if we can use molecular mass of the air.

Molecular speed of gas is generally $$v=\sqrt{\frac{3RT}{M}},$$where R is gas constant and M is molecular mass. Can we use this formula for the air as well, when the air is a mixture of different gasses?

 

[Baluncore]

You can use the molecular speed of gas for air.
I believe the computed RMS velocity gives you the speed of sound.

The molecular weight of air is close to 28.96 g/mole.
Given single percentages and integer atomic weights.
N2 + O2 + Ar = (14*2)*0.78 + (16*2)*0.21 + (40)*0.01 = 28.96 g/mole.

 

[Herman Trivilino]

You can model the air as a diatomic ideal gas and get some good results. Air is made mostly of nitrogen and oxygen, both of which are diatomic gasses.

 

[jbriggs444]

I believe the computed RMS velocity gives you the speed of sound.

For a given gas, the two are proportional.

In an ideal gas, the speed of sound $v_s$ is related to the r.m.s. molecular speed $v_m$ by $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}}$$where $\gamma$ = $C_p/C_v$ = 7/5 for a diatomic gas.

The article above goes on to provide an explanation for the relationship.