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What is air pressure?

  1. Jul 18, 2011 #1
    Reading a website and I noticed that the author claimed that air pressure is essentially equal to the weight of the atmosphere. I googled that fact and sure enough, everywhere I go there is that statement. But...

    Caveat. I have no maths or science background, so won't cope with too many equations in answering my question...

    I assume the concept pressure=weight is a sort of generalisation. Because it does not seem obvious to me that this could be so.

    Here is a thought experiment. I have a safe of solid steel 1 metre on all sides with an airtight seal. With the safe open and a barometer inside, the air pressure inside will be whatever the extant air pressure is at my location. If I close my safe, there is no longer a column of air acting upon my barometer. True, the atmosphere may be weighing heavily upon my safe's surface, but I see no way for that to affect my barometer. The parcel of air available to exert some kind of vertical pressure is little more than a few cm high. It won't weigh much...

    What do I not understand?
  2. jcsd
  3. Jul 18, 2011 #2


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    Welcome to PF!

    Hi Graeme! Welcome to PF! :wink:
    Yes, you're right to be suspicious :smile:

    technically, the air pressure is essentially equal to the weight of the atmosphere plus any external forces (other than weight) …​

    we usually take a column of air that extends to "outer space", where the external force is zero,

    but in your example the column extends only to the roof of the safe, which is exerting a downward force on the air.

    (in practice, of course, the air pressure inside the safe is simply whatever it was when you closed the door, and from good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=373" from the roof is equal and opposite to the force of the air on the roof :wink:)
    Last edited by a moderator: Apr 26, 2017
  4. Jul 18, 2011 #3
    Thanks tim. Hope you can bear with me on this, just a few more questions to clarify that. I'll have to read up on what the third law says (and the first and second too clearly!).

    I would have imagined that weight is the force exerted on a surface by an object that is accelerated by gravity. That is (and I am sorry if I don't know the correct physics terms/concepts to describe what I am saying), any object with mass will, in the presence of a gravitational field, be accelerated by that field, presumably only in a direction downwards perpendicular to the surface of the gravitational object. That object will not 'weigh' anything while being so accelerated. It will only exhibit 'weight' when it is prevented from accelerating. So weight is the effect of an object being prevented from responding to a gravitational field. All objects on earth's surface will fall to the surface, where weight can be measured.

    However, the atmosphere is not falling. As I understand it, the atmosphere is composed of free moving molecules which are in effect unconstrained.

    If those molecules are not 'connected' and not falling, then they can exert no force from the effects of gravity on any surface ?
  5. Jul 18, 2011 #4


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    Are you sure those websites said "air pressure" and not "atmospheric pressure"?
  6. Jul 18, 2011 #5
    Ummm... I am unaware of the distinction. I mean the pressure that one experiences at the surface of the earth and which is measured by a barometer.

    I just read tiny_tim's reaction force link. This is exactly my point. The magic is contained in the statement "between two bodies in contact". Which is precisely what I said above. There must be a surface connection for weight to be exhibited, or for a force to be realised. The atmosphere is not composed of a single object or body - it is free moving molecules which do not seem to compose a 'body'. Whilst gravity may affect each molecule, it would seem to do so independently. Solid objects are composed of molecules in some form of bond (is that E/M forces or chemical bonds?) and thus the effect of gravity on each molecule is effectively communicated across all molecules in that object. Not so an atmosphere I'd have thought?
  7. Jul 18, 2011 #6


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    Hi Graeme! :smile:
    The molecules are moving freely, but only until they hit something.

    Usually, they just hit each other, but when they hit a solid surface they bounce off it, and that change in momentum exerts (indeed, is) a force on the surface. :wink:

    (that's https://www.physicsforums.com/library.php?do=view_item&itemid=26" … force = rate of change of momentum)

    (and Newton's third law applies as between the surface and the molecules that hit it)
    Last edited by a moderator: Apr 26, 2017
  8. Jul 18, 2011 #7
    Yes, but it will only be those molecules striking the surface that can impart a force. The molecules 200 feet further up, or 5 km further up, are not striking that surface. Or are you suggesting some kind of instantaneous cascading collision force through the entire atmospheric column at any instant?
  9. Jul 18, 2011 #8


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    Yes :smile:, except that it doesn't need to be instantaneous, does it? :wink:
  10. Jul 18, 2011 #9
    Hmmm... yes, it would be largely wouldn't it?

    I guess I am talking from ignorance here, but a solid object is solid at most instants isn't it? I mean if we slice down time to ever smaller slices then our solid object remains solid I assume? I am getting into very fuzzy territory now as I have no idea what actually makes a solid object solid, but it is the state of solidness that allows an object to be accelerated by gravity isn't it?
  11. Jul 18, 2011 #10
    But getting back to my question, it seems to me that a solid object is a bound object and it is that binding that allows it to exhibit 'weight'. So I can easily conceptualise such an object bearing on a surface. I can't see how individual free moving molecules can transfer the effect of 'weight' so effectively throughout the whole vertical column.
  12. Jul 18, 2011 #11


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    You can think of a solid as being made of very tight springs.

    A force at one side of a solid is transmitted at the speed of sound towards the other side.

    Same thing for a fluid (liquid or gas), except that the transmission is by collision instead of by the electromagnetic forces that make up the "springiness" of a solid.
  13. Jul 18, 2011 #12
    Forgive me for taking so much time with what must be very basic to many of you, and thanks for your replies so far, it is certainly helping me develop a decent mental model.

    I must admit I've never heard of forces in solids being transmitted at the speed of sound! But there you go, you learn something new all the time.

    So, you are saying that the molecules in the column of the atmosphere are all colliding with the molecules below them as they are pulled earthwards by gravity and this force is cascading through the column, and at each 'layer' this force is accumulating to create the pressure at the surface? Do air molecules only move downwards, or are they free to move in other directions? if other directions, would there equally be a force in another direction. For example, if I heated the air, the molecules would be excited and I would imagine them to move in all sorts of directions, including up. That force in a sideways or upward direction would be 'pressure' but it wouldn't be 'weight' would it?
  14. Jul 18, 2011 #13
    They can move in other directions, absolutely! In general, you don't need to worry about differences in air pressure with respect to height, except when you start considering near-airtight structures that cover a significant vertical part of the atmosphere. There is almost no difference in air pressure as you move up by, say, 1 meter or 2.
    Absolutely! Consider the equation [tex]PV=nRT[/tex], which says that Pressure x Volume = number of molecules of gas (in moles) x R (a constant) x Temperature. Notice that nowhere does it make mention of mass of the gas involved. If you heated a volume of gas, the gas would exert more pressure on the walls of the container, but since the pressure would be equal across all of the walls of the container, the forces would cancel, and the mass would remain unchanged.

    I think that the model of pressure being equal to the weight of the atmosphere has its benefits, but it must be properly illustrated, or it just leads to more confusion. Here's my take:

    Air has mass. In the absence of any sort of gravitational field, the air has mass, but no weight. If you subject the air to a gravitational field, now the air has weight. It is attracted to the object that is producing this field. Assuming that there are a lot of molecules of gas, they will all try to get as close as possible, but will stack up on each other. Every molecule of gas wants to be as close to the source as possible, and so the molecules will "push" and "shove" (physics talk: collide) in an attempt to get closer. As you get closer and closer to the graviational source, the collisions become more aggressive. These collisions are what we call "air pressure." The cumulative effect of many, many collisions can produce a substantial force
  15. Jul 18, 2011 #14
    Air pressure is the result of gravity pulling down on the atmosphere and stopping the air from drifting off into space. So at sea level the air pressure is about 14.7 pounds per square inch, thats the weight of a 1 square inch wide column of air from sea level to the top of the atmosphere.

    When you open your safe door the air inside the safe is at a pressure of 14.7 pounds per square inch, when you close the door you are trapping the same volume of air at the same pressure so the pressure remains the same inside.

    Even if your safe was sent into space the pressure inside would remain the same as long as the safe didnt leak and the temperature stayed the same.

    In the vacuum of space the air inside the safe would be pushing against the inside of the safe walls with a pressure of 14.7 pounds per square inch and since the vacuum outside is not pushing against the outside of the safe, the walls of the safe are stressed and the safe is trying to inflate like a balloon. Of course nasa has to make sure that spacecraft have strong enough skin to withstand this.
    Last edited: Jul 18, 2011
  16. Jul 18, 2011 #15


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    There is: atmospheric pressure is the pressure of the atmospere. Air pressure is of any volume of air: it can be pressure in a tank.
  17. Jul 18, 2011 #16
    Graeme M
    You have hit the jackpot with this one!
    No-one can explain how air pressure works!
    Congratulations, in the spirit of pure thinking.
  18. Jul 18, 2011 #17


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    "no one can explain"?
    That's a bit sweeping, isn't it?
    The pressure in a gas is due to the motion of the molecules. If the gas is in contact with the walls of a container then the pressure is due to the molecules bouncing against the container sides. Each molecule hitting the sides has it momentum, normal to the side, reversed. That involves an equal and opposite impulse against the side. The rate of the molecules hitting the side and their average velocity (related to the temperature) will tell you what the actual force is on every unit of area. Pressure acts in all directions equally; up down and the sideways directions. That is what pressure is and what 'causes' it. You don't need a surface to be there; the pressure is there, keeping the molecules in one region from encroaching (on average) into a nearby region of a gas, across a virtual surface between them.
    The reason that there is pressure in the atmosphere is that all the molecules above us are pulled towards the Earth by gravity. The downward force on a 1square metre just above us is the same as the upward force and is due to sum of the downward forces (the weights) of all the molecules in a 1msquare column , all the way out into space. The fact that molecules are zapping about in all directions doesn't alter the above because it just averages out. The actual temperature affects the speed of the molecules, hence the pressure and, hence, how far the atmosphere extends out into space. If the whole Earth were much colder then the thickness of the atmosphere (assuming the same number of molecules) would be much less but the pressure would be much the same. ~(Very simplified model because, for a start, all the water would have condensed etc. etc. and gravity gets a bit less as you go up).
    That was explained to me about 50years ago and it still is a pretty good explanation of what is happening.
  19. Jul 18, 2011 #18
    Sophie (or "Centaur")
    Thank you for providing a reasonable explanation.
  20. Jul 18, 2011 #19
    Thanks again, this is good and I am making progress. But still having trouble with some conceptualisation.

    I'll come back to Sophie's explanation in a moment. EnglishScientist states that my theoretical safe 'locks' in air pressure, even if my safe were in space (ie a vacuum) air pressure remains at what it was. However that ruins the earlier explanation which invoked the weight of the column acting on the safe and using Newton's third law to accumulate weight inside the safe. EnglishScientists' explanation therefore must explain air pressure as a force caused purely by molecular collisions with the barometer in the safe, surely?

    Sophie's explanation suffers the same fate in my view. In fact, he/she invokes a virtual surface but also says that a surface is not needed in the atmosphere. However that leads me to contemplate the nature of weight. Weight it seems to me cannot be expressed without a surface when we are talking about objects, which I assume we are. The atmosphere is not an object is it? Therefore, it is the molecules we must consider, and these are the 'objects' being acted upon. Without a surface to bear upon, how can we have weight? Weight seems to me to be a function of the extent to which an object accelerated by gravity is prevented from reaching the velocity gravity imposes on it. But our molecules are not doing that, on the whole.
    Last edited: Jul 18, 2011
  21. Jul 18, 2011 #20
    I also have trouble with the notion that 'collisions' impart weight. Any mass that is accelerated which collides with another mass will impart a greater force than if that first object merely rested on the second object wouldn't it? My thinking suggests that a collision is a different event to the 'contact' proposed by Newton in expressing weight. Gas molecule collisions will impart a force, but that force wouldn't be 'weight' would it?
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