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The temperature does not change during a phase change because the heat being added or taken away (in the case of solid to liquid; added) is being used to break the forces (hydrogen bond, etc.) between the molecules rather than increasing the average kinetic energy of the molecules (the average kinetic energy is what temperature is in reference to)
Let's say we are talking about the process of melting. Once we hit the melting point of the substance, the molecules gain enough energy to move past one another rather than being locked in a solid form. All the added energy at this temperature is being used to overcome the attractive forces between molecules. So, while the heating is continuing, the temperature remains the same until the entire substance has melted. Hope this helps!
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