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

AI Thread Summary
The molecular speed of gas formula, v = √(3RT/M), can be applied to air, which is a mixture of gases, by using its average molecular weight of approximately 28.96 g/mole. Air primarily consists of nitrogen and oxygen, both diatomic gases, allowing for effective modeling as an ideal gas. The computed root mean square (RMS) velocity of air correlates with the speed of sound. In an ideal gas, the speed of sound is proportional to the RMS molecular speed, with the relationship expressed as vs/vm = √(γ/3), where γ = Cp/Cv = 7/5 for diatomic gases. This demonstrates that the molecular speed formula is valid for air and provides insights into its acoustic properties.
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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?
 
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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.
 
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.
 
Baluncore said:
I believe the computed RMS velocity gives you the speed of sound.
For a given gas, the two are proportional.
https://physics.stackexchange.com/questions/78879/simple-explanation-of-relation-between-speed-of-sound-and-r-m-s-speed said:
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.
 
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