[Physics] Why does temperature remain constant at the boiling point of the liquid? And what kind of an equilibrium is boiling

Question

When we were in school, the teachers used to tell us that heat increases the kinetic energy of the particles (reflected in the temperature) until the boiling point is reached. Afterwards, all the heat goes into breaking the intermolecular bonds between the liquid particles until all of them change phase. I realize that this is the answer, but I cannot conceptually relate to it for several reasons:

1) I do not understand if the temperature being measured is that of the liquid or of the entire system.
2) Doesn't breaking the intermolecular bond automatically mean that the particles have become faster?

I have another explanation for this phenomenon but this assumes that the temperature being measured is that of the liquid only. Please let me know if it is correct:

Since evaporation has a cooling effect, when the boiling point is reached, the rate at which the liquid cools down because of evaporation becomes equal to the rate at which heat is added to the container, thus keeping the temperature of the liquid constant.

Correct or not?

Answer 1

1) I do not understand if the temperature being measured is that of the liquid or of the entire system.

You have thermometer in liquid. I can't see why it will measure system's (Referring to the Latent heat of vaporization experiment we all must have witnessed in 10th grade or so)

2) Doesn't breaking the intermolecular bond automatically mean that the particles have become faster

I may not agree with you on this (see end)

Since evaporation has a cooling effect, when the boiling point is reached, the rate at which the liquid cools down because of evaporation becomes equal to the rate at which heat is added to the container, thus keeping the temperature of the liquid constant.

Now see, Evaporation is phase transition from liquid to vapors while Boiling is a phase transition from liquid to gases. More over. Evaporation may occur when the partial pressure of vapor of a substance is less than the equilibrium vapour pressure while Boiling, as opposed to evaporation, occurs below the surface. Boiling occurs when the equilibrium vapour pressure of the substance is greater than or equal to the environmental pressure. I can''t see how you are correlating them

If heat is coming into a substance during a phase change, then this energy is used to break the bonds between the molecules of the substance. The example we will use here is ice melting into water. Immediately after the molecular bonds in the ice are broken the molecules are moving (vibrating) at the same average speed as before, so their average kinetic energy remains the same, and, thus, their Kelvin temperature remains the same.

Note: The above explanation is borrowed from this Link