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Lets's say I make two solar ovens. They each have a set of reflectors angled to direct sunlight into a box topped with glass, and all other sides of the box are covered with insulation that can stand temperatures of ~300o F.

One oven's box is made of cardboard, and the other is metal. Both box interiors are coated with the same thin black paint. (The paint is thin because it is only here to change the albedo, and not the other material properties). For the sake of discussion, the sides can be 1 cm thick. Other than the lining, the ovens are identical, and are put out in the full sun with exactly the same conditions.

Which one reaches the hotter maximum/equilibrium temperature, and why?

(Or do they reach the same temperature?) The internal air temp. is being measured.

Intuition tells me it is the metal one. After all, a sheet of metal lying out in the sun is much hotter than a sheet of cardboard. However, I want the science principles:

The incoming sunlight must be either absorbed or reflected. Does the black coating control this entirely?

In equilibrium, the energy being absorbed by the box' sides must be equal to that being lost by the box' sides. If the thin black coating entirely controls the absorption, then both metal and cardboard transfer the same total energy to their surroundings. The only difference can be in the type of heat transfer. I believe the percentage of heat transer that is in the form of conduction is higher for metal than for cardboard. Air absorbs all of the heat from conduction, but radiation only imparts some of its energy to the air it passes through. Is this significant in determining the equilibrium air temperature? Is my first assumption incorrect?

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  • $\begingroup$ Both boxes will reach the same internal temperature because they both form what's called a "black body cavity". As the other answer noted, however, metal is less insulating and will therefore dissipate more heat away from the cavity. So you want to insulate the cavity in both cases. $\endgroup$ Aug 17, 2020 at 17:06

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Note that metal lying out in the sunlight feels hotter than cardboard because of its higher thermal conductivity. When thermal equilibrium is achieved for the oven, heat flow in from the absorbed sunlight will be balanced with heat flow out by blackbody radiation as well as conduction into the air.

Between cardboard and metal, the metal will allow a much greater heat flow out of the box. Thus, the cardboard oven can get hotter, but it is possible that the metal oven will "feel" hotter / burn you more easily if you touch it.

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  • $\begingroup$ In the simple situation where two sheets are lying out in the sun, does the metal not truly have a higher temperature as well? $\endgroup$ Aug 17, 2020 at 15:15
  • $\begingroup$ Also wouldn't greater heat flow also conduct more heat into the air inside the box, thus increasing the oven's temperature? I thought real insulation on the outside negated the metal's capacity to lose heat that way, because it is still only a small fraction of the total insulation. $\endgroup$ Aug 17, 2020 at 15:22
  • $\begingroup$ @CatSculpture Why would the metal sheet have a higher temperature? (our sense of temperature is surprisingly deceiving for creatures who depend on careful temperature regualtion to survive) $\endgroup$
    – Cort Ammon
    Aug 17, 2020 at 18:01
  • $\begingroup$ Ok, then with the insulation, they end up with the same internal air temp? (As Drew said in a comment) Or do other effects come into play as detailed in the edits to my question? $\endgroup$ Aug 17, 2020 at 22:45
  • $\begingroup$ Also, does this mean that a metal sheet would actually get to a cooler temperature than a cardboard sheet, given its greater ability to lose heat to its surroundings? $\endgroup$ Aug 17, 2020 at 22:49

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