At room temperature, what fraction of the nitrogen molecules in the air are moving at less than 300 m/s?© BrainMass Inc. brainmass.com March 4, 2021, 7:31 pm ad1c9bdddf
Please see the attached file.
1) As per Maxwell speed distribution law :
a) The number of molecules per unit volume having speed v is given by :
f(v) = n (m/2ΠkT)3/2exp( -mv2/2kT) where n = total number of molecules, m = mass of a molecule, k = Boltzmann constant, T = Absolute temp. ...............(1a)
Or f(v) = n (M/2ΠRT)3/2exp( -Mv2/2RT) where n = total number of molecules, M = molecular mass of the gas, R = Universal gas constant, T = Absolute temp. ...(1b)
b) The fraction of molecules of a gas having speeds between v and v+dv is given by :
F(v) dv = 4Π (m/2ΠkT)3/2 v2 exp (-mv2/2kT) dv ............(2a)
Or F(v) dv = 4Π (M/2ΠRT)3/2 v2 ...
Problem solved with application of Maxwell speed distribution law.