It gets colder because the water in the pipes in your house are about as warm as the inside of your house.
So you turn on the tap and the water might feel about skin temperature.
As the water in the pipes of your house runs out of the tap and drains away, water in the pipes underground gets into the pipes in your house. This water is cooler than the water that was in the pipes in your walls.
So as you let your fingers dangle in the water it goes from room temperature to cooler as the farther away water reaches your fingers. 😉
The tap is mixing water from the boiler with the water from the main water supply. A lot of mains water sources comes from under ground where the temperature is steady all year round. So you get a steady cold water supply all the way to the tap. The thermostat in the mixer will regulate how much of the water comes from the boiler and how much comes from the cold mains to make sure the temperature is what you set it to.
Whether the water is coming from a well or coming from a city water pipe, both are located underground which is cooler usually than the ambient air temp (except for winter) and the temperature of the pipes in your house. Well water will stay consistently colder while city laid pipes may be subject to greater temperature variations due to the seasons if they aren’t very deep enough.
Don’t confuse this with geothermal heat extraction in which Wells are dug very very deep to extract/exchange heat which can be used for heating and or energy production on the surface. (Basically when you go a few feet down the soil temperature is in a consistent range that you feel when you run your well water for a while but if you go much much deeper especially in areas with shallow geothermal reserves the Earth starts to heat up quite a bit).
YOur wall has two pipes. One comes from the water heater and is thus filled with hot water. One is not heated, and because it’s colder underground than above ground, the water pumped to your house will be cooler than the air tempature. Since it takes a very long time for water to absorb enough heat energy to heat up, the water stays cold for a good long time in your home’s pipes too. Your tap simply changes the ratio of how much water comes from the hot pipe, and the cold pipe.
All the way hot closes the cold pipe entirely, all the way cold closes the hot pipe entirely.
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