The root mean square velocity of air molecules can be found from the formula:
vrms=M3RT.Let's express MRT in terms of P and ρ. From the ideal gas law, we have:
PV=nRT,here, n=Mm.
Let's divide both sides of the equation by V:
P=VmMRT.Since ρ=Vm we have:
P=ρMRTFinally, we get:
MRT=ρP.
Then, we can calculate the root mean square velocity of air molecules at normal temperature and pressure:
vrms=M3RT=ρ3P,vrms=1.293 m3kg3⋅1.013⋅105 Pa=485 sm.Answer:
vrms=485 sm.
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