Mean free time

Definition

Mean free time is the average time interval between successive collisions of a gas particle. It quantifies how frequently particles collide in a given medium.

5 Must Know Facts For Your Next Test

1. Mean free time is inversely related to the collision frequency of gas particles.
2. It is directly proportional to the mean free path and inversely proportional to the root-mean-square speed of gas molecules.
3. The formula for mean free time can be expressed as $\tau = \frac{1}{\nu}$, where $\nu$ is the collision frequency.
4. Increases in temperature generally decrease the mean free time due to increased molecular speeds and collision frequencies.
5. Higher gas density reduces mean free time because more particles are present, leading to more frequent collisions.

Review Questions

• How does an increase in temperature affect the mean free time of gas particles?
• What is the relationship between mean free time and collision frequency?
• Explain how mean free path and root-mean-square speed influence mean free time.

Related terms

Mean Free Path: The average distance a particle travels before colliding with another particle.

Root-Mean-Square Speed: A measure of the average speed of particles in a gas, calculated as $v_{rms} = \sqrt{\frac{3kT}{m}}$ where $k$ is Boltzmann's constant, $T$ is temperature, and $m$ is particle mass.

Collision Frequency: The number of collisions a gas particle undergoes per unit time.