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Science nerds of Lemmy: Is there an upper limit on the volume of a "confined gas"?
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this post was submitted on 29 Sep 2025
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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!
The understanding of a "confined" gas I got from high school physics class is one in a sealed rigid container, so both the volume and mass of the gas was constant. I did a lot of solving PV=nRT a lot, and there was a lot of "What is the pressure of x kilograms of this gas in a y liter container at z celsius?" Convert kilos of that gas to mols, convert celsius to kelvin, plug and chug. Or we'd calculate things like, you have a pneumatic cylinder with this much gas in it, the cylinder's dimensions are this by that, there's a weight on the piston, increasing the temperature by this much, how far will it lift the piston? So, maybe a more robust way of stating it is we're holding all factors constant except one independent variable and one dependent variable.
It occurs to me that we only did that kind of thing to dimensions of human machinery. That kind of math can reasonably model the physics of, say, a steam engine. But you can scale the apparatus up to the point that other factors become significant, I suppose is the breakdown here.
Earth's atmosphere is held to the planet by gravity but the force of pressure can resist gravity; heat up the atmosphere and it expands up into space. Gravity works almost like a balloon in that way, heat the contents of a balloon and it expands. Except gravity causes a pressure gradient throughout the gas in a way an elastic balloon doesn't. When we're talking about planetary atmosphere scale, we get into different areas of it being heated unevenly, and it taking significant time for air to move around and equalize pressures and densities...
When I initially asked the question, I imagined encasing the earth in a rigid shell at Armstrong's line, which I don't think would have much of an effect on the behavior of atmospheric pressure. I was trained to model the gas in a sealed bottle as one parcel of fluid that behaves as one thing, the pressure everywhere in a 1L bottle of gas is the same, but by the time you get to the size of a planet's atmosphere you have to take gravity and sloshing and such into account.
TL; DR: There's a gulf between 150 level college physics class and aviation meteorology.