The Horace de Saussure Hot Box
First I must credit Joseph Postma for alerting me to the existence of Horace’s (easier to write than de Saussure) hot box. For May 31, 2016 he posted an article—The Radiative Greenhouse Effect & Ontological Mathematics—on his website—Climate of Sophistry. Horace’s hot box was the focus of this article. 
So having no knowledge of Horace’s hot box I went to the internet and found: “He [Horace] had constructed the first known Western solar oven in 1767, trying several designs before determining that a well-insulated box with three layers of glass to trap outgoing thermal radiation created the … highest temperature—230 °F.” (Wikipedia)
At http://solarcooking.org/saussure.htm I read: “the increased use of glass during the eighteenth century made many people aware of its ability to trap solar heat. as Horace de Saussure, one of Europe’s foremost naturalists of the period, observed: “it is a known fact, and a fact that has probably been known for a long time, that a room, a carriage, or any other place is hotter when the rays of the sun pass through glass.”
This French-Swiss scientist was quite surprised that such a common phenomenon had not led to any empirical research on the maximum temperature attainable in a glass solar heat trap. when experimenting with solar energy, his contemporaries preferred to work with burning mirrors, which could perform such amazing feats as burning objects at a distance or melting the hardest metals within seconds. in 1767, de Saussure set out to determine how effectively glass heat traps could collect the energy of the sun.”
What followed on this technological website is a great illustration of good experimental science so I strongly suggest that one should go to the referenced site to read about this. However the focus of this article is to understand the functioning of Horace’s hot box using the necessary knowledge, which Horace could not have known about at that time and which seems not commonly known today. But there is one bit of information, which Carl Allen shared with Joe and which I have not found written elsewhere, that I consider is critically important to this understanding of the functioning of Horace’s hot box.
Carl had written to Joe: “Another thing that your thought experiment overlooks is the fact that glass is not 100{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117} transparent to sunlight since sunlight carries a lot of infrared energy. Set a piece of glass up against a south-facing wall that 1) is protected from the wind and 2) receives direct sunlight at noon. By 1:00PM the glass will be too hot to touch due to the sunlight that it has absorbed. Then touch the wall behind the glass and you will discover that this clear plate of glass has been “shading” the wall, which will be significantly cooler than the glass.”
This remark caused me to search for something I had been taught in a theoretical physics course. The textbook for the course wasIntroduction to Theoretical Physics—Classical Mechanics and Electrodynamics and its author was Roald K. Wangsness. And it is very true that I understood little of the mathematical reasoning taught in this book.
However, I can read and in Section 29 (Reflection and refraction of plane waves) I read (pp 309): “In other words, waves which are most strongly absorbed are very strongly reflected. A good example is afforded by the optical properties of thin sheets of gold. They appear yellowish by reflection; this means that, in the originally white light transmitted through the sheets, the yellow is practically all absorbed. As a result, the transmitted light appears greenish or bluish.” So this stated consequence of the theoretical considerations I could understand. However, I also recognized that gold as a metal is a good conductor and not a very poor conductor like glass or water.
Hence, I looked for more conformation that “a good absorber is a good reflector”. And I found it in The Feynman Lectures on Physics Vol II pp 33-11. “Metals do not reflect 100 percent, but many do reflect visible light very well. In other words, the imaginary part to their indexes is very large. But we have seen that a large imaginary part of the index means a strong absorption.
So there is a general rule that if any material gets to be a very good absorber at any frequency, the waves are strongly reflected at the surface and very little gets inside to be absorbed. You can see this effect with strong dyes. Pure crystals of the strongest dyes have a “metallic” shine. Probably you have noticed that at the edge of a bottle of purple ink the dried dye will give a golden metallic reflection, or that dried red ink will sometimes give a greenish metallic reflection. Red ink absorbs out the greens of transmitted light, so if the ink is very concentrated, it will exhibit a strong surface reflection for the frequencies of green light.
“You can easily show this effect by coating a glass plate with red ink and letting if dry. If you direct a beam of white light at the back of the plate, as shown, there will be a transmitted beam of red light and a reflected beam of green light.”
And even though Feynman taught that “very little gets inside to be absorbed” we know from Carl’s report that the glass facing the sun got too hot to touch even though the wall behind the glass did not. Hence, we know that Horace’s hot box was strongly heated at two locations: by the IR portion of the solar radiation at the top surface of the top glass and by the visible portion of the solar radiation on the ‘black’ surface beneath the bottom glass, where the absorbed visible radiation heated the surface to the reported maximum temperature of 230oF.
The obvious key to obtaining this high temperature was to reduce the transfer of energy, via conduction or radiation from the hot box’s interior. To reduce conduct through the walls and bottom of the box required that they be ‘insulated’ as well as possible. And because glass, because it is a poor conductor, served this function for the top. And the panes of glass were separated from each other because air has a low thermal conductivity as long as there is no convection. Which later research by modern technologists found that a spacing of about 0.7 cm prevented vertical convection.
It is possible that Horace experimented with the spacing as I read that he had started with five panes of glass. But that he discovered his hot box achieved its greatest temperature by using only three. Now, it should be acknowledged that Horace in his experimenting was not being a scientist as chemists, at least, define a scientist. He was being a technologist because he goal was to achieve the greatest temperature and not to understand how (why) he achieved this greatest temperature.
What Horace probably did not know was that glass was a very good absorber of the radiation being emitted from the bottom of his box which was absorbing the visible radiation which was transmitted through the glass. Hence, the glass effectively eliminated the loss of energy via radiation from the interior of the box because a good absorber is a good reflector.
So the major loss of energy from the interior to the exterior out of the top of the box was thermal conductivity and the rate of thermal conductivity is now commonly known to be proportional to the temperature gradient. And here is the critical importance of Carl’s observation. The fact that the top surface of the top absorbed a portion of solar radiation’s invisible IR radiation to heat that surface so it was too hot to touch, greatly reduced the temperature gradient driving the heat flow via conduction from the interior.
So given our presently known scientific knowledge, it is easy (simple) to understand (explain) how Horace’s hot box achieved such a great temperature.
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