Question

So I've been trying to figure this out: What is the average collision duration of a gas in terms of macroscopic variables?

What I have figured out. Whenever two molecules collide they must reach a potential barrier (before behaving like a turning point) of

V_barrier = 1/ 2μv²rel (1)

where, V_barrier is the height of the potential before behaving as a turning point, μ is the reduced mass and vrel is the relative velocity. Thus, on average the gas molecule's collisions goes upto a potential height

⟨V_barrier⟩∝T

Any help will be appreciated.

Answer 1

The average collision duration of a gas molecule can be expressed in terms of macroscopic variables such as temperature.

Step-by-step explanation:

The average collision duration of a gas molecule can be expressed in terms of macroscopic variables such as temperature. When two gas molecules collide, they must overcome a potential barrier before they can behave like a turning point. The height of this potential barrier is given by V_barrier = 1/2μv²rel, where V_barrier is the height of the potential, μ is the reduced mass, and vrel is the relative velocity. On average, the gas molecule's collisions reach a potential height ⟨V_barrier⟩ that is proportional to the temperature T.