It’s because metal is a better heat conductor than say carpet. When you are touching metal, your body heat is being transferred at a much faster rate than if you touched carpet. The temperature that you feel it being cool is because the heat from your skin is being absorbed by the metal and being loss by your body.
We don’t detect temperatures like a thermometer based on how hot or cold it actually is, we do it based on how slowly or quickly heat enters/leaves the skin.
This means if something pulls the heat out of us faster, it will feel colder. And if something pushes heat into us faster, it will feel hotter.
Carpet insulates very well, so heat transfer will be much slower compared to a wooden floor, which will be slower than a tile floor. So a carpet will feel warmer than wood, because it pulls the heat out slower.
On the flip side, if the floor was heated up to like 50C, much hotter than your feet, the carpet would feel the coolest, because it would push the heat into your feet the slowest.
Thermal conductivity, you don’t feel the temperature of material you are touching, you can’t because you don’t have any nerves in the flooring. You can only feel the temp of your own nerve endings in your feet. Standing on a cool material of poor thermal conductivity doesn’t chill down your feet as much as standing on same temperature but higher thermal conductivity material.
Temperature is a product of energy. For objects, different materials can hold different amounts of energy before radiating that energy outward as heat. It’s the same reason why you need to microwave some foods longer than others to warm them up. Even when they’re stored at the same temperatures (like next to each other in the fridge).
The same thing applies to things you don’t eat, and getting energy from other sources.
Lots of good answers so far, so I’ll say the same thing, slightly differently.
In your example (your room), everything is colder than you. All the objects are “room temperature”, and your body is warmer than that. So everything you touch (the fabric carpet, the metal doorknob, the ceramic mug, the air) is absorbing heat from your skin.
What you are sensing in terms of what materials feel cooler than others is heat conductivity, the rate that each material transfers heat from the warmer surface to the cooler surface.
If you think of an example like a hot car, the hard surfaces will feel really hot while cloth seats will feel less hot, even at the same temperature.
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