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Is it equal to atmospheric pressure? If so why? Surely the amount of air particles inside the bottle is much lower than the amount of the air particles above the bottle (i.e. the column of air above it) which should make it collapse as soon as the container gets sealed?

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  • $\begingroup$ when you say empty, do you mean it has zero matter inside it? or is full of normal air? $\endgroup$ – Alex Robinson May 11 '17 at 8:45
  • $\begingroup$ much lower air particles...? much less space too inside the bottle $\endgroup$ – user8718165 Apr 12 '19 at 6:33
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Taking your argument about the column of air above the bottle and how it should crush it:

You are not getting crushed right now. Whilst you are correct that this will mean that lower down in the atmosphere there will be slightly higher pressure, it is essentially negligable compared to a few metres above the bottle.

Consider unbalanced forces, if the pressure in the bottle was substantially lower than the pressure outside, there would be an unbalanced force and the material of the bottle will accelerate inwards (you can see this in a cheap plastic bottle if you suck some of the air out).

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  • $\begingroup$ Thanks. yes I realize that we can assume that the difference in pressure due to the height difference is negligible (and can be balanced by the properties of the material of the bottle). But what I don't get is why do we say that the forces balances (mechanic equilibrium is achieved) since masses outside and inside the container are obviously not the same and so is the acceleration (acceleration of both gas samples point towards the center of the earth because of gravity). Does this mean that we have to adopt a different model to explain this phenomenon (such as the Kinetic theory) $\endgroup$ – dimyak May 11 '17 at 8:59
  • $\begingroup$ because it takes X amount of force to bent a material, and if you have something less than that force acting on it, it of course won't do anything to the material $\endgroup$ – Alex Robinson May 11 '17 at 9:07
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What is the pressure inside a closed empty container (example: closed empty bottle)? Is it equal to atmospheric pressure? If so why?

Let's assume that you can completely empty the air inside a bottle and that you can seal it perfectly that no air from outside can enter. Then you would have a perfect vacuum in the bottle and the pressure would be essentially zero inside the bottle.

Doesn't the amount of air particles inside the bottle much lower than the amount of the air particles above the bottle (i.e. the column of air above it) which should make it collapse as soon as the container gets sealed?

Yes, for sure, the amount of air particles above the bottle (not only above but all around) and therefore the pressure outside the bottle will be higher than inside which would cause the bottle to collapse.

After answering your questions let me comment about this situation in practice. If you have a bottle which is not sealed then you have air inside and outside the bottle with equal pressures and everything is fine. If you close the lit and start pumping the air out from the bottle then the pressure will start to decrease and there would be some inward force on the surfaces of the bottle. If the bottle is plastic it would start getting smaller as soon as you start pumping. If it is a, say, glass bottle then it would resists the force for certain time and crack afterwards.

You can test this by putting the opening of a bottle in your mouth and suck the air into your lungs. If it is a plastic bottle if will immediately start shrinking but if it is a glass bottle nothing would happen because the glass bottle can resist the pressure difference that a human can create by his/her lungs.

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  • $\begingroup$ Thanks for the answer, but I meant to say that the bottle has normal air in it rather than being completely devoid of matter. $\endgroup$ – dimyak May 11 '17 at 9:05
  • $\begingroup$ i see, the question has changed while I was answering :). Because as I quoted you said "empty bottle" before. Then the answer of your question is very simple the pressure inside and outside of the bottle is equal irrespective of the bottle being closed or not. Therefore it would never crush as long as it is in the same altitude where the lit is closed and temperature is the same. $\endgroup$ – physicopath May 11 '17 at 9:12
  • $\begingroup$ @dimyak Are you asking that how the pressure inside a bottle whose height is so less match up exact with the pressure due to the great height of the atmosphere , knowing that P= hpg and the column of air in the bottle is so small ? I think that is due to the collision of the air molecules with bottle. Their speed is the same so the same pressure. But you might wants to know that if the total pressure = pressure due to wight of air + collision pressure as I wanted physics.stackexchange.com/questions/277033/… $\endgroup$ – Shashaank May 11 '17 at 11:21
  • $\begingroup$ Probably linuxick will like to see it $\endgroup$ – Shashaank May 11 '17 at 11:22
  • $\begingroup$ @Shashaank That's exactly what I was asking...and I read the link you sent except that it is not conceptually easy to understand. What anna was basically saying is that pressure can be stratified (for approximation reasons) and that within each strata, pressure is attributed to the collisions of gas particles (in all directions) rather than the weight of the air column acting on an area. This is why the pressure of the gas inside the bottle is equal to that just outside of it because it has the same density which exhibits the same rate of collision (has the same rate of momentum change). $\endgroup$ – dimyak May 11 '17 at 12:19
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Pressure=Force (or thrust however you consider)/ Area.

You are right, however they do balance out each other i.e attain equilibrium. Above the cap mass and height is greater than inside so the pressure is more but the air inside the bottle also increases in pressure by increasing their(air molecules or atoms) speed thus increasing the force and thereby the pressure.

This is what the link shashaank gave meant(or at least I believe).

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