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.
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.
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