Mean Free Path Calculator
Calculate molecular mean free path from temperature, pressure, and molecular diameter.
What Is Mean Free Path?
The mean free path is the average distance a gas molecule travels between collisions with other molecules. In an ideal gas, molecules move rapidly and collide elastically. The mean free path depends on temperature, pressure, and molecular size.
Mean Free Path Formula
For an ideal gas, the mean free path is:
$$\lambda = \frac{k_B T}{\sqrt{2}\,\pi\, d^2\, P}$$Here \(k_B\) is the Boltzmann constant (\(1.380649 \times 10^{-23}\) J/K), \(T\) is absolute temperature, \(d\) is the effective molecular diameter, and \(P\) is pressure. Higher pressure means more frequent collisions and a shorter mean free path.
Applications
Mean free path appears in vacuum technology, kinetic theory, diffusion, and semiconductor processing. At atmospheric pressure and room temperature, air molecules have a mean free path of roughly 68 nm. In high vacuum, the path can reach kilometers.
Related tools: Ideal Gas Pressure Calculator, Gas Density Calculator, and Drift Velocity Calculator.
Frequently Asked Questions
What is the mean free path of air at room temperature?
At about 300 K and atmospheric pressure (101.3 kPa), nitrogen molecules have a mean free path near 68 nm. Our calculator uses the kinetic diameter of the selected gas.
How does pressure affect mean free path?
Mean free path is inversely proportional to pressure. Halving the pressure doubles the average distance between collisions.
What is the Boltzmann constant?
It links temperature to energy per molecule: k_B = 1.380649 × 10⁻²³ J/K. It appears in the ideal gas law and kinetic theory equations.
Why use molecular diameter instead of radius?
The formula uses the kinetic diameter, the closest approach distance during a collision. It is roughly twice the atomic radius for many gases.
When does the ideal gas formula break down?
At very high pressures or very low temperatures, intermolecular forces and molecular volume matter. The van der Waals equation gives better results in those regimes.
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