The temperature will only remain constant whilst the heat source is still being applied. The temperature of the water will not exceed 100 degrees because above this the water will no longer be a liquid, it will be in a gaseous state (steam). At the boiling point all the Thermal energy is being converted to kinetic energy, causing the particles to move faster, and as they reach the surface they will ‘escape’ the liquid and become gas particles. This will continue until all the particles have left the liquid state.
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