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Comment by CorrectHorseBat | Hacker News Reader

>Ignoring the pressure that the walls of the container "feel", which is presumably not being modeled

But that is exactly what pressure (of an ideal gas) is? No intermolecule collisions are required to model the behavior of a gas as we know it.

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No, free molecular flow is a very different regime with very different behavior.

If you assume the gas is spread evenly throughout the space, you can model the pressure the gas exerts on the container it is in without intermolecule collisions. You (somewhat obviously) cannot model the pressure the gas exerts on itself this way, which is important if you're looking at the dynamics of how the gas will respond to a non-uniform distribution (the steady-state will still be uniformly distributed, but a gas with intermolecular collisions will spread out faster than one without: this is actually extremely relevant to achieving an ultra-high vacuum: when pressures are low enough you can't easily pump a volume out through a small hose, you need the pump to occupy a large enough part of the surface area of the volume you're pumping for the molecules flying around to actually hit it).

The thermodynamic definition of pressure is just how much work it takes to compress the system. This definition still works locally, you can just imagine compressing a small volume of gas.

I'm not 100% sure if fluid dynamics uses a subtly different definition (though how hard the medium is to compress is a fairly universal definition).

Obviously thermodynamics does break down if you've only got a small number of particles, but then 'pressure' also kind of stops working as a concept when you've got mostly vacuum.

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