Why do you think that liquids have less kinetic energy compared to gasses?
Equipartition theorem (https://en.wikipedia.org/wiki/Equipartition_theorem) states that average kinetic energy is the same per degree of freedom and is 1/2 * k * T. The motion of a molecule of water inside a liquid is jittery, but still the molecule has 6 degrees of freedom so the kinetic energy should be the same.
This may look counter-intuitive. We heat water, water evaporates, energy consumed => molecules in gas should move faster. Isn't it? Actually the energy goes to breaking the attractive forces between molecules in liquid.
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
Best Answer
Imagine a container containing just ice at $-1^\circ \rm C$. When you heat it, the energy goes into kinetic motion of the molecules, and its temperature increases. Similarly, if the container is filled with liquid water at $1^\circ \rm C$ its temperature will increase for the same reason.
But now imagine the container is filled with 90% ice and 10% water at $0^\circ \rm C$. If you heat the water part up, it's temperature will temporarily increase a little. But now the water is hotter than the ice, so heat will be transferred from the water to the ice. When the ice is heated above $0^\circ \rm C$ it melts, and this uses up some energy, cooling the water. This will continue until the ice and the water are the same temperature again, so you'll end up back at $0^\circ \rm C$, but with a higher proportion of liquid water and less ice.
This is why, if you heat a mixture of the two phases slowly enough, all the energy will go into melting the solid rather than increasing the temperature. It continues until all the solid has melted, which is when the temperature starts increasing again. The same thing happens in reverse if you decrease the temperature.