It takes heat energy to turn ice at 0°C into water at 0°C.
-- You start off with a block of ice.
-- Some heat energy hits the ice, the ice absorbs it, a little bit
of ice melts, and a puddle forms around it. Now you have an
ice/water system, all at 0°C.
-- If no more heat comes in from somewhere, then no more
ice can melt.
-- When some more heat energy comes in, some more ice
can melt, and become liquid at 0°C.
-- As heat comes in, more and more ice melts. The temperature
of the whole system remains constant. Any heat that comes in
is used to change the state of some ice from solid to liquid, with
no temperature change.
-- Finally, when all of the solid is gone, any more heat energy
begins to raise the temperature of the water.
