# Mean Free Path

on . Posted in Classical Mechanics

Mean free path, abbreviated as $$\lambda$$ (Greek symbol lambda), is a concept used in physics to describe the average distance that a particle, such as a molecule or an atom, travels between collisions with other particles in a gas, liquid, or solid.  It's a measure of how far a particle can travel before encountering another particle and experiencing a collision.

In gases, for instance, particles are in constant motion and collide with each other.  The mean free path provides insight into how often these collisions occur and the typical distance traveled before such collisions.  It's important in understanding the transport properties of gases and the behavior of particles in various environments.

The mean free path can vary greatly depending on factors like the density of the material, the temperature, and the type of particles involved.  In gases at low pressure, particles may have longer mean free paths, while in dense materials or at higher pressures, the mean free path can be much shorter.  The concept of mean free path is widely used in fields such as fluid dynamics, kinetic theory of gases, and solid-state physics to model and understand the behavior of particles in different states of matter.

### Mean free path Formula

$$\lambda = k_b \; T \;/\; \sqrt{ 2 } \; \pi \; d_m^2 \; p$$
Symbol English Metric
$$\lambda$$ (Greek symbol lambda) = mean free path $$in$$ $$mm$$
$$k_b$$ = Boltzmann constant $$lbm-ft^2 / sec^2$$ $$kJ / molecule-K$$
$$T$$ = temperature of gas $$F$$ $$K$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$d_m$$ = molecular diameter $$in$$ $$mm$$
$$p$$ = pressure of gas $$lbf / in^2$$ $$Pa$$