Understanding the Boiling Point: Thermodynamic Proof

[Termotanque]

If we add a small amount of heat δq to a liquid at its boiling point T_b, it could either increase its temperature a small amount dT = δq/C_v, or suffer a phase change into vapor.

Experimentally, we see that liquids remain at T_b until the phase change is complete, and only then continue increasing their temperature. Why is this?

I want to prove this macroscopically, that is, from thermodynamics, but I don't know where to start. Any leads?

 

[K^2]

The way you do this is by looking at free energy. Bellow the T_b, the free energy of a liquid is lower. Above, free energy of gas is lower. At T_b, the free energy of the two phases is the same. So to get an absolute lowest free energy, the substance must convert part of liquid to vapor in response to added energy, until there is no more liquid left.

 

[Termotanque]

Can what you just said be proved from the laws of thermodynamics, without looking up ΔG values on tables?

 

[K^2]

Like I said, if you take for granted that different phases have different rate at which free energy changes with temperature, that's all you need to prove that phase transition happens at a specific temperature for pure substance.

If you want to derive the actual dependence of free energy on temperature, then you need statistical mechanics. As far as I know, thermodynamics by itself is insufficient.