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I cook frequently with aluminum foil as a cover in the oven. When it's time to remove the foil and cook uncovered, I find I can handle it with my bare hands, and it's barely warm.

What are the physics for this? Does it have something to do with the thickness and storing energy?

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    $\begingroup$ Related: Why is my hand not burned by the air in an oven at 200°C? $\endgroup$ – Wrzlprmft Feb 12 '18 at 18:54
  • $\begingroup$ Similarly, if you put hot water from the tap in a aluminium can it gets really hot really fast compared to if you do the same with a pot. $\endgroup$ – Viktor Mellgren Feb 16 '18 at 10:31
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    $\begingroup$ Now if you crush the aluminium in a little ball and try doing the same, I'd expect you to get burned (depending on the total mass of the piece). $\endgroup$ – Vendetta Feb 16 '18 at 16:50
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You get burned because energy is transferred from the hot object to your hand until they are both at the same temperature. The more energy transferred, the more damage done to you.

Aluminium, like most metals, has a lower heat capacity than water (ie you) so transferring a small amount of energy lowers the temperature of aluminium more than it heats you (about 5x as much). Next the mass of the aluminium foil is very low - there isn't much metal to hold the heat, and finally the foil is probably crinkled so although it is a good conductor of heat you are only touching a very small part of the surface area so the heat flow to you is low.

If you put your hand flat on an aluminium engine block at the same temperature you would get burned.

The same thing applies to the sparks from a grinder or firework "sparkler", the sparks are hot enough to be molten iron - but are so small they contain very little energy.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Feb 14 '18 at 18:20
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    $\begingroup$ @ACuriousMind: They are for "[asking] for more information", though. $\endgroup$ – Hurkyl Feb 15 '18 at 0:28
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    $\begingroup$ It's not that bad to touch molten iron :) youtube.com/watch?v=KNUVnIpcChs $\endgroup$ – Viktor Mellgren Feb 16 '18 at 10:37
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While it's true that difference in specific heat capacity is to your advantage, its effect is really dwarfed by the mass difference. Typical aluminium foil is 0.016mm thick and weighs 0.043kg/m², while human skin is about 1.3mm thick (and even thicker on your palms/fingers) and weighs about 1.3 kg/m², assuming 1000kg/m³ density.

So there's about 30 times of difference in mass multiplied by 5 times difference in specific heat capacity.

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    $\begingroup$ Not to unnecessarily quibble, but isn't it the difference in specific heat capacity what is dwarfed. It is the difference in heat capacity that matters, which is a product of the mass difference and the s.h.c. difference... right? $\endgroup$ – Dancrumb Feb 13 '18 at 1:13
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    $\begingroup$ "So there's about 30 times of difference in mass in addition to 5 times difference in specific heat capacity." In multiplication, more like. $\endgroup$ – M i ech Feb 13 '18 at 9:12
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    $\begingroup$ @Dancrumb Yes, that word was really missing, thanks! I also fixed the controversial "in addition" part, though "in multiplication" doesn't sound like good English to me. $\endgroup$ – Dmitry Grigoryev Feb 13 '18 at 15:37
  • $\begingroup$ There's also an extra factor of ~2 if you actually grab the foil, because you're probably touching a lot of the same area on both sides with thumb and fingers. (But I guess by the time you start worrying about that you might have to worry about conductivity in the aluminum, i.e. drawing heat from a larger area of foil than you're touching.) $\endgroup$ – Cascabel Feb 14 '18 at 17:26
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    $\begingroup$ "compounded with" might work also work in place of "in addition". $\endgroup$ – Eric Feb 17 '18 at 1:46
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What's in discussion here is specific heat capacity. The flow of heat is based around temperature, and whilst that may seem like a fairly obvious statement, there are important distinctions to be made here.

It's commonly said that temperature flows from hot to cold. What this really means, is that heat energy flows from a higher temperature to a lower temperature. But again, why the distinction between heat and temperature?

Well, because the two are not the same, they are intrinsically linked, but they are not the same. The heat energy stored by an object varies due to the material of the object. This is why people go surfing in the autumn - water takes more energy to raise its temperature than the surrounding areas, so even when the air is cold, the water is still relatively warm, whereas in summer, it has yet to heat up.Our bodies are mostly water, raising the temperature of which requires far more energy than aluminium does (5 times as much has been stated in two previous answers - I thought it was closer to 6 times, but without Googling it, the point still stands).

The effect responsible for this is known as specific heat capacity, the amount of energy required to raise the temperature of a given mass of a given material by a certain amount:

$$E=mcθ$$

As confusing symbols goes, this formula does pretty well. Rather than $θ$ being an angle, it is the change in temperature. $c$, rather than being the speed of light, is the specific heat capacity, and $E$ is sometimes written $Q$...

However, what this formula shows us, is that your aluminium foil, whilst it is as a high temperature, doesn't actually have much heat energy inside it, the $θ$ term may be high, but the $m$ and $c$ terms are both low.

This energy is then transferred to your hand over a period of time, until the two reach thermal equilibrium (same temperature, not same energy). As your hand absorbs energy, for every degree it increases in temperature, the foil will decrease 6 degrees.

Getting more pedantic now, but this will also not happen instantly (and technically, this is almost a diffusion process - sometimes modeled as the transfer of phonons of heat - and so can never be completed), so added to the fact that the foil has low mass (and thus low heat), and the fact that the heat distribution will prevent all of the heat going to your hand, and added to the fact that even if all the heat does go to your hand, your hand's greater value for $c$ will mean that the temperature change of your hand is far less than the temperature loss of the foil, the process will also not transfer all of the energy to reach equilibrium, and you would certainly have enough time to remove your hand (especially as, if you waited that long, the oven itself would begin to be heating your hand, and you might actually want to remove it).

Suffice it to say, you should feel pretty safe with your aluminium foil!

P.S. My general knowledge was wrong, it is about 5 times as much (slightly under, actually), basically replace all '6's with '5's.

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There are three categories of heat transfers:

enter image description here

Convection and radiation transfers happen over the whole area (both sides!) of the aluminum foil while the conduction only happens over the area touched by your fingers. Assuming that the foil is the size of an A4 letter ($≈ 1250\mathrm{cm}^2 $) and the contact area is $10\mathrm{cm}^2 $, the ratio is larger than 100.

The foil cools down fast as soon as the oven is open (and even more so when taken out of the oven) because its A/V ratio is large. There isn't much energy to transfer in the first place (as others mentioned, the foil is extremely thin) and it mostly flows to the environment, not to your hand.

Here's another example :

enter image description here

The swarfs coming out of the grinder are much hotter than your foil (they glow), yet aren't painful to touch because they don't have much mass or energy.

The opposite example would be dipping your hand into hot water. It can be much cooler than the aluminum foil but would still be painful at anything over 50°C. The water has high density, high heat capacity and wouldn't cool down very fast because it isn't much hotter than the environment.

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    $\begingroup$ "and it mostly flows to the environment, not to your hand." I'm not sure if that part would be true. Hands are pretty good at taking heat; we even have a forced fluid circulating under our skin that can quickly carry heat away. Although your hands are only a small area; they also provide a really effective cooling route for the foil. $\endgroup$ – JMac Feb 12 '18 at 16:08
  • $\begingroup$ @JMac: Thanks for the comment. I've added a comparison of areas. There are at least two orders of magnitude between the foil area and the contact area. $\endgroup$ – Eric Duminil Feb 12 '18 at 16:20
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    $\begingroup$ @EricDuminil presumably the inside of the oven is much closer to the temperature of the foil. In fact, that's how the foil got hot in the first place. It cools down a bit when opened but it's still pretty hot relative to your body. $\endgroup$ – JimmyJames Feb 12 '18 at 16:57
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    $\begingroup$ It should probably be noted that the heat loss by radiation for aluminium is rather low because it has a very low emission coefficient. It's in the order of 4 %. So radiation is a rather small contributor even if the area is rather large. $\endgroup$ – Arsenal Feb 13 '18 at 16:28
  • $\begingroup$ @Arsenal That might actually play a substantial role in this scenario. A non-convection oven primarily transfers heat through radiation. That means that the foil is at a disadvantage there, and would be getting a lot of heat through secondary sources (conduction and convection). There's definitely a chance that the foil is significantly cooler than the oven temperatures; even though other exposed surfaces are near the oven temperature. That would just compound onto the cool feel. $\endgroup$ – JMac Feb 13 '18 at 17:46

protected by Qmechanic Feb 12 '18 at 19:57

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