Timeline for What is (local) pressure within a gas on the microscopic level?
Current License: CC BY-SA 4.0
11 events
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| Nov 19, 2021 at 6:47 | comment | added | Roger V. | note that I am interested in the microscopic mechanism: I can calculate density and then calculate the bouyancy force - this gives the answer, but it does not explain the difference between a baloon and an open mass of air (or why there's no difference). | |
| Nov 18, 2021 at 23:42 | comment | added | 2b-t | @RogerVadim One possible way to answer your question would be based on the temperature dependence of the probability distributions (e.g. Maxwell-Boltzmann distribution) and the resulting effect of gravity. I will try to give it a go tomorrow evening. | |
| Nov 18, 2021 at 20:02 | comment | added | 2b-t | @RogerVadim The microscopic behaviour causes this macroscopic phenomenon. On the microscopic level you might be interested in the rules that cause it, but all you care on the macroscopic level is this coarse-grained large-scale view. Some things can't be explained on this blurred macroscopic level, some things are not obvious on the microscopic level. The different descriptions coexist. The interesting thing about kinetic theory is that you can bridge the two levels and find connections between the two worlds, e.g. with the aforementioned Chapman-Enskog expansion. | |
| Nov 18, 2021 at 19:58 | comment | added | 2b-t | @RogerVadim Nonetheless you can describe it that way on a larger scale with an accuracy that is enough to predict this situation. Similarly you might have heard about "Conway's game of life". It is a cellular automaton with very basic rules, you react to your neighbouring cells. But complex life emerges from it. There has been some maniac on Code Golf Stackexchange that created a digital clock by designing an appropriate initial distribution. | |
| Nov 18, 2021 at 19:52 | comment | added | 2b-t | @RogerVadim You have probably heard about traffic waves, that the behaviour of drivers in some scenarios can be described with a wave equation. Each individual sitting there makes the decision to speed up and slow down, influenced by what the people in front of them do. If you ask the drivers why they reacted the way they did, they might tell you a lot, but I guess nobody was planning for a wave equation. Maybe this wave equation is also not perfect: There is this one old grandma that drives slowly and that one guy overestimating himself crashing his car into the one of the guy in front. | |
| Nov 18, 2021 at 19:41 | comment | added | 2b-t | @RogerVadim You are welcome. I can recommend you "An Introduction to the Theory of the Boltzmann Equation" by Harris Stewart. The topic is very interesting, I hope you will like it. I will have a look at the question and try to answer it. I think you should not think about a segregation of macroscopic and microscopic. In the end both are describing the same thing. The macroscopic equations emerge on a much larger scale from the microscopic description. | |
| Nov 18, 2021 at 8:13 | vote | accept | Roger V. | ||
| Nov 18, 2021 at 8:09 | comment | added | Roger V. | Thank you! I have myself began looking in the direction of how hydrodynamics emerges from the Boltzmann equation, and I am glad to have an input from an expert. Could you comment on my other question How does hot air rise? - what remains unclear to me is how macroscopic and microscopic motions segregate, as both ultimately result from collisions. | |
| Nov 18, 2021 at 7:51 | history | edited | 2b-t | CC BY-SA 4.0 |
Added reference to Boltzmann distribution
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| Nov 17, 2021 at 21:56 | history | edited | 2b-t | CC BY-SA 4.0 |
Added remark on non-ideal gases
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| Nov 17, 2021 at 21:48 | history | answered | 2b-t | CC BY-SA 4.0 |