Mean free path

Definition

The mean free path is the average distance a particle travels before colliding with another particle. It is crucial for understanding gas behavior under various conditions.

5 Must Know Facts For Your Next Test

1. Mean free path ($\lambda$) is inversely proportional to the number density of particles in a gas.
2. It depends on both the temperature and pressure of the gas.
3. The formula for mean free path is $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$, where $k_B$ is Boltzmann's constant, $T$ is temperature, $d$ is particle diameter, and $P$ is pressure.
4. Higher temperatures generally increase the mean free path as particles move faster and collide less frequently.
5. In low-pressure environments, particles travel longer distances between collisions, increasing the mean free path.

Review Questions

• How does an increase in temperature affect the mean free path of gas particles?
• What factors are included in the formula for calculating mean free path?
• Why does mean free path decrease with an increase in particle number density?

Related terms

Boltzmann's Constant: $k_B$, a physical constant that relates energy at the individual particle level with temperature.

Root Mean Square Speed: The measure of the average speed of particles in a gas, represented by $v_{rms} = \sqrt{\frac{3k_BT}{m}}$.

Pressure:

The force exerted by gas particles per unit area on the walls of their container.