Suppose we have a pot of known dimensions filled to level L with boiling water on a stove, covered by a lid with a vent of known dimensions. Given the steady-state temperature of the stove (bottom of pot's surface), how to quantitatively estimate the ambient pressure and temperature of steam in the pot, at 1 atm pressure outside the pot?
All I can think of is that the pressure will be a function of the vent size (monotonically decreasing) and stove temperature (monotonically increasing). That's because more steam will be produced at higher stove temperature and the velocity of steam escaping through the vent is a monotonically increasing function of pressure; at equilibrium the amount of steam escaping == the amount of steam produced per unit time. But is it only the pressure that's increasing as stove temperature increases? In the limiting case of no water and zero-sized vent, the temperature of steam will be increasing until it reaches the temperature of the stove. Does the presence of 100°C water affect the temperature of steam?
One way to attempt to solve this problem might be to consider the amount of energy entering and exiting the pot (the rate of mass lost due to steam escaping is low, so assume no mass is lost).
I expect the answer to the whole problem would be a set of simultaneous equations to solve. But what equation to use to find the rate of energy input? It would be to do with the temperature of the stove and the temperature of the water, 100°C, but I can't think of how to find it.