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.
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.
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.
I suppose yeah, it does boil down to “At what point does adding another factor add another factor?”
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.
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.
When it comes to temperature changes, they are generally much slower. Sorry, I don’t know the models that describe how temperature changes propagate.
Having solved the heat equation for a solid as an example problem for my partial differential equations class, I don’t want to know how bad it gets for gasses
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:
Well I mean, before you get that dense, what happens if you put Jupiter in a Jupiter-sized airtight box?
I would think putting Jupiter in a Jupiter size box would be a good experiment to see how much the sun affects the currents in Jupiters atmo. Like, you’re basically getting rid of sunlight as a confounding variable in studying the effects of the cores gravitational pull.
*assuming the Jupiter size box is massless xP
Would that massless box also be a perfect insulator? My understanding of thermodynamics breaks at “massless”. Assuming it’s a solid, sunlight would heat it, and that heat would be conducted to Jupiter, but again an object with a mass of zero breaks the math.
Is your massless box a better thermal insulator than the vacuum of space?
It is also my understanding that Jupiter, unique among our planets, radiates more heat into space from it’s own contraction than it receives from the Sun.
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.
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.
That would be a lower limit on the volume. OP is asking if a large enough container for a given mass of gas is functionally infinite (and thus the gas acts as if it were unconfined).
What are your thoughts on how Jupiter and other gas giants behave?
I’m thinking something the scale of the Earth’s atmosphere, where the air isn’t at high enough pressure or low enough temperature to condense, but the mass and volume are great enough for gravity to cause pressure gradients.
Imagine a 1 liter container with 1 atmosphere of N2 inside, floating in space. Sunlight or something is keeping it constantly warm enough to remain gaseous. The gas laws I was taught in school like Boyle’s Law and Charle’s Law would accurately describe the behavior of the gas in that container.
Now scale it up the container, and the gas inside.
as it approaches the size of a planet, gravity will start being a significant factor in the behavior of the gas, that you’d get an area of relatively high pressure at the center of mass of this vast container, and relatively low pressure near the container wall. Then start playing around with the temperature.
