In the ideal gas, the volume of a molecule and the interactions between the molecules are assumed to be negligible. Why aren't the interactions between the molecules and the walls of the container assumed to be negligible? Why are they much larger than those between molecules?
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3$\begingroup$ At some point (after your first contact with the subject) it is worth opening six or ten different books that treat the kinetic theory of gases and seeing how different authors set up or describe the problem. There are many ways to deal with the walls, and even more ways to talk about them. I've seen them described as non-interacting, as interacting with a hard-core, as weakly interacting, as the mechanism for energy transfer between the molecules, and simply ignored by treating a subsystem that doesn't include them (you need stat. mech. for this one). The i.g. model is robust in that way. $\endgroup$– dmckee --- ex-moderator kittenCommented Nov 6, 2016 at 19:15
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3$\begingroup$ Because otherwise the pressure would be zero? $\endgroup$– user207421Commented Nov 7, 2016 at 0:11
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4 Answers
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One important answer is simply that experimentally ignoring the interaction with the walls is clearly a terrible approximation. If that were true any gas would instantly escape from any container we put it in.
More theoretically, an idea gas does not assume there are no interactions between particles, it assumes that the interactions have 0 range (i.e. the particles have to be in contact) We can apply the same idea to the wall of the container, but we get a very different result, because the wall has a finite cross sectional area, rather than being point like, so the particle will always hit the wall if it travels far enough, but it will almost never hit another particle.
answered Nov 6, 2016 at 13:44
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When they say "assume interactions are negligible," they really mean "assume the only interaction is when they elastically bounce off each other". What this really means is you are ignoring any attractive or repulsive force between the molecules, but you are allowing them to bounce off each other like billiard balls. You make the same approximation for the boundary of the box: the molecules bounce elastically off the boundary of the box, but they don't otherwise interact with the boundary.
I'll add that you can also derive the ideal gas law assuming the molecules never even bounce off each other, but this is an unnecessary restriction. You can't derive the ideal gas law by assuming molecules don't bounce off the walls of the box, since then you'd never be able to find the pressure of the gas.
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9$\begingroup$ I'm pretty sure that you don't actually get the ideal gas law just by assuming that molecules act like billiard balls, unless you also assume that the diameter of the molecules is negligible compared to the average distance between them. Otherwise you get something like a hard sphere gas, whose behavior diverges from ideal at high particle densities. $\endgroup$ Commented Nov 6, 2016 at 17:07
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For particles to interact meaningfully, they have to be very close.
If the density is low, the probability that 2 particles will reach interaction distance is small, and thus the effect can be ignored.
The probability that a particle will reach interaction distance from a wall is 100%. If it travels far enough it reaches the wall. The wall is contiguous and dense so the particle will interact with it once it reaches it. And the wall is still there no matter how low the density of the gas is.
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The interaction between the atom in an ideal gas is assumed to be basically zero because the atoms are assumed to be of low density so that they rarely interact among each other. Also the volume they occupy is so small so that they do not ever interact with the box. So both kinds of interactions are considered negligible.
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1$\begingroup$ The interaction between ideal gas atoms and the box are not negligible; that interaction accounts for the pressure of the gas. $\endgroup$– pentaneCommented Nov 7, 2016 at 21:43