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If one googles "gas pressure", one will find many seemingly authoritative sites that say things like "Gas pressure is caused by the force exerted by gas molecules colliding with the surfaces of objects" (https://opentextbc.ca/chemistry/chapter/9-1-gas-pressure/), or "When the molecules of a gas bounce off the walls of their container, they exert a force. Gas pressure is defined as the force per unit area produced by the gas." (https://sciencing.com/what-causes-gas-pressure-13710256.html) Or " Gas pressure is caused when gas particles hit the walls of their container." (https://www.bbc.com/bitesize/guides/zc9q7ty/revision/7). If I didn't know anything about gas pressure, and I started trying to use the internet to understand it, I would very quickly conclude that gas pressure is produced by encounters with walls or objects, and when there are no walls and no objects, there is either zero gas pressure, or the concept of gas pressure has no meaning or usefulness.

Of course that is all nonsense, because gas pressure is a very useful concept, and is easily quantified, in situations where all you have is gas-- no walls, no objects. So what justification can be given for claiming that gas pressure is defined by its interaction with objects, or worse, that it is produced by said interaction? I can't see why this language is propagated so widely, it seems clear to me that gas pressure should be regarded as that property of a gas such that when it exhibits a gradient, it produces a force on the gas (in a fluid description of said gas, where we average over many indistinguishable particles). I don't see why we would ever want to define it as a force on an object, or worse, claim it is produced by the interaction with the object-- as so many sources do. Why would anyone want to think of gas pressure as a force on an object, instead of thinking of it as something whose gradient produces a force on the gas itself?

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In the case of a rigid wall, the molecules bounce off the wall and change momentum, which translates into a force per unit area on the wall. There is a momentum flux impinging on the wall and a returning momentum flux from the wall.

In the case of a portion of gas away from a wall, if we envision a small imaginary surface within the gas, there are gas molecules flowing to the surface in one direction, but they are not bounding off a rigid wall. Instead, they are bouncing off other molecules located immediately on the other side of the surface. Thus, the transfer of momentum is similar to that at a rigid wall. There is a momentum flux at the surface and a returning momentum flux from the surface. The mean free path between collisions for gas molecules at atmospheric pressure and ordinary temperatures is only a fraction of a micron.

You do not need to have a gradient in the gas for pressure to exist. All that is needed is molecules with momentum fluxes in all directions and molecular collisions. This gives rise to isotropic pressure.

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  • $\begingroup$ Ah, but there is still gas pressure when there are no collisions between the particles, because gas pressure is fundamentally about momentum flux (it's the momentum flux tensor), not about collisions-- either off walls, or off other particles. Collisions only matter because they are a good way to maintain the fluid approximation that is central to concepts like the density and pressure of a gas. But no one would say you need collisions to have density-- so why pressure? $\endgroup$
    – Ken G
    Commented Feb 9, 2019 at 0:32
  • $\begingroup$ Yes. I agree. The key feature is really momentum flux (isotropic). It sounds like you've answered your own question. $\endgroup$
    – Chet Miller
    Commented Feb 9, 2019 at 1:43
  • $\begingroup$ Not quite, because my question was why is the claim that gas pressure is about bouncing off walls to widely tolerated? Most sources will actually say gas pressure is "produced by" interactions with walls! They don't even say the pressure is there when the wall isn't. So why doesn't that get corrected? It seems like an indefensible error to me, so I'm asking if anyone else can see why it's tolerated. $\endgroup$
    – Ken G
    Commented Feb 9, 2019 at 2:16
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    $\begingroup$ Many times, concepts are simplified and even taught incorrectly as a way of introducing new students to the concepts. Personally, this bothers me very much also. Another example is heat capacity, which is first taught in terms of heat to raise temperature, but then later corrected to more properly and precisely represent the change in internal energy or enthalpy (state functions) as a result of a temperature change. This confuses almost all thermo students. I can cite other examples as well. $\endgroup$
    – Chet Miller
    Commented Feb 9, 2019 at 3:35
  • $\begingroup$ I agree. We need to say only what students are prepared to understand, but that shouldn't require explaining it completely wrong and having to fix all the misconceptions later. We can just say gas pressure is something that when it exhibits a gradient, implies a force on the gas that equals the gradient of that pressure. It's not like gradient of pressure as force per unit volume is that difficult! Then gas pressure acts on gases, and what happens to a wall is just the completely mundane "normal force" that students learn within three or four weeks of being introduced to physics. $\endgroup$
    – Ken G
    Commented Feb 9, 2019 at 14:46

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