A thin layer of water can *very* briefly protect you from hot temperatures by absorbing the energy and evaporating before the heat transfer reaches your skin. For an object with very little residual heat like a candle wick, this is sufficient.
A much more massive metal pan has vastly more heat to give, and the large volume of water only serves to conduct it to your hands more efficiently.
Even if they were the same temperature to start with, there’s very little hot matter in a candle flame compared to the hot pan. The total amount of energy in a candle flame at any given time is quite low, and the water on your fingers is sufficient to absorb the heat by the time the flame goes out. In contrast, a pan hot out of the oven holds significantly more heat, enough to heat the water in the mitt to sufficient temperature to burn you.
It’s a matter of surface area and water being a great conductor of heat.
A candle is very hot but only a small point at the end of the wick is actually burning. if you snuff it out with wet fingers, that tiny point of heat is distributed across the much greater surface area that is your fingers squished together and you barely feel it.
A pan is large and thus contains *vastly* more actual heat energy. The metal of the oven mitt is a great conductor, as is water in a wet oven mitt. All of the heat from the pan is conducted almost instantly through the water and into your hand. The surface area ratio of “hot thing : hand” is much greater with a pan than it is with a candle, and all the heat from the pan doesn’t “go out” instantly like it does with a candle. It just keeps pumping heat in until the temperature of the pan and your hand are the same.
the candle side seems to have been covered pretty well at least. As for the oven mitt, think of snowboarders. Most of them, rather than wear one big puffy coat, will wear multiple layers of thinner material. That’s because the trapped air between layers is itself actually a really good insulator, meaning it takes a while to change temperature, so it’s a good material to keep a hot space hot, or a cold space cold.
Actually, they tried to use this principle for houses too, by making air filled walls sealed in plastic sheets. It worked great for temperature, but eventually some really toxic mold grew in the air pockets, so it didn’t take off.
But yeah, your hot pad is made (usually) of something with air trapped in it. Because it takes so long for that trapped air to get warmer, you have time to do what you’re doing with the really hot thing, then put it back down before a dangerous amount of heat reaches your hand. But the water is a much better conductor… it gets hot or cold really fast and then spreads that temperature on to the next thing. So if you’re out in the snow and sweat through your wool jacket, now you’re also in tons of danger because your body heat gets out through the damp stuff way way faster than before. Same concept with the oven mitt getting wet, and transferring heat.
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