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

AI Thread Summary
The Maxwell Boltzmann distribution does not change based on the shape of the container, provided that pressure and volume remain constant. The available states for gas particles are considered independent of the container's shape in macroscopic systems. In microscopic systems, the Maxwell Boltzmann distribution is not applicable. Additionally, the distribution does not look the same in two dimensions due to differences in the density of states, necessitating a different normalization factor. Overall, the shape of the container has minimal impact on the distribution in macroscopic scenarios.
sol47739
Messages
38
Reaction score
3
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?
 
Physics news on Phys.org
sol47739 said:
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.
 
Thread 'Gauss' law seems to imply instantaneous electric field'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
Back
Top