During boiling, the temperature of a container of water remains constant because thermal energy of the water is constant during the transformation from liquid to gas.
Kinetic energy is energy possessed by a particle by virtue of its motion. Molecules that compose matter are in constant random motion according to the kinetic theory of molecules.
The temperature of a container of water stops increasing right before it starts to boil and turn into gas because the thermal energy of the water remains constant as it transforms from liquid to gas. The heat that is required to turn the liquid into gas at the boiling point is called the latent heat.
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