According to simple kinetic theory, in which all the gas molecules but one are considered stationary, the mean free path L is given by L = 1/N π σ2 , where N is the number of molecules per cc. and σ is the molecular diameter. Clausius, considering all molecules to be moving with the mean relative velocity, finds L = 3/4N π σ2. Again, Maxwell, applying his law of velocity distribution, obtains the result L= 1/√2N π σ2. This value found by Maxwell is the one most generally accepted. If we consider it to be correct, then the value from simple kinetic theory is 41% too large, while that found by Clausius is 6% too large. An approximate value of L, much more nearly correct than the first one given, may be derived very simply by considering the gas molecules to be vibrating in sheets. The result obtained is L = 1/ 4 N σ2. This value is 11% higher than that found by Maxwell, as compared to 41% for the first value given above. The mathematical difficulties encountered by Clausius and Maxwell in deriving their formulas are entirely avoided in this development.
Proceedings of the Iowa Academy of Science
©1926 Iowa Academy of Science, Inc.
Davis, George E.
"A Simple Derivation of the Equation for Mean Free Path,"
Proceedings of the Iowa Academy of Science, 33(1), 250-250.
Available at: https://scholarworks.uni.edu/pias/vol33/iss1/70