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Because the more energy provided the more the substance starts to become the next phase, but this energy must go to maintaining that phase so increasing heat won't increase temperature until the substance has completely achieved the next phase
The temperature only changes once the substance has reached solid/liquid/gas. The transition between them doesn’t increase or decrease in temperature because it is using the energy being put into the system to change the phase and only focuses on that before increasing or decreasing the temperature.
The temperature remains constant during boiling even though heat is supplied because the heat supplied is being used as energy to break the bonds. It takes energy to break a bond so all of the heat applied will be used to break these bonds.
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