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How long would it take for a medium-sized human caster remaining inside a demiplane after the spell expires to suffocate. Assume no other mass displacing volume in the space.

Per the rules of the demiplane spell (PHB, p. 231):

the demiplane appears to be an empty room 30 feet in each dimension, made of wood or stone. When the spell ends, the door disapears, and any creatures or objects inside the demiplane remain trapped there as the door also disappears from the other side."

(Or, if I am making an incorrect assumption in this question, why wouldn't they suffocate?)

NOTE: Following on some initial comments this is not a question about extra-planar travel to demiplanes in general, but specifically about the demiplane spell and the space it leads to. Question hopefully now clarified.

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There's no way to reason one way or the other about this outside a DM's particular campaign, since this is explicitly the DM's domain to decide and the game provides no defaults.

In the context of the Dungeon Master's Guide chapter on the planes, the DM is given instructions explicitly and repeatedly to decide — according to their taste and campaign-design needs — how planar areas work and are laid out. In that context, it has only this to say about how demiplanes work:

Demiplanes […] boast their own physical laws. (DMG, p. 68)

The spell demiplane creates a demiplane, and that demiplane that it creates is not an exception to this rule. Beyond size, shape, and wall composition (and the implicit feature of having a non-lethal atmosphere, which I think we can take as read) all other parametres are the DM's bailiwick.

Should this eventuality come up, the DM will have to think about what physical laws the demiplane has, such that it boasts a human(oid)-breathable atmosphere. Perhaps it creates infinite air as needed; perhaps it suspends the need for air; perhaps it has a fixed quantity of air; perhaps it (like a modern house) maintains its breathable air by exchange via the cracks around its outer fixtures (i.e., its door) and becomes a deathtrap once those cracks disappear with the door.

The game is silent on this: consult your DM — or if they're an immersionist DM and won't tell you because your PC wouldn't know, I suggest that a responsible wizard will do due diligence and research this issue before it becomes a matter of life and death.

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About a month at most.

This article explains that the real issue here isn't actually oxygen deprivation, but Carbon Dioxide poisoning. In a 10 foot cube room, he calculates that a person at rest could survive for ~24 hours, half that if they're moving about and actively doing things (ie: looking around for an exit), and half again if they're doing strenuous work (ie: trying to break down the walls).

Extrapolating from there, a 30 foot cube room has 27 times the volume, and thus you should last ~27 days at most, if you do nothing but sit there. Depending on how active you are, that could drop down to as little as 2 weeks. Theoretically it could go even lower, but you would have to really work yourself hard every day and essentially not sleep.

However, there are also other factors to consider:

Water

However, there is also the matter of water. If you brought along a good supply, then great! You'll probably live long enough to suffocate to death. If not, then you'll start running into problems around day 3.

Exactly how long you can survive without water is difficult to predict, but 5 days without water is probably about as much as you should expect, though depending on circumstances and your condition, you may last a few more days after that, but no more than 12 at the very most.

Food

Food is also a problem, but less of one. You can live for about 3 weeks without food, though it'll start causing problems before that, especially if you're being active. You can probably squeeze through that last week before you suffocate, and if you brought any kind of food along, even if it's just leather to chew on, you should have no problem lasting the full month.

Sanity

Of course, before any of this becomes an issue, you'll have your sanity to consider. Being alone in a completely silent room can be pretty devastating. Solitary Confinement is often considered a form of torture, and while I don't have any exact numbers to share, it's definitely a possibility that you will run into this in the timespan given. You could very well survive the full month and be rescued just in time...only for your rescuers to find that you've gone completely insane from the isolation.

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