Ask Lemmy

It's important to remember the word 'ideal' that dictates the conditions needed. The gas cannot be mixing with an 'external' source, gaining or losing energy to it's surroundings beyond the changes being specifically examined, is not subject to any forces or conditions not considered, and so on...

You're literally asking 'at what point are perfect conditions, impossible to every truly achieve, implausible?'. The answer to that: as soon as any factor cannot be simply ignored for the sake of simplifying the math.

Ah the spherical cow problem. Idealized math isn't always relevant to real world.

That said without doing anything special to earth the atmosphere is (theoretically) responsive. Gravity is a planets way of keeping atmospheric gases, as such it does at least partially confine them. The problem with trying to treat atmosphere as a confined gas is the scale of it which is why you have so many extra considerations mentioned. Even all the co2 we've released is only 0.0427% (427ppm) of atmospheric gases. If it didn't cause a greenhouse effect we probably wouldn't care.

The ideal gas laws don’t deal with gravitation. The earth’s atmosphere behaves the way it does because of earth’s strong gravitational field (relative to the same volume of gas without earth).

It should also be noted that real gases are not ideal gases. Instead of being point particles, real gases can have asymmetric molecular shapes. This can lead to all kinds of funky effects as the particles bounce off one another and acquire both angular momentum and linear momentum.

While I think your thought experiment is likely correct, I also think you might be able to insert enough gas into, say, a sun-sized container to make it act as if it were confined.

This might just cause it to collapse in on itself and solidify at the center, though, almost like a less-extreme Schwarzschild radius, which I guess would lead to it acting unconfined again.

Don't take my word as anything more than the ramblings of a layman, though.

neutron stars and black holes:

If I understand the question, it would be the point where the gas would lose its state and become a liquid or solid. This variable is influenced by pressure, the container and the external vs internal temperatures.

I guess there has to be an upper limit to the volume and/or mass of air that can be "confined

No fixed limit.

When your confinement is "bigger than ideal", and for example the pressure changes "here", then later pressure changes "over there".

Sound is the physical model that describes how pressure changes propagate from here to there.

The speed of sound tells you how long it takes before the pressure change goes from here to there (and maybe to everywhere) in your confinement. The behaviour of sound tells you if the change even goes to everywhere in your scenario.

So, for the question of the limit, your answer is this:

If your confinement is much smaller than the wavelength of the sound in your scenario, then you can call it "ideal" in this regard, because the pressure is the same everywhere.

When it comes to temperature changes, they are generally much slower. Sorry, I don't know the models that describe how temperature changes propagate.

I guess you can simply decide how much time you want to spend with observing, and so you define what is still a "confined" or "ideal" scenario to you, regarding temperature changes.

I think I'm following, but for clarification, when you say "unconfined" you mean bound within a vessel, but the vessel is able to expand? As in your example with heating the planet and the volume getting a little bigger? Or a like balloon?

Likewise with "confined" you mean like a steel can. Completely rigid?

If that's the case, this is my take. It's like having a spherical balloon with a spherical concentric interior hamster ball (stick with me). The balloon can expand and contract with an change in temperature or a change in number of molecules. It contains the entire volume. The hamster ball on the other hand only contains its own fixed volume. Molecules can flow into or out of the vents. The total weight contained within the ball can increase or decrease, but the volume will not.

The force that determines the expansion rate of the balloon and the mass contained within the ball is gravity. Density is diffusive. It decreases with increase in altitude. Increase the temperature and the gas molecules will run faster and faster. Being able to push the balloon out futher. Or, add more gas it will "stack higher".

If you had a purely confined system (i.e. the hamster ball has no holes). You have a pressure cooker. As you increase the temperature of the gas, the molecules move faster and faster, slamming into the walls of the ball. Eventually it will rupture.

All that said, you're correct. So far as I know as I know, earth shattering though it may be, there is no "glass ceiling" which will shatter from climate change (I definitely did that one on purpose and I'm not sorry). The model of the earth's atmosphere is as you say "unconfined" (caveate it is actually confined by gravity)

Final point. You could continue to add gas "indefinitely". That is, until the density at the surface of the earth is large enough to create a black hole. For that, you'd have to consult Stephen Hawking or read one of his paper on Black Hole Thermodynamics. Spoiler: Things can escape the grip of a black hole!