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The independent variable is the input variable in an experiment. So in this case the independent variable is heat. The heat affects the kinetic energy of the molecules of the solvent (water). The more heat the water has, the more kinetic energy the water molecules have and the faster they move around. The faster the water molecules move around, the faster and easier that they can surround the salt molecules, thus causing the salt to dissolve in the water. So that is why salt dissolves faster in hot water versus cold water.
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