A lot of the laws of physics I’ve studied, like Boyle’s Law and Charles’ Law, describe the behavior of “An ideal confined gas.”
I’ve had to tell several flight students to unlearn what they’ve learned about that in the meteorology chapter, because, for example, in a confined gas, increasing the temperature causes an increase in pressure while the density stays the same. In the Earth’s atmosphere, increasing temperature does nothing to the pressure and decreases the density. Because the Earth’s atmosphere isn’t “confined,” there’s no lid, the air is relatively free to change volume. Heat the entire planet up and the atmosphere will just get a little taller.
But, I think, even if we put a magical vacuum tight shell around the planet 200 miles up, making the volume finite, I think the atmosphere would still act like an unconfined gas, because 1. it’s so vast that it never homogenizes, parcels of different temperatures, pressures and moisture content take days to slosh across the available space, and 2. the Earth’s gravity will cause a pressure gradient; most of the air is at the bottom and if you heat it up, it may not change volume but the pressure at the top will increase.
So I guess there has to be an upper limit to the volume and/or mass of air that can be “confined” and it’s somewhere below planetary scale.
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.
There are what are called 1st and 2nd order effects. Gravity is first order. The sloshing is second order. So as you say, scaling the model up does make additional factors matter relative to your 1 liter of gas on the table. But it’s only the first order effects which make an appreciable difference when looking at it on a planetary scale.
Then if you say want to extend the model to your meteorogical model, you have to say, well… the density of air is different over the ocean because of evaporation. The gulf stream moves clouds consistently this way etc. But those things only matter after you’ve introduced gravity, and understood the earth’s atmosphere as the “gravitational balloon” model. Then you introduce your sloshing to understand the next stage.
This way of thinking about things in terms of leading or second leading order effects when considering systems at varied scales is pretty common in physics.
Btw from lived experience I can tell you the only gulf between you and a 150 level physics class is that you are actually trying to learn it.