Molecular Mean Free Path
Change molecular size and number density to compare collision distance, thermal speed and collision time in a dilute gas.
Free theory articleChange molecular size and number density to compare collision distance, thermal speed and collision time in a dilute gas.
Concept & interpretation
In a dilute gas, molecules travel along nearly straight free-flight segments between binary collisions. Modeling the gas as identical hard spheres of diameter d gives a collision cross-section σ = πd2. Accounting for the relative motion of target and test molecules in a Maxwellian velocity distribution yields the mean free path λ = 1 / (√2 n σ), where n is the molecular number density.
Experiment
Use the Molecular Mean Free Path interactive module to explore how number density, hard-sphere diameter, and temperature control collision kinematics:
- Start at Density units1e20 =
1, Diameter nm =2/5, and Temperature K =300, then double Density units1e20 to2. Notice that Mean free path mm halves from 14.067442439955 mm to 7.0337212199774 mm while thermal mean speed stays constant. - Increase Diameter nm from
2/5to4/5. Because σ ∝ d2, doubling the molecular diameter quarters the mean free path. - Set Density units1e20 to
0to inspect the vacuum collision limit, where pressure and collision rate drop to 0 and mean free path/time becomeUnavailable.