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Where does air pressure come from?

I thought it was from gravity or the speed of the gas resulting from its heat. However, analyzing my own hypotheses, I think that my 'heat conjecture' is probably incorrect. Gravity seems more likely, as once you go farther away from Earth, the air pressure decreases, as does gravity. So it seems that air pressure results from the air being sucked downward by gravity, even culminating in toxicity at the end of a mine shaft.

Thanks to smart guys from here, I found out why gas particles don't maul us to death from their high velocity. - they don't have enough concentrated energy; instead they apply pressure. So the question is, where does that pressure come from?

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    $\begingroup$ I don't understand your comment about mine shafts? Are you suggesting that the risks of suffocation in mines are caused by high air pressure in a mine? $\endgroup$ – innisfree Apr 24 '15 at 12:51
  • $\begingroup$ @innisfree Sorry for the confusion, I meant that oxygen becomes toxic at such levels as it is heavier than air, basically purifying itself as you go down. $\endgroup$ – HyperLuminal Apr 24 '15 at 17:55
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In some sense yes. Let me explain a little. If we were to take a sealed container of gas and put it into free space far away from other bodies so that the gravitational force on the box is negligible would you agree that there would still be some pressure in the container? If we assume we have an ideal gas then the pressure is simply given by $$P=nk_{B}T$$ Where $n$ is the number density of the particles.

So if the temperature of our box doesn't change then we have no change in pressure, it's determined by the number of particles we have inside our box.

So if we consider the Earth, generally the density of particles in air decreases with increasing altitude. This is due to the gravitational force of the Earth. So the number density is largest near the Earth's surface and smaller when air becomes more rarified at altitude. This is ignoring the fact that the temperature is not constant at different heights in the atmosphere.

So in a way the air pressure we experience at ground level is due to gravity, but pressure generally is not a function of gravitational potential. Pressure is just a measure of the force the gas particles exert on the container when they collide with the walls. So as you would expect it depends on the speed of the particles (their temperature) and the number of particles we have bouncing off the wall at any one time.

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  • $\begingroup$ So gravity sorta acts as a container? Meaning it attracts more particles nearer to the earth, making more collisions between molecules and the resulting higher pressure possible? $\endgroup$ – HyperLuminal Apr 24 '15 at 18:06
  • $\begingroup$ Essentially yeah $\endgroup$ – Chris2807 Apr 24 '15 at 20:03
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In general, air pressure in the Earth's atmosphere is hydrostatic pressure, caused by the Earth's gravitational field. If there was no gravity then there wouldn't be any centripetal force and all the air molecules would just float away into space. This is why there is no atmosphere on the moon - because it doesn't have enough gravity to sustain one.

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Air pressure exists because if we place something in a gas, then the molecules/atoms flying around will keep banging into it, and in this way produce a net constant force per unit area.

As explained by @Chris2807 in the neat formula $P=n k_{B} T$, this is proportional to how many particles there are (since this is proportional to the amount of "banging" in a given time), and also the temperature (since the temperature represents the average energy of these gas particles randomly moving).

The way gravity comes in is it has a strong effect on the equilibrium for $n$ and $T$ as a function of altitude. Since it pulls down, we get a concentration of particles closer to the Earth. Then of course this becomes somewhat complicated by the weakening of gravity at higher altitude but that's more of a detail. As far as temperature goes, let's just say that's very complicated. Just think about how tough it is to predict the weather.

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Pressure of a gas comes from the average, collective change of momentum as its particles bounce against each other and the walls of anything encountering it. What gravity does is provide a counter-pressure - the weight of the gas itself - which stops it from expanding freely into space. The weight of the air above Earth's surface averages about 101,325 newtons per square metre - but as we're not used to newtons as a unit of 'weight', that's 10.33 metric tons. Equivalent to about 10 metres deep of sea-water. On the Moon gravity is 16.56% of Earth's, so the same depth of sea-water produces only 1.711 tons of downwards force per square metre. To weigh the same, it needs to be ~60 metres deep.

Incidentally, the Moon has enough "gravity" to retain an atmosphere for billions of years, if the only thing trying to strip it away was air pressure. However the solar-wind and soft x-rays from the Sun conspire to remove gas quicker. Of course, even then, the pressure would only decline noticeably over millions of years.

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