Question

Account for the observation that at the melting point even though heat is constantly supplied the temperature does not rise till all the solid has changed into liquid

Answer 1

the heat supplied is used to overcome the intetmolecular spaces for changing the state of matter.So the temperature remains constant.
hope it helps you !!

Answer 2

The temperature remains constant during the change of state of a solid to liquid, because the eneegy which is actually supplied to change the state is used up in breaking down the force of attraction between the particles of solid.

$\textbf{Then when temperature will rise of heat is supplied continuously ? }$

Tempertaure will only increase when the whole solid get melted to form liquid, then the heat supplied will start to break the force of attraction between the particles of liquid.