The lid would lift up and vent the steam. It is unlikely that the pressure from the water vapour would be precisely the same over the whole area of the lid, so chances at that it would vent more at one side of the lid than the other. In other words, I think the square lid would tilt up in one direction or another, just enough to vent some steam along one edge of the pot. Once the pressure in the pot reduced sufficiently, the lid would settle back down onto the pot. Then pressure would build again until it was sufficient to raise the lid again, and the process would repeat.If you had a square pot on the stove and a square flat lid oversized by perhaps 1 inch all around its edges.
The surfaces are all flat and the pressure can equal that of the lids weight.
What would the lid do if the water boiled?
If there was enough friction between the edges of the lid and the lid itself, then we would not expect the lid to slide around on top of the pot. It would just repeatedly lift and then settle back into position after some of the steam had vented. In practice, this could be like the lid vibrating up and down, possibly on more than one edge at a time.
So...
Why would it do that? If the lid is simply resting on top of the pot, then the pressure inside will never get much higher than it needs to be in order to raise the lid enough for steam to start venting. You're not talking about locking the lid down somehow, are you?The pressure gets extremely more powerful for this example.
It would move up and down.Would it
a) Not move
Up and down.b) Move in one direction or another
Yes, based on the pressure. It could depend a lot on how the water was being heated, too. Like, is the bottom of the pot being heated uniformly, or more in some places than others? That would certainly affect things.c) move randomly based upon geometry and pressures.
Unlikely, unless there was very low friction between the lid and the top of the pot.d) Would the lid move straight along a linear left/right, forward/backward motion?
The pressure wouldn't get higher and higher. Venting results in a pressure decrease every time.e) would the lid just lift at one end and let the pressure escape even as the pressure gets higher an higher?
But yes, it would just lift along once edge at a time, unless things were completely uniform (which we wouldn't expect in a real situation). If, by some miracle, it was completely uniform, then the whole lid would lift vertically off the pot then settle back into position, repeatedly.
The lid wouldn't try to find "maximum exhaust". Any exhaust that relieves the pressure enough to allow the lid to settle back would be sufficient. Like I said, the most likely thing is that it would lift along one edge.f) Would the lid find maximum exaust by moving straight in any direction unitl more of pot is exposed and then stop moving as pressure subsides?
Unlikely, unless the friction was very low. If it was, then the lid could drift in any direction and expose either an edge or a corner.g) Would the lid float and skew slightly until a corner is exposed