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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?

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  • $\begingroup$ if the foil is thin, the ratio between thermal emissivity and thermal capacity is maximal for any given "classical" material $\endgroup$ – lurscher Mar 23 at 23:37
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    $\begingroup$ There are many problems for which specifying a quantum explanation doesn't add anything (indeed there are many problems for which quantum mechanics hides the essential character). What makes you think this is a problem that benefits from a quantum flavored consideration? $\endgroup$ – dmckee Mar 24 at 0:27
  • $\begingroup$ @dmckee I would like to know whether the loosely bound electrons have to do anything with this phenomena, or is it just the lattice structure of AL? The answer states that AL indeed gets hot. So the molecules' vibrational energy (heat) must be as high as the other stuff that is in the oven. The reasoning in classical is simply that the AL foil is so thin, it does not really have much mass, so little energy content. My hand is heavier, and has more energy content, and so I don't get burned. $\endgroup$ – Árpád Szendrei Mar 24 at 16:54
  • $\begingroup$ @dmckee How can the AL indeed get hot (so the molecules' vibrational energy is high), but this heat cannot transfer into my hand? Does this have anything to do with the fact that AL is a metal and is a good conductor and has loosely bound electrons that able to move? I would like to know if someone has a description at the QM level, or atomic or molecular level, and explain what happens with the lattice and the loosely bound electrons when AL gets hot in the oven, so that this heat does not transfer into my hand? I believe as you say, QM hides the essential character. $\endgroup$ – Árpád Szendrei Mar 24 at 16:55
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    $\begingroup$ @ÁrpádSzendrei Rule number one for these problems: don't worry about temperature, worry about energy (or even better about power). Just because something is hot does not mean that it carries enough thermal energy to matter, and just because something carries enough thermal energy to matter doesn't mean that the energy can be transferred fast enough to matter. If you happen to be using an aluminum roasting pan you could (but shouldn't) try grabbing that, too. If there was something magical about the structure of aluminum that was protecting you, then that ought to be safe. It isn't. $\endgroup$ – dmckee Mar 24 at 21:10
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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.

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