When you heat water, the water molecules begin to move around more quickly. They travel farther apart as they bounce off each other. A volume of hot water has fewer molecules and weighs slightly less than a volume of cold water because there is greater space between the molecules. As a result, heated water has a lower density than cold water. When you combine the two with the hot water on the bottom, the hot water rises to the top, mixing with the cold water and resulting in purple water.
