Pressure - Average Trajectories

[realitybugll]

Pressure -- Average Trajectories

The question is this: if we have two distinct three-dimensional but hallow objects, might the average trajectory (the average distance between ANY two points on the object's surface) vary between the objects?

I am lead to believe the answer is yes between a cube and a sphere of equal volume - though not by much. For circles/squares I've confirmed the average trajectories to differ, though these are 2-d shapes. What's really problematic is calculating the average trajectory for the cube.

If I'm drawing logical conclusions, then this would seem to mean that the pressure experienced in the objects of EQUAL volume by the SAME gaseous particles would be different. At least if your treating them as point particles -- if you consider intermolecular forces and trajectory deflections, etc., its less clear, though I would still think that the principle would hold.

Any insight would be great. Thanks.

 

[eljose79]

Hello,

Thank you for your interesting question. I can confirm that the average trajectory between two distinct three-dimensional objects can vary, even if they have the same volume. This is due to the shape and surface area of the objects, which can affect the distribution and movement of gas particles.

For example, a sphere has a smaller surface area compared to a cube of the same volume, which means there are fewer points for gas particles to collide with. This can result in a slightly different average trajectory compared to the cube.

However, as you mentioned, the difference may not be significant. In fact, for larger objects, the difference in average trajectory may become negligible. Additionally, as you also noted, the presence of intermolecular forces and trajectory deflections can further complicate the calculation of average trajectory and pressure.

Overall, while the average trajectory may vary between different three-dimensional objects, the difference may not be significant enough to affect the overall pressure experienced by the gas particles. I hope this helps to clarify your question. If you have any further inquiries, please let me know. Thank you.