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

Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
3 replies · 2K views
Lotto
Messages
260
Reaction score
16
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?
 
Physics news on Phys.org
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.