I'm trying to think about how fast the rate of pressure will increase in an idealized boiler filled with water starting at 100°C, standard pressure, and supplied with 1000W of power. I'm assuming a constant volume process.
Initially, the boiling point of water at standard pressure is 100 °C, and the latent heat of vaporization is 2257 Joules/gram, and I assume I'm adding 1000W = 1000Joules/sec, so I'm converting 0.443 grams/second into steam. That works out 0.0246 moles/sec.
My naive assumption was that I could simply use the ideal gas law and solve for delta-P, but now I don't think that's correct. My reasoning is that as the pressure builds, the water is suddenly below the new boiling point of the water at the increased pressure, and thus the rate of vaporization will slow as the temperature of the water lags behind the increasing boiling point. Of course, the water is still evaporating at this sub-critical temperature, and heat energy is still being supplied at the rate of 1000W, so the pressure will continue to climb. But it's not at all obvious to me how quickly it will increase in this dynamic system.
This seems like it must be a solved problem, but I'm struggling to find an approach to developing even an approximately solution to estimate how quickly pressure will increase over time.