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According to zonalandeducation.com "During a change in state the heat energy is used to change the bonding between the molecules. In the case of melting, added energy is used to break the bonds between the molecules. In the case of freezing, energy is subtracted as the molecules bond to one another. These energy exchanges are not changes in kinetic energy. They are changes in bonding energy between the molecules."
I believe that it is because during the phase change, all the heat added is being used to break the bonds between the molecules to convert them to a different state, and so the temperature of the substance will not begin to rise again until the phase change is complete. At the freezing or boiling point, the temperature will not rise again until the correct phase state has been reached.
So basically, the temperature wouldn't change because that heat is required to change the phase. The temperature would stay constant until the phase transitions and then it would start changing its temperature if more heat is given/lost.
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