A single molecule diffusion in ideal gas

  • Context: Graduate 
  • Thread starter Thread starter Galedon
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the diffusion of a single molecule in an ideal gas, emphasizing the movement of an atom characterized by straight-line paths interrupted by collisions. After each collision, the atom acquires a new random velocity according to the Maxwell distribution, leading to a spherical Gaussian distribution of its position after multiple collisions. The variance of this distribution is linked to thermodynamic parameters, and the conversation references the concept of self-diffusion as discussed in Hirschfelder's work. The participants explore the complexities of velocity exchange in a hard-sphere model and the implications of distinguishability in molecular interactions.

PREREQUISITES
  • Understanding of Maxwell distribution in statistical mechanics
  • Familiarity with Gaussian distribution and its properties
  • Knowledge of self-diffusion concepts in thermodynamics
  • Basic principles of collision theory in gas dynamics
NEXT STEPS
  • Research the mathematical derivation of variance in diffusion processes
  • Study the implications of distinguishable vs. indistinguishable particles in statistical mechanics
  • Explore the hard-sphere model and its applications in molecular dynamics
  • Investigate advanced topics in kinetic theory related to velocity distribution post-collision
USEFUL FOR

Physicists, chemists, and students studying thermodynamics and statistical mechanics, particularly those interested in molecular diffusion and kinetic theory.

Galedon
Messages
4
Reaction score
0
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?
 
Science news on Phys.org
Galedon said:
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.
 
Galedon said:
focus on a single atom,
"Distinguishable or indistinguishable;" i.e, mixture, or not? See "self diffusion" in Hirschfelder, et al.
 
Bystander said:
"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.
 
jbriggs444 said:
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.
 
Galedon said:
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.
 
jbriggs444 said:
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?
 
Galedon said:
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.
 

Similar threads

  • · Replies 35 ·
2
Replies
35
Views
5K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 69 ·
3
Replies
69
Views
7K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 22 ·
Replies
22
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K