How do you explain that there is a change in heat as water freezes even though there is no change in temperature?

This is primarily due to molecular motion. When water is liquid, there is considerable motion -- the molecules roll over each other and there is internal molecular vibration (hydrogen-to-oxygen bonds vibrate). When you freeze the water, the molecular vibration is lessened. The molecules become fixed in a crystalline lattice (usually) and they don't roll over each other as much. All of this rolling and vibrating contribute to the latent heat of fusion. If you melt the ice, you need to add that back in.

The colder a substance gets, the less the molecules move until they reach absolute zero, which causes the complete halt in motion of molecules. The more molecules move, the more energy is being emitted from their electrons, which is one factor in temperature change; the motion of the molecules slowing down and producing less energy being emitted as heat.

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The colder a substance gets, the less the molecules move until they reach absolute zero, which causes the complete halt in motion of molecules.

The more molecules move, the more energy is being emitted from their electrons, which is one factor in temperature change; the motion of the molecules slowing down and producing less energy being emitted as heat.

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Well, this isn't really true -- energy isn't emitted from their electrons -- but he's got the general idea.