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A sample of water is boiling as heat is added at a constant rate. Which statement describes the potential energy and the average kinetic energy of the water molecules in this sample?

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The statement which describes the potential and the kinetic energy of the water is this: THE POTENTIAL ENERGY INCREASES AND THE AVERAGE KINETIC ENERGY REMAINS THE SAME.
At boiling point of water, the heat that is been added to the water is used to break the chemical bonds that holds the molecules of the water together so that they can turn into vapour. At this point, the average kinetic energy of the water remains the same while the potential energy increases.