How is absorbed thermal energy invested during a phase change?

[fog37]

Hello,

I was pondering on the well known fact that a certain amount of substance, when absorbing heat, increases in temperature up to a certain temperature and then phase (state) transformation takes place. Any energy supplied at that point does not increase the temperature any further but is solely invested in producing the phase change. For examples, $1Kg$ of liquid water at $100$ celsius will turn into vapor and more vapor as we heat it until all the water becomes vapor.

Question: let's say that at time $t$ only $0.3$ Kg of the liquid water has turned into vapor while the remaining $0.7$ Kg is still liquid. Why is the entirety of any of the newly absorbed thermal energy used only for phase changing the remaining liquid water and none of it is used to warm up the newly created vapor? If all the initial liquid water was inside a spherical and closed container whose surface is uniformly heated, wouldn't some of the vapor get warmed up?

I guess the concept that there is not heat but only phase change is true if the heat source is in contact with the liquid and the liquid converted into vapor does not come into contact with the heat source...

Thanks
Fog32

 

[mitochan]

Hi.
If some of the vapor warmed up, its temperature raise. Then thermal equilibrium requires the gained energy be transferred to water liquid, which is waiting vaporization, until the temperature of vapor goes down to that of liquid.

 

[Herman Trivilino]

Any energy supplied at that point does not increase the temperature any further but is solely invested in producing the phase change.

That's assuming that the substance is in equilibrium at all times. Try putting an immersion heater in a cup of liquid water. Bubbles of vapor will appear on the surface of the heater even though the liquid that's furthest away from the heater is at a lower temperature than the vapor bubbles. Heat is making vapor near the heater, but it is also raising the temperature of the liquid water furthest from the heater. You do not have an equilibrium situation. Eventually, though, you'll get a full rolling boil going in the cup and the temperature will be uniform throughout. You now have equilibrium whereas before you didn't.

Why is the entirety of any of the newly absorbed thermal energy used only for phase changing the remaining liquid water and none of it is used to warm up the newly created vapor?

This just follows from the assumption of equilibrium, which is that the vapor and the liquid have the same temperature.

Imagine a pressure cooker on a stove top. You have water in both liquid form and vapor form, the liquid is boiling and vapor is escaping through the release valve. Now take a propane torch and let the flame hit a small spot on the side of the pressure cooker, above the liquid so that heat is transferred to the vapor. That vapor near that spot will be at a higher temperature than the surrounding vapor. You do not have equilibrium!