Question

why does a temperature of a substance remains constant during melting and boiling even when heat is being supplied to it continously

Answer 1

When heat is being supplied during the change of phase, when the substance reaches it boiling or melting point, then, at that point the heat being supplied is used up in converting the substance from one phase to another till the phase is changed completely to another.

This heat is known as Latent heat.

So as the heat is used up in doing the above work, no heat is able to increase the temperature.

Answer 2

During melting, the heat being added to a substance goes into breaking apart the "molecules" or breaking down the crystal lattice, not into raising the temperature. During the phase change all the molecules continue to have the same kinetic energy, and therefore the temperature remains constant.

The same thing happens at the boiling point. The energy goes into breaking the intermolecular bonds, but the average kinetic energy stays constant and so does the temperature until all of the bonds are broken and the substance is in the vapor state.