Temperature is a measurement of the average speed of molecules. Not to be confused with how fast the water is flowing out of the tap, but on a micro-level there are molecules even in apparently still water that are sliding past each other and bumping into each other. When the molecules come into contact with the molecules in your skin, momentum gets transferred from one set of molecules to the other giving you a sensation of hot or cold. The speed of these molecules isn’t visible to you, but in addition to changing how the water feels, it subtly changes how the water flows and sounds when it comes into contact with the surface of your sink.
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