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I've been thinking about air pressure and vacuums recently and a (for me at least) interesting question came to mind:
If there is an area with lower pressure than the surrounding air, the air distributes itself equally until the pressure is even everywhere.
For simplicity's sake let's say it's not only a low-pressure area but a complete vacuum so we can ignore any confusing forces that might still happen somehow otherwise.

Now to the question: As the air from the outside fills the vacuum, meaning it moves, some force must be acting on this air. I can not find the counter-force to this though. So my question is: What is the counter force of pressure force acting on the gas to fill a vacuum (or any other area with lower pressure in a gas)?

I have though about the following 3 solutions, but both have some major issues with them:

  1. If the vacuum "pulls" the air in, there must be a counter-force acting on the vacuum . This isn't possible though, as force cannot act on a "nothing". Also, vacuum doesn't pull in the surrounding but it is pushed in by the surrounding pressure.
  2. If the surrounding air "pushes" onto itself with its own pressure (which it does), a counter-force would have to act on it (the surrounding air itself). This cannot be true either, because that would mean that either the vacuum would not fill up (because the air should stop moving) or, at a certain distance the air should not be affected at all (which it isn't, that is true but only because the surrounding area is so large the effect is negligible).

I hop this description is clear enough, if not, feel free to ask for an explanation.


EDIT: Alright, I think I have understood it now. So the vacuum fills up because gas molecules move "randomly" around all the time and bump into each other. If there is a vacuum somewhere, they can freely move into there because there is nothing to bump against, so a lot of them end up in there, causing the pressure to equalize, because when it is, the molecules continue bumping around but do not "favour" a certain direction because there is less resistance there anymore.
Wind exists, because of course when many molecules have moved a certain direction, there are less of them where they used to be, which again is a lower-pressure area so it also fills up. This happens untill everything is mostly calm again.
Also, does this mean that pressure is the sum of the forces acting on the walls by the molecules randomly hitting the walls?

Is this correct?

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    $\begingroup$ May be the word suction force is misleading you. Have you ever wondered how to mark suction force in a FBD? $\endgroup$
    – ACB
    Jul 28 at 7:59
  • $\begingroup$ The counter-force comes from Inertia. $\endgroup$
    – PcMan
    Jul 28 at 8:18
  • $\begingroup$ @ACB I just didn't know what to call it so I put "Druckkraft" or something into google translate and used the result. $\endgroup$
    – Robbe
    Jul 28 at 12:51
  • $\begingroup$ The "fluid-dynamics" tag should probably be replaced by "fluid-statics." In fluid dynamics, the assumption of uniform pressure would no longer be applicable. $\endgroup$
    – D. Halsey
    Jul 28 at 13:04
  • $\begingroup$ @D.Halsey yep, will do! I didn't know fluid-statics existed as a tag. $\endgroup$
    – Robbe
    Jul 28 at 13:49
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'Pressure' of a gas is generated because of the collisions between gas molecules-gas molecules or gas molecules-wall of the container. Unless they collide, gas molucules move in straight lines with uniform velocity, which requires no external force (The impulsive forces act at the collisions are internal forces to the system).

If you put some gas molecules into a bottle, they spread throughout the bottle because there are no barriers inside the bottle. But they cannot go through the wall of the bottle. If you open the lid of the bottle, some of them come out to equalize the pressure inside and outside, because they like to minimize the number of collisions between them [ peace-loving :) ]. That is simply called they move due to pressure difference. But the real reason is you removed the barrier which prevented them from moving freely.

Imagine this way, you are running along a straight line and you see a door closed, so you turn back and again run. Next time you come and the door is opened so you freely move through the opened door. Did any force act on you? No.

In your example, the air is moving to the vacuum simply abolishing the pressure difference (This is explained in more details above) with uniform velocity. Therefore no force acts on the air. Thus no counter-force!


In response to comments:

Suppose there are two adjacent rooms. One room is filled with air molecules and the other one is a vacuum. There is a door between the rooms. When the door is closed the air molecules just hit the door and bounce back because they can't penetrate. If you open the door, the air molecules those were coming towards the door will enter the other room. Until door is opened, this process happens. What happens if the pressures of two rooms become equal? The process continues. The air molecules are still moving through the door. But you can't observe it. That is why we say that the air diffuses abolishing the pressure difference. But this is true unless you close the door. If you close the door at the middle of the procedure, the pressures of two rooms will not become equal.

All in all, what I wanted to imply through this example is that no external force acts on the air to push it to fill up the vacuum.

Hope this helps.

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  • $\begingroup$ Alright, I think I understand most of your solution, but the last phrase seems to contradict the rest: If you say it's just the air molecules moving about and they fill the vacuum because they don't bounce back anywhere there, how can they be "moving to the vacuum simply to abolish the pressure difference"? The first part seems to imply they can't move anywhere TO (as in, to achieve) anything. $\endgroup$
    – Robbe
    Jul 28 at 12:57
  • $\begingroup$ @Robbe, I've made an edit. Yes, you're right. The preposition 'to' is not suitable. The air molecules have no intention to equilize the pressure. But they do that undeliberately. $\endgroup$
    – ACB
    Jul 28 at 14:32
  • $\begingroup$ Thank you, your answer is pretty helpful now! Just to get this straight: That would mean the vacuum fills up faster if there is more pressure (and the pressure on the walls is higher as well) because there are more air molecules either just passing through the hole or hitting the wall? $\endgroup$
    – Robbe
    Jul 28 at 14:55
  • $\begingroup$ @Robbe, More pressure means more collisions. More collisions means more molecules. That means, yes, more molecules will go through the 'door'. Eventually, it means that they fill up the vacuum faster if there is more pressure. $\endgroup$
    – ACB
    Jul 28 at 15:45
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The answer to your dilema is that there is no need for any counter force.

Statistically it's likely that many molecules would come into the region where the vacuum was - however no force pushes them there.

In the kinetic theory of gases, intermolecular forces and collisions are ignored, but there will be, by chance, many molecules travelling towards the vacuum region. They continue in a straight line with no force acting, as in Newtons 1st Law.

Since there were no molecules in the vacuum region to leave, it just happens by chance that a short time later, more molecules will be in the region than before and the vacuum region has been 'filled'.

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  • $\begingroup$ Of course there is no NEED for a force to fill the vacuum. But isn't it the case that the air pressure, and by that force, actively "pushes" into the lower-pressure area? Otherwise, how would wind exist? $\endgroup$
    – Robbe
    Jul 27 at 17:00
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    $\begingroup$ It's true that if there were a barrier between a high pressure area and a low pressure area, there would be a force on it caused by wind, but it's caused by by collisions of millions of molecules each imparting a tiny force on the barrier. The equal and opposite force to all those tiny forces is a force on each molecule causing it to change direction. In the vacuum case, as there is no barrier there to feel the force, we can say that there is no need for a counter-force in that case $\endgroup$ Jul 27 at 17:15
  • $\begingroup$ If there were a barrier between the two areas, how could there be wind? Doesn't wind mean "air flowing from high- to low- pressure area"? It can't if there is a barrier. $\endgroup$
    – Robbe
    Jul 27 at 17:32
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    $\begingroup$ Imagine that a person was the barrier, they would feel a force from the wind pushing on them and it would be flowing past them on either side. It would still count as a windy day even though the force you felt from the wind caused that part to stop. There is a 'counter force' acting on the molecules of the 'stopped wind' but not on the rest. Good question, that's the best explanation I can do - best of luck with it. $\endgroup$ Jul 27 at 17:38
  • $\begingroup$ Oh well, I thought you were talking about it being completely sealed. Thanks for you efforts anyway! (Although I'm not happy / I don't quite understand how the pressure of the air would not affect all of this (or I'm just reading your explanation wrong)). But thanks anyway! $\endgroup$
    – Robbe
    Jul 27 at 17:43
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As the air from the outside fills the vacuum, meaning it moves, some force must be acting on this air.

It might be useful here to contrast the "push back" of compressed air with the "push back" of a compressed metal, for instance. For the latter (and for all familiar condensed matter), bulk stiffness is what we call "enthalpic"; in other words, compressing the material increases the internal energy. The molecules resist being pushed together for electrostatic reasons; i.e., involving one of the fundamental forces. If we differentiate the internal energy (in joules) with respect to the compression distance (in meters), we obtain a force (in newtons).

In contrast, in the ideal gas, stiffness is what we call "entropic." Compressing the gas (at constant temperature) does not increase the internal energy, and thus, differentiating the internal energy by the compression distance gives... nothing. The resistance to compression—and tendency to expand without limit—arises solely from our tendency to more often notice arrangements that occur more often. (This is one statement of the Second Law of Thermodynamics.) None of the fundamental forces are involved; there are simply many more arrangements possible when a gas spreads to occupy its container.

This distinction may be connected with the challenge you've found of identifying some "force" that pushes a gas into a vacuum. No such enthalpic force exists.

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If I understand correctly, this question is about Newton's third law. If a gas exerts a pressure on something, something must provide an opposite force to the gas. Keep in mind that counter-forces in Newton's third law don't prevent motion. When I push a ball with my finger, the ball moves forward, my finger wants to move back. I stop my finger moving back with my arm, and my arm now wants to move back. I stop my arm with my legs connected to the ground, so the ground wants to move back. The ground is enormous, so we don't notice it moving back.

Let's imagine a layer of air called l or L. In front is our vacuum, V. Behind it is the rest of our air, A. Now I have a text diagram:

V l A

Microscopically, air molecules from A are colliding with air molecules from L, so whenever a molecule from L gets a kick, air molecules from A get a kick in the opposite and equal direction. This is true of any layer in the gas.

Now let's think about V and A as regions of space where particles can move in and out, like voxels in Minecraft, and l is the boundary between two voxels. The equal/opposite 'force' is more like this: in the L rest frame, equal numbers of particles of L are going towards V and towards A. Hence, equal and opposite momentum is moving both towards V and towards A. This is $F = \frac{dp}{dt}$, a change in momentum over time for a region of space.

The vacuum region V gains momentum from A because it is gaining stuff with velocity. So it experiences a positive force in the wind direction.

The air region A is losing momentum to V as particles with momentum move from A to V. So it experiences the opposite and equal negative force.

Now, after a moment, the vacuum region V is no longer a vacuum. It is now a region with mostly vacuum, and a thin layer of stuff that moved into it.

If you don't want to account for the force this way, and let's imagine there are no collisions either, then you just follow a bunch of particles not experiencing any forces. There are no forces, but because there are more particles on one side than the other, the ones who were already moving toward the vacuum end up continuing, hence filling up the vacuum. Because in a gas, we assume the particles were moving in random directions, so some were bound to point towards the vacuum.

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  • $\begingroup$ "The air region A is losing momentum to V as particles with momentum move from A to V. So it experiences the opposite and equal negative force." wouldn't that mean that air stops closing in after the first layer because A is pushed away by the distance it will move in by in the next frame, pushing it back again and so on? (I think I am missing something I should have read... sorry) $\endgroup$
    – Robbe
    Jul 28 at 12:47
  • $\begingroup$ Although A loses momentum to V, it gains momentum from the air even further back which keeps the chain going. But moreover, this momentum transfer does not mean A stops. If A has momentum p, and loses dp, p-dp can still be positive, so it can continue moving forward. Experiencing a negative force can be like lightly tapping on the brakes. You can slow down but still move forward. $\endgroup$
    – Alwin
    Jul 28 at 14:01
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A farmer has 10 acres of land which is fenced off from the surrounding area and divided in the middle into two portions of 5 acres each. There is a gate in the middle that allows passage between the two halves. He puts his sheep in one half of the land with the gate closed. One day he decided to open the gate and left it open. After a day or two, he found out that some of the sheep are in the formerly empty other half of the land. The sheep start filling the empty half just by wondering around. The same applies to how air fills a vacuum. No one pushed the sheep to go to the other side, they just wondered into it because sheep tended to move around. Air molecules are not stationary. They move around and stumble into the unfilled vacuum. Just as there is nothing to stop the sheep from moving around. There is no counterforce.

Continuing with this analogy, the sheep bumping into each other and the fence would be the pressure. The more sheep there are, the more chance that they bump into each other and the more likely that some of them got pushed into the empty half of the land. The higher the pressure the faster the vacuum will be filled.

When I say there is no force to push the sheep, I meant no external force. The sheep will still bump into and pushing against each other.

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  • $\begingroup$ so does that mean that if the pressure was lower the vacuum would fill up just as quickly instead of slower? $\endgroup$
    – Robbe
    Jul 28 at 12:48
  • $\begingroup$ @Robbe No, I edited my answer. The higher the pressure, the faster the air spreads around into the vacuum. $\endgroup$ Jul 28 at 13:26
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As the air from the outside fills the vacuum, meaning it moves, some force must be acting on this air.

Force is needed for acceleration. If the air is travelling with a constant velocity, no force is needed. Of course, some force was needed to get the molecules moving, and that force with a collision with another molecule. That molecule will then travel in the opposite direction. So analyzed at a molecular level, what we see as "suction" is not producing a force itself. Rather, it is produced by already existing forces.

Analyzing the system macroscopically, however, there will be a "missing" momentum; the molecules that go through the hole will take some momentum with them, causing the remaining molecules to have a net momentum in the opposite direction. The molecules that go through the hole would have, had the hole not been there, hit the wall, and imparted a force on the wall. There is therefore an imbalance, with more molecules hitting one side than the other, and that will cause a net force.

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  • $\begingroup$ I like the second part! So to recap, does that pressure is caused by more molecules hitting a wall on one side than on another? $\endgroup$
    – Robbe
    Jul 28 at 12:52
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Creating a vacuum does require an outside force. To create it the pump is constantly pushing air out. To maintain it the walls of the sealed chamber are being pushed on from the outside air.

Creating a high pressure zone is similar, with the pump pushing air in and then walls keeping air in (walls being pushed on outward by the higher pressure gas inside).

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