A single molecule diffusion in ideal gas

[Galedon]

Let us have an ideal gas. When we focus on a single atom, its movement should consist of straight lines from collision to collision. After each collision it should get a new random velocity according to Maxwell distribution. After N collisions, the position of the atom should correspond to a spherical gaussian distribution around its original position.

The question is: What should be the variance of this distribution in terms of thermodynamic parameters?

 

[jbriggs444]

Let us have an ideal gas. When we focus on a single atom, its movement should consist of straight lines from collision to collision. After each collision it should get a new random velocity according to Maxwell distribution.

Surely the new random velocity is not obtained directly from the Maxwell distribution. The distribution of resulting velocities should show bias based on the prior velocity.

 

[Bystander]

focus on a single atom,

"Distinguishable or indistinguishable;" i.e, mixture, or not? See "self diffusion" in Hirschfelder, et al.

 

[Galedon]

"Distinguishable or indistinguishable;" i.e, mixture, or not? See "self diffusion" in Hirschfelder, et al.

Thank you for answer.
Lets make an imaginary marker on it to make id distinguishable. I will look into the article (you mean the one from 1949, right?), but if you could point me a little further, I would be grateful.

 

[Galedon]

Surely the new random velocity is not obtained directly from the Maxwell distribution. The distribution of resulting velocities should show bias based on the prior velocity.

In a hard-sphere model it should "exchange" its velocity with the random molecule it collided with.

 

[jbriggs444]

In a hard-sphere model it should "exchange" its velocity with the random molecule it collided with.

In a head on impact, yes. But not all impacts are head on.

 

[Galedon]

In a head on impact, yes. But not all impacts are head on.

I see - but how to model it? The assumption is that "a lot" of collisions appeared, how to connect the final state with the original velocity?

 

[jbriggs444]

I see - but how to model it? The assumption is that "a lot" of collisions appeared, how to connect the final state with the original velocity?

I do not know.