Very high surface area:mass ratio.
Heat capacity is related to density (mass per unit volume), heat transfer (moving heat out of an object) is related to surface area.
The aluminum heats up to the same temperature as everything else in the oven (quite a but faster than anything else in the oven – aluminum is a good thermal conductor), but a sheet of foil has almost no mass, but tons and tons of surface area.
This means is ‘exhausts’ its heat very quickly.
If you touch foil *right* out of the oven, it is hot – but within a few seconds it has cooled down to air temperature.
Not only does aluminum change temperature rapidly and lose heat to the air before you can touch it, but a sheet of aluminum foil has very little mass. This means that the total amount of stored heat in the area you touch is very low. This means that even a very hot sheet of aluminum foil can’t transfer much heat into your skin, so you don’t get burned.
Aluminum has a very low specific heat capacity and foil is very thin, these combine together to get it a very low thermal mass (it cannot hold a lot of heat). It also has a very high surface area to volume ratio and a very high thermal conductivity. This means that the heat that it can store can move in and out of it very very fast.
When you combine these, Aluminum foil can go from red hot to room temperature in a matter of seconds. The very low thermal mass means that with very thin foil it might be 400 degrees, but putting that heat into your finger only raises your finger by 20 degrees, and results in no burn.
A very tiny cup can only hold a very tiny amount of water. Pouring a very tiny cup of water over your head will not make you wet because you are very big.
In the same way, tinfoil is a very tiny bit of metal and it can only hold a very tiny amount of “heat”. Touching a very tiny amount of heat will only make your finger a very tiny amount warmer because you are very big.
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