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We all know from every day experience that if you touch metal that's been left outside in direct sunlight, it'll burn you. Why is that?

I've read that it's related to the specific heat capacity and/or conductivity, but that doesn't make sense to me. What I've read explains this by saying that the metal is technically the same temperature as everything else, but is very conductive, and hence pours the heat into your hand faster than everything else. However, it seems to me that if this were how it works, it would stop doing that as soon as you reach the same temperature as the metal -- and the air around you, which is theoretically the same temperature as well, doesn't burn you like that, even if you stay out in it for a long time, yes? Sunburn is from radiation, not conduction.

What am I not understanding?

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By "left outside", I presume you mean "left in direct sunlight". Metal just outside on a hot day but not in the sun usually doesn't feel significantly warmer to me. Because as you say, it tends to equilibrate to about air temperature.

Materials left in the sun gain energy from direct solar radiation and can reach temperatures quite a bit above the ambient air temperature. So the first bit is that the solar radiation is driving the surface of the material to be warmer than the air. Objects in sunlight can reach over 150F.

Now if you have a big chunk of metal and a big chunk of plastic that have been left in the sun, the surface of both might reach about the same temperature. But when you touch the plastic some heat will flow into your hand. After that heat leaves the surface, that thin layer on the surface will cool down very quickly. Even if the rest of the object were very warm, the heat from the interior would flow very slowly and wouldn't be able to keep the surface hot.

This isn't true for the metal. After the surface sends some energy into your skin, the metal is able to draw thermal energy rapidly from the interior to keep the surface hot. It's this extended time that the surface will remain hot that you notice.

This is the same reason that a cold metal pole is dangerous to touch with your tongue, but a much colder ice cube from your freezer wouldn't be. While the ice cube might freeze a bit of moisture on your body, it doesn't have great conductivity. The outer surface of the ice cube will pretty quickly be warmed to freezing and start melting. But the metal pole can remove large amounts of heat and not warm up much at all, staying very frozen.

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    $\begingroup$ And conversely, a thin sheet of aluminum foil straight from a 450 F oven (or left in the hot sun) is almost immediately safe to touch; because while it has both a high temperature and a high rate of heat conduction, it lacks the interior mass to retain and keep feeding more heat. So it cools rapidly and can't transfer a lot of thermal energy into your hand. $\endgroup$ Commented yesterday
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    $\begingroup$ The relevant material property is "thermal effusivity". NASA's Human Integration Design Handbook (PDF) has detailed formulas relating this quantity to the maximum tolerable skin contact time with hot or cold objects (section 9.12.3). $\endgroup$ Commented yesterday
  • $\begingroup$ So you said that the metal is hotter than the surrounding air due to solar radiation, which makes sense, but then what about the metal pole being colder then? $\endgroup$ Commented yesterday
  • $\begingroup$ @yellowguardling45, the metal pole would be expected to be nearly at ambient temperature, not significantly different from air temp. In fact I compared it to an ice cube which might be much colder coming from your freezer. $\endgroup$ Commented yesterday
  • $\begingroup$ So... you're saying that it's just that the ice cube won't cool your hand all of the way to its own temperature, then? $\endgroup$ Commented yesterday
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To make is simple: The sun light has a mean temperature of the sun surface as can be observed in a sun power plant with focusing mirrors.

The equilibrium temperature of the surface of a body is given by equality of input energy density (1 kW/m²) and convective cooling of the surface. For a black car in Greek sunlight in summer I've measured 110°C on top, the red tail-light plastics becoming soft at the temperature limit for roof lining adhesives :-(

The difference between a metal and and an insulator: metals have a free electron Fermi gas in the conduction band at an mean thermal energy at the Fermi level of roughly 10 000 K equivalent. As Fermions the lower electron states are effectively frozen at temperatures below melting point (~1300 K) and do not take part in diffusive energy transport.

Only a thin layer of electron states are at this Fermi level, where a sharp descent from density 1 to density 0 is in a temperature state in contact with an external body on a small part of the surface.

These facts make clear that the thermal conductivity is practically the same as the electric conductivity in metals.

In the moment you touch the surface you come into contact with the complete body of the electron gas in much the same way as if you touch an electrically charged conducting body.

The difference between the electric shock and the thermal shock is the great difference in electric and thermal conductivity of the human tissue and the fact that the electric charge is proportional to the total surface of the body, electron gas only, while the thermal charge of a metal is proportional to the total volume with the oscillating ion lattice as a very large thermal container.

The electron gas serves as a transport medium only at a not so small fraction of the speed of light. The insulator in contrast transports at speed of sound only.

So the electric shock mainly shocks the conducting nervous system; in contrast the thermal shock burns the skin layer of the hands only because of the low thermal conductivity of the tissue.

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There are actually two reasons:

  1. Thermal conductivity. Metals conduct heat better than most other materials which can be quantified as how much energy flows from one face to another face of a a 1m^3 cube of material given a 1K temperature difference. Higher heat transfer amplifies how hot or cold they feel. Aerogel is the opposite.

  2. Radiant heat trapping. Metals are shiny but still absorb a fair amount of UV and visible light. However, they are excellent reflectors of infrared. The best emitter is a material that absorbs all light, thus the term black body radiation, because thermodynamics requires absorbance and emittance to be equal for any given wavelength. Metals have a lot of trouble re-emitting the heat they absorb from the sun since they are not hot enough to emit it as visible light.

What if a material reflected visible light well but absorbed infrared? Even when left out in the sun it will end up cooler than the surrounding air. In the shade with access to open sky it would cool down even more.

Metals in the shade do not feel that warm, even in hot weather, since air is rarely much above skin temperature. But in sunlight they heat up efficiently and are ready to dump all that accumulated heat into whoever touches them.

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