Shape & Dimensions of Containers: Impact on the Maxwell Boltzmann Distribution

[sol47739]

TL;DR

I have some basic questions about the Maxwell Boltzmann distribution

1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid?
Why does/doesn’t the distribution change depending on the shape of the container? 2.Does the Maxwell Boltzmann distribution look the same in 2 dimensions?

 

[Philip Koeck]

TL;DR Summary: I have some basic questions about the Maxwell Boltzmann distribution

1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid?
Why does/doesn’t the distribution change depending on the shape of the container?2.Does the Maxwell Boltzmann distribution look the same in 2 dimensions?

No to both, I would say.

For 2.: The density of states is not the same in 2D so the Normalization factor has to be different.

For 1.: I would think that the available states don't depend on the shape of the container if the container is macroscopic. For a microscopic system the MB-distribution can't be used anyway.