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Mean Free Path of Gases Formulae and Calculator

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Thermodynamics and Heat Transfer

Mean Free Path of Gases Formulae and Calculator

The kinetic theory of gases states that molecules can be viewed as spheres which by the energy contained create collisions between them. The approximate mean distance traveled by a molecule between collisions is defined as the mean free path l and is related to the molecule diameter.

The mean free path formulae:

l = ( k · T ) / ( π · P · d² · 2^0.5 )

Where:

l = mean free path given in pico meters (pm),
P = pressure (Pa),
T = absolute temperature (K),
d = atomic radius pico meters (pm)
k = Boltzmann constant (1.380649 · 10^-23 j / K)
standard conditions (P = 100,000 Pa and T = 298.15 K)

The collusion diameter may be determined from the molecule viscosity and the kinetic theory relation formulae:

η = ( 2.67·10^-20 · ( M · T )^0.5 ) / d²

Where:

η = Viscosity ( mPa s),
M = molar mass ( g/mol ),

The formulae for the relation of the mean velocity v of molecules of mass m:

v = [ ( 8 · k · T ) / ( π · m ) ]^0.5 = 145.5 ( T / m )^0.5

Where:

v = mean velocity (m/s)
T = absolute temperature (K),
M = molar mass ( g/mol ),

Mean time τ between collisions formulae:

τ = l / v

Typical Molecule Diameter and Molar Mass
Molecule	Diameter m	Molar Mass g / mol
Air	3.66 ·10-10	28.960
Ar	3.58·10-10	39.948
CO2	4.53·10-10	44.01
H2	2.71·10-10	2.0159
He	2.15·10-10	4.0026
Kr	4.08·10-10	83.800
N2	3.70·10-10	28.014
NH3	4.32·10-10	17.031
O2	3.55·10-10	31.999
Xe	4.78·10-10	131.290
CH4	3.80·10-10	16.043
Ne	2.75·10-10	20.180

References:

1. Reid, R.C., Prausnitz, J.M., and Poling, B.E., The Properties of Gases and Liquids, Fourth Edition , McGraw-Hill, New York, 1987.
2. Lide, D.R., and Kehiaian, H.V., CRC Handbook of Thermophysical and Thermochemical Data, CRC Press, Boca Raton, FL, 1994.
3. Vargaftik, N.B., Tables of Thermophysical Properties of Liquids and Gases, Second Edition, John Wiley, New York, 1975.
4. Kaye, G.W.C., and Laby, T.H., Tables of Physical and Chemical Constants, 15th Edition, Longman, London, 1986.