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I have read this question:

Why can I touch aluminum foil in the oven and not get burned?

But the answers therein only explain on a classical level why aluminum foil being a very good conductor and the heat capacity of AL is low, and the mass is very low.

I understand, but I do not see what happens in the lattice of the AL foil when it is in the oven, and I did not find anything that would explain at the QM level why the thin AL lattice structure does not store heat. Is it simply because the electrons in the lattice are loosely bound to the valence shells? And the electrons are able to move (good conductor)? But why does the electrons movement cause the molecule's vibrational motion (heat) capacity to be low?

Question:

  1. Is there a QM level explanation for why AL foil does not heat up in the oven?

  2. Is it simply the lattice structure of AL, and the loosely bound electrons that can move easily, causing the foil to stay relatively cool?

Qmechanic
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Árpád Szendrei
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1 Answers1

5

Of course it gets hot, according to classical physics, thermodynamic equilibrium because of radiation. The spectrum of that radiation follows the Planck distribution, which is the only quantum thing about it. But zeroth law of thermodynamic says that it will have the same temperature as the chicken, potato, fish, whatever you are cooking.

The heat capacity follows the Dulong & Petit law, it is three times the gas constant per mole, because of equipartition, $3k_BT$ per atom.

You can safely touch it, because it is just 18 micrometers thick. The energy content is small compared to that of your skin.

Numerical example: oven $280^\circ$C, aluminium foil $280^\circ$C, hand $30^\circ$C. Skin is about 100 times thicker than aluminium foil. One takes a piece of hot foil between thumb and index finger. Ignoring all differences in heat capacity per volume and conduction into the hand, the skin temperature goes up by about $\frac{280-30}{2\times 100} \approx 1^\circ$C.

It does not matter in this case that aluminium is a metal. It does not have anything to do with quantum mechanics. Grade school calorimetry is sufficient.