Gas equation of state and shape of container

[techmologist]

Does the equation of state of a gas of interacting particles depend on the shape of the container they are in? For instance, if the interaction force is gravity (a central force) and the particles are in a spherical container, then it seems reasonable that the pressure on the wall of the container is determined by the volume of the sphere and temperature of the gas. But if the gas is in a box, it isn't obvious to me that the pressure would be the same everywhere on the walls, because the corners of the box are farther away from the center and fewer particles would be there.

By the way, if someone could tell me how to derive the equation of state of a gas of gravitating particles I would be grateful.

 

[Bloodthunder]

What has it got to do with the center of the box? Anyway, with the effect of gravity, air particles are slightly weighed downwards. However, it's erratic movement in the volume is what gives it pressure. Nothing to do with the shape.

I'm assuming you're talking about the equation for an ideal gas. You just need Boyle's law and Charles' Law.

 

[SteamKing]

You are also assuming that the gas molecules are not moving inside the container. For a box, it is just as likely that you will find molecules of a gas in the corners as in the center of the box. The pressure and temperature of a gas are related to the motion of the molecules of the gas.

 

[techmologist]

I'm not talking about an ideal gas. In an ideal gas, the particles don't interact in any way. I'm talking about particles that exert gravitational force on each other. They are not in an external gravitational field.

 

[techmologist]

Maybe this problem is harder than I thought. Some googling told me that Van der Waals got the Nobel Prize for finding the approximate equation of state assuming a weak interaction (where the shape of the container is irrelevant, and the density is close to uniform).