When the pressure on the liquid surface is less than the vapor pressure of the liquid at a given temperature, the liquid will start to evaporate. This is common sense.
The problem is more difficult when the liquid and its vapor are heated inside a rigid container, with the specific volume of the mixture less than the critical specific volume:
According to my professor's notes, the level of the liquid in the container would rise. Why? What is the physics (or the thermodynamics) behind this? If a mixture is heated in a constant volume what happens to it? I know that it will not boil completely because it would attain equilibrium pressure with its vapor soon enough, but how do we fix the state when it would stop boiling? Why is it that if the specific volume of the mixture is less than the critical specific volume, the level of the liquid will rise when heated?
Hi, sorry for bumping this old question! It's been six years and I have a master's degree now but still haven't been able to solve this question! However, I asked around a lot and I received a very crude answer to this, but it did make sense nonetheless.
Suppose we take the T-v diagram of water. For the first case, let us assume the specific volume of the mixture is above the critical specific volume at that temperature. We can mark an arbitrary point under the vapor dome and mark it as state 1. Suppose now we heat the mixture at constant volume, the temperature of the mixture should increase because of conservation of energy. We can mark state 2 under the dome at the same volume but at a higher temperature. If we keep heating the mixture, after some time state 2 will lie on the saturated vapor line. This essentially means that we started with a mixture of water and vapor, but ended with all vapor.
If we do the same exercise but this time the specific volume of the mixture being less than the critical specific volume, we will find that we end up with all liquid at one point.
While this does make sense intuitively, I still haven't found any luck in mathematically proving this. If anybody can work this out, I'd be very relieved!