Mean Free Path
The average distance a molecule travels between collisions, λ = 1/(√(2) π d2 n).
What is Mean Free Path?
The average distance a molecule travels between collisions, λ = 1/(√(2) π d2 n).
Key formula / rule: λ = 1/(√(2) π d2 n), inversely proportional to number density.
Key points
- Compute mean free path for stated gas conditions.
- Analyse how pressure and temperature change the mean free path.
Common exam trap
Assuming mean free path depends on molecular speed.
Definitions
- Term
Mean Free Path
- Meaning
The average distance a molecule travels between collisions, λ = 1/(√(2) π d2 n).
- Term
Mean Free Path — explanation
- Meaning
Mean free path grows as the gas becomes rarer, which is why low-pressure systems behave very differently from atmospheric ones.
Learning objectives
Compute mean free path for stated gas conditions.
Analyse how pressure and temperature change the mean free path.
Formulae
- Key point
λ = 1/(√(2) π d2 n), inversely proportional to number density.
- Key point
It rises with temperature at constant pressure.
- Key point
Typical air value at STP is around 10-7 m.
Prerequisites
PHY-U3-KTG-T1-S1-C2
Common mistakes
Assuming mean free path depends on molecular speed.
Using pressure without converting to number density.
Practice preview
Which of the following statements about the mean free path of gas molecules is INCORRECT?…
medium
A gas is enclosed in a container. If the volume of the container is reduced to half, and the temperature is simultaneously increased such that the pressure remains constant, how does the mean free path of the gas molecul…
hard
Calculate the mean free path for an ideal gas at 27 degrees Celsius and 1 atm pressure, given that the molecular diameter is 3.0 x 10^-10 m. (Boltzmann constant k_B = 1.38 x 10^-23 J/K, 1 atm = 1.013 x 10^5 Pa).…
hard