Water transfers heat much faster than air, and takes more energy to heat up. So when you’re on contact with air, the air absorbs your heat slowly, but changes temperature pretty quickly. You’re not surrounded by a blanket of warm air. In water, the water absorbs your heat quickly, and takes a lot of heat to warm up to skin temperature. When you’re feeling hot or cold, you’re not feeling *temperature* you’re feeling heat enter/leave your body.
So first; its important to note that what you can’t actually feel “temperature,” but instead you feel rates of heat transfer. Now, heat transfer *is* partially dependent on the difference in temperature between you and the object you’re touching, **but** its also dependent on the heat capacity and conductivity of the material in question.
Water has a much higher heat capacity than air, and as a result water at room temperature fill soak up more heat from your body than the air, which your body will interpret as the water being “colder.” This is also why room-temperature metals feel cool to the touch.
Because when your skin is wet, even if the water is the same temperature as the room, evaporation is taking place, which causes heat to dissipate from the surface of your skin, thus making you feel colder.
It’s the same principle for how sweat cools you off. Your sweat is the same temperature as your body, and yet it makes you feel cooler.
The air in the room is actually quite cold, but that’s OK since air has so little density and therefore isn’t very good at removing heat from your body. Sure, the air takes a little heat from you, but it’s roughly the same amount as your body is producing so your body and skin temperature is comfortably stable.
Water, on the other hand, has a high density and is really good at taking heat from you. Room temperature water flowing over your skin will take heat away from your skin faster than it’s being replaced by your body, so your skin temperature lowers and you feel that cooling/chilling sensation.
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