The temperature of boiling water remains the same because once it hits the boiling point it will turn into vapor.
Boiling is the process by which a liquid (in this case; water) turns into a vapor when it is heated to its boiling point. The change from a liquid phase to a gaseous phase results when the vapor pressure of the liquid is almost equal to the atmospheric pressure exerted on the liquid.
The temperature remains constant during the boiling of water because all the heat energy provided is consumed in changing the state of water from liquid to water vapor. Hence all the heat energy supplied increases the kinetic energy of the particles and the temperature doesn't increase and remains constant.
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