Timeline for What is (local) pressure within a gas on the microscopic level?
Current License: CC BY-SA 4.0
13 events
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| May 2, 2022 at 13:44 | history | edited | Roger V. | CC BY-SA 4.0 |
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| Nov 18, 2021 at 8:32 | answer | added | Thomas | timeline score: 0 | |
| Nov 18, 2021 at 8:13 | vote | accept | Roger V. | ||
| Nov 17, 2021 at 22:18 | comment | added | 2b-t | @RogerVadim Clearly macroscopic models that work on a larger scale can neglect collisions but models in kinetic theory do not, even though it might not be obvious: E.g. the 1/6th model in kinetic theory assumes molecular chaos, meaning $\overline{v^2} = \overline{v_x^2} = \overline{v_y^2} = \overline{v_z^2}$. This is actually not neglecting internal collisions but instead assuming isotropy of these collisions (no Cartesian direction is preferred) such that their precise effect does not have to be modelled. | |
| Nov 17, 2021 at 21:48 | answer | added | 2b-t | timeline score: 3 | |
| Nov 17, 2021 at 12:43 | comment | added | Roger V. | @MichaelM if we use the treatment from the standard statistical mechanics, the collisions are neglected - one uses the Hamiltonian function for free particles (in partition function, etc.) But there is usually underlying reasoning that the collisions do exist and lead for the establishment of the thermodynamic equilibrium, and that we waited long enought. I suspect the transmission of pressure through gas is considered on microscopic level in physical kinetics (i.e., non-equilibroum stat physics) using Boltzmann equation. | |
| Nov 17, 2021 at 11:38 | comment | added | Michael M | Actually, I thought the ideal gas law was able to neglect these collisions not because they are rare but because they average out... | |
| Nov 17, 2021 at 11:37 | comment | added | Michael M | Hmm... If you have a free gas with a higher concentration at some point it will tend to disperse. On a macroscopic level you would say there is a high-pressure center which leads to the motion. However, on the microscopic level it is just the molecular interactions leading to equilibrium. I think that internal pressure has to come from molecular collisions. | |
| Nov 17, 2021 at 11:26 | comment | added | Roger V. | @MichaelM ideal gas law is for the pressure on the walls of the container - derivations typically neglect collisions within the gas. For liquids and solids we clearly do not neglect the interaction between the particles, so the origin of the force/pressure is clear. | |
| Nov 17, 2021 at 11:23 | comment | added | Michael M | The forces can arise from many sources, as you describe in your question. I think that fact is evident in the variety of constitutive equations that exist for different media. Gases can often be described by the ideal gas law, while I don't know of any constitutive equation that works for arbitrary amplitudes in liquids or solids (usually you just assume a Taylor expansion for wave motion). | |
| Nov 17, 2021 at 11:19 | comment | added | Roger V. | @MichaelM Pressure is a force pur unit area, so it doesn't make much difference whether we talk about one or the other. The question is more of how a macroscopic force and motion arise... from atomic collisions? | |
| Nov 17, 2021 at 11:10 | comment | added | Michael M | Isn't pressure a macroscopic concept? Think about the statistical mechanics view you described: the "pressure" is the cumulative result of many atoms striking a wall. If you are interested in a molecule-by-molecule analysis, you shouldn't be talking about a "pressure", but should be analyzing the forces directly. | |
| Nov 16, 2021 at 12:25 | history | asked | Roger V. | CC BY-SA 4.0 |