Depends on container size and how much water is in it. If you’ve ever seen one of those water phase diagrams you can get a good notion of how its state varies, not just with temperature but also with pressure. In theory it’s possible to have liquid water at any temperature, so long as the pressure inside the container is high enough.
At higher pressures liquids have to get hotter before they turn into a gas. Assuming the container doesn’t explode, the pressure would build as it heats up. This pressure makes it harder for more water to boil off, which allows the water to actually go above 100C. This continues until you can’t put in more heat, or all the water becomes high pressure steam.
Two things would happen. First, just like you said, it would continue to be water but really hot since the boiling point of water rises with pressure. You get this interesting cycle of water boiling, turning to steam, increasing the pressure, the increased pressure stops the boiling until it gets hot enough to boil again at that pressure. This cycle repeats until the pressure overcomes the ability of the vessel to hold said pressure. Then you get a steam explosion where the vessel explodes and rapidly reduces the pressure but not the temperature causing the water to turn to steam very quickly and violently. For reference, water boils at 100c at 14.7psi (atmospheric pressure) but at 225psi water don’t boil until 200c.
There would be some steam but mostly, it would stay as water.
The boiling point of water increases as pressure increases. So after a little water becomes steam which increases the pressure, the rest will remain as liquid.
If you continue heating the water past its *new* boiling point the water will turn into steam and the pressure will get higher and higher. Any real-world container will blow up.
Because the water is above its normal-pressure boiling temperature, as soon as the container breaks it’s going to very rapidly turn into steam and basically explode. This is called a BLEVE (boiling liquid expanding vapor explosion) and is extremely dangerous.
The pressure would raise the boiling point of the water. As the temperature continues to rise you’d have more water boil but this would in turn raise the pressure. At each temperature you’d find an equilibrium between steam and water. This will continue until you’re left with an container full of steam, a container full of plasma, or a container that exploded.
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