For gas pressure to exist must the gas be in a container?

Question

I’m not a physics student. I'm just trying to understand if there are gases making up our atmosphere, what makes up the “container” preventing all the gases diffusing into the galaxy or universe?

score 24 · Answer 1 · answered Jan 21 '25 at 04:44

You don't need a container, you need a force. Walls of a container can provide a force, but gravity also works. The escape velocity of the earth at sea level is about 11.2 km/s. The mean velocity of air molecules is 500 m/s. So for an air molecule to have escape velocity, it needs to have a velocity more than 20 times the average. The distribution of velocities is such that only a tiny percentage have a velocity that high. There is the further complication that an air molecule at sea level is going to bump into another molecule long before escaping the atmosphere, but that doesn't change the ultimate result much.

Flat earthers often claim that you can't have atmosphere next to vacuum, but the atmosphere never transitions directly from air to vacuum. At each point in the atmosphere, the pressure above is slightly lower for air above. The pressure then asymptotically approaches zero, but doesn't ever completely reach it.

score 12 · Answer 2 · answered Jan 20 '25 at 15:01

I remember reading a FlErF's complaint: if the Earth is a ball, then space would vacuum the atmosphere away.

Believe me: it's trying.

An order magnitude estimate proceeds like this:

We approximate the earth as a gravitating sphere with a static atmosphere in equilibrium.

Actually, I am going to approximate it as a flat Earth in a uniform gravitational field $g$.

The gas molecules then occupy states, and the relative probability of a state being occupied is given by the Boltzmann factor:

$$ f(h) = e^{-\frac E {kT}} $$

where $h$ is the height above ground, $T$ is the temperature and the energy of the state is:

$$ E =mgh $$

You can then integrate $f(h)$ from $0$ to infinity to get an absolute probability, but we don't need to do that; rather, we can estimate the scale height by setting gravitational energy equal to the thermal energy:

$$ mgh \approx kT $$

or

$$ h \approx \frac{kT}{mg} $$

For N$_2$:

$$ m = (2 \times 14.007) M_{AMU} $$

and $T=250\,$K, you get:

$$ h \approx 7570\,{\rm m}$$

which agrees with observation.

For lighter gases, like helium and hydrogen, the 1/2 height is 20-40 miles so that the tail ends of the distribution leak out to space (or get vacuumed up if you want) over geologic timescales, and now we don't have an abundance of those gases in the atmosphere.

score 7 · Answer 3 · answered Jan 20 '25 at 14:54

A gas need not have a "container" in the sense of being enclosed inside some material to have pressure. The particles of a gas need to have a minimum mean kinetic energy for the substance to even be in a gaseous state. As long as the gas sits in some kind of potential which is on average stronger than the mean kinetic energy of the gas particles, the gas will have a volume, and hence an associated pressure. There are basically no restrictions on what this potential can look like, as long as it interacts with the gas: It can be the walls of a container, or the gravitational field and the surface of earth, or even the gravitational effect of the gas on itself.

score 4 · Answer 4 · answered Jan 20 '25 at 16:09

Loss to space is not the major way that the atmosphere changes.

Here is an Ars Technica article summarizing the history of Earth's atmosphere. The complicated history of how the Earth’s atmosphere became breathable.

Essentially the entire atmosphere has been replaced over geologic time. Life played a major role in this. The original atmosphere had no oxygen. Free oxygen began to be generated when photosynthesis evolved about 3 billion years ago. Even then, geological processes ate the free oxygen as fast as it was produced. It wasn't until about 2.4 billion years ago that appreciable oxygen began to accumulate in the atmosphere. This is called the Great Oxidation Event.

Currently about 90 tons of gas, mostly H and He, are lost to space every day. Before the Great Oxidation Event, loss was much higher. About $1/4$ of the original ocean was lost to space. On Mars there was no Great Oxidation Event. This Nature article says that $5/6$ of the water on Mars was lost. Water vapor high in the atmosphere is dissociated, producing H$_2$ and H. These lighter gasses escape more readily. When oxygen is available, there will be much less H$_2$ in the atmosphere.

Even so, today there are still much bigger processes adding and removing gasses from the atmosphere than loss to space.

Roger V. · Answer 5 · 2025-01-21T08:02:18.830

The pressure can be defined as a derivative of the internal energy in respect to volume: $$ dU=TdS-pdV\Rightarrow p=-\left(\frac{\partial U}{\partial V}\right)_S, $$ see internal pressure for more detailed discussion.

This formula leads to a result identical to the one that is obtained by summing the molecular collisions against the wall. For a liquid however one may have to correct for effects like surface tension.

Related: What is (local) pressure within a gas on the microscopic level?

score 2 · Answer 6 · answered Jan 21 '25 at 02:51

No. Consider the simple fact of daily weather. Wind is caused by air moving from higher pressure to lower pressure region. The very fact that a higher pressure region can exist proves that you can increase air pressure without a container.

Of course, this effect is only temporary. But even a container is temporary. Almost any humanly made container will degrade over time or slowly leak over a long enough time period. As such, other forces that can contain air: geographical distance, magnetic field, gravity, wall of fire, wall of water etc. can also allow you to increase the pressure of air it contains. The question is for how long. In the case of gravity (yes, it's leaks air slowly) that would be billions of years. In the case of a plastic bottle it may be decades. In the case of geographic distance it could be several hours or several minutes or for large enough storm cells even several days.

JimmyJames supports Canada · Answer 7 · 2025-01-21T22:08:09.190

Air pressure and vacuums are, to my estimation, one of the most commonly misunderstood topics in the physics of everyday life. I've come to learn that this misunderstanding is not at all new. This article: "History of the Barometer" describes how people have struggled with this concept for many centuries based largely on a few incorrect pre-scientific notions. Somewhat astoundingly, even the great Galileo had a confused understanding of the topic.

The history of the barometer and how it was discovered is, I think, greatly helpful in dispelling the main misconceptions. The story really begins with the invention and use of (what we now call) vacuum pumps to remove water from mines. As noted in the article above:

It was noticed, by Giovanni Batista Baliani, among others, that pumps would not draw water higher than around thirty-four feet, and that siphons would not work over hills of that same height.

This is a really crucial observation for this issue because it makes it clear that a vacuum does not pull. If a vacuum were to have a pulling force, it makes no sense for one to form above a water (or mercury) column. The vacuum would pull the water (or mercury) into the empty space. But it doesn't. No matter how much you try, you simply cannot 'pull' water higher than 34 feet (at sea level) using a vacuum. If you are at a higher elevation, the height a vacuum pump can achieve is even less.

The reason why that is that a vacuum produces no force. The reason a vacuum pump works to lift water at all is 100% caused by the weight of the atmosphere above what you are pumping. When you reduce the pressure at one end of a straw (for example) the weight of the atmosphere pushing on your drink is no longer balanced from the end of the straw in your mouth, this allows the drink to be pushed up the straw by atmospheric pressure.

Some of the atmosphere is lost to space but it's not because the vacuum of space is 'sucking' it away, it's mainly due to the solar wind sweeping away molecules from the outer edges of the atmosphere.

So coming back to the headline question: