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Freezing and melting are the same process and occur at the same point in temperature; whether the temperature is lowering or rising determines if something is freezing or melting. What's curious about a substance at this point of transition is that the temperature, either increasing or decreasing, will "level off" for a time. If heating, the increase in thermal energy is being used not to increase the vibrations of the molecules or atoms, but is used to overcome the internal forces of attraction within the solid to transform it to a liquid. The same is true in reverse -- when freezing, the temperature remains the same for a time, as the decreasing thermal energy allows those forces of attraction to reestablish themselves to transform the liquid to a solid.
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