Solving Global Warming & the de Saussure Device Paradox
A lament: When I have entered into discussions about the greenhouse effect, global warming, climate change, I have been routinely criticized as not understanding science and/or its method by those on both sides of the controversies. And John O’Sullivan, editor of PSI, has recently shared with me: “As you correctly identify, the main complaint I get about your articles is that they seem rambling and confusing. Best to keep to simple points and remember that most readers have shorter attention spans. Few are retired with time on their hands and prefer to come here to get neat ‘packets’ of information.” 
I conclude these critics might not be familiar with the science of chemistry, and if they once were, maybe they have forgotten. I have this forgetting problem all the time. But I consider this is not the entire answer because I know as a chemist I was not the scientist I am today. For near the end of my career as a chemistry instructor at a small community college I began to read the classic books written by the founders of what I term—modern science. These authors were Galileo Galilei and Isaac Newton.
About the same time, I also read a short article written by Lauren B. Resnick (Mathematics and Science Learning: A New Conception, Science, Vol 220, April 29, 1983, pp 477,478). She wrote: “Several studies show that successful problem solving requires a substantial amount of qualitative reasoning. Good problem-solvers do not rush in to apply a formula or an equation. Instead, they try to understand the problem situation; they consider alternative representations and relations among the variables. Only when they are satisfied that they understand in it a qualitative way do they start to apply the quantifications that we often mistakenly identify as the essence of ‘real’ science or mathematics.”
At about the same time, I read a book with an introductory note by Lane Cooper, a professor of English language and literature at Cornell University. It was published in 1917 and its title was Louis Agassiz As a Teacher. Louis Agassiz (pictured)was a noted naturalist of the latter half of the 19th Century who is probably best known for the fact that he had drawn attention to the evidences that glaciers had covered, more than once, the northern portion of Europe.
And this was also found to be the case for the northern portions of North America and Asia. But as a naturalist, neither geology nor meteorology nor climatology was his special area of scholarship. It was the study of fossil fishes. However, as a Harvard Professor, the teaching of natural science (which geology, meteorology and climatology obviously are) became his passion.
Cooper began his introductory note: “When the question was put to Agassiz, ‘What do you regard as your greatest work?’ he replied: ‘I have taught men to observe.’ And in the preamble to his will he described himself in three words as ‘Louis Agassiz, Teacher.’
A portion of the book is a collection of short narratives by Agassiz’s former students. One, (http://www.bio.miami.edu/dana/151/agassiz.pdf), is titled: How Agassiz Taught Professor Scudder. Professor Scudder wrote: “Agassiz’s training in the method of observing facts and their orderly arrangement was ever accompanied by the urgent exhortation not to be content with them. ‘Facts are stupid things,’ he would say, ‘until brought into connection with some general law.’” This statement of Agassiz directs my scholarly efforts. As, a student (learner), I must observe facts and then bring possibly diverse facts into connection with each other.
Another, (http://www2.phy.ilstu.edu/pte/209content/agassiz.html), is How Agassiz Taught Professor Shaler. A longer quote from this narrative illustrates the extreme, unique method of Agassiz’s teaching: “When I sat me down before my tin pan, Agassiz brought me a small fish, placing it before me with the rather stern requirement that I should study it, but should on no account talk to anyone concerning it, nor read anything relating to fish until I had his permission to do so. 
To my inquiry, “What shall I do?” he said in effect: “Find out what you can without damaging the specimen: when I think that you have done the work, I will question you.” In the course of an hour I thought I had compassed that fish; it was rather an unsavory object, giving forth the stench of old alcohol, then loathsome to me, though in time I came to like it. Many of the scales were loosened so that they fell off. It appeared to me to be a case for a summary report, which I was anxious to make and get on to the next stage of the business. But Agassiz, though always within call, concerned himself no further with me that day, nor the next, nor for a week.
“At first, this neglect was distressing; but I saw that it was a game, for he was, as I discerned rather than saw, covertly watching me. So I set my wits to work upon the thing, and in the course of a hundred hours or so thought I had done much—a hundred times as much as seemed possible at the start. I got interested in finding out how the scales went in series, their shape, the form and placement of the teeth, etc.
Finally, I felt full of the subject, and probably expressed it in my bearing; as for words about it, then, there were none from my master except his cheery “Good morning.” At length, on the seventh day, came the question, “Well?” and my disgorge of learning to him as he sat on the edge of my table, puffing his cigar. At the end of the hour’s telling, he swung off and away, saying, “That is not right.” Here I began to think that, after all, perhaps the rules for scanning Latin verse were not the worst infliction in the world. Moreover, it was clear that he was playing a game with me to find if I were capable of doing hard, continuous work, without the support of a teacher and this stimulated me to labor.”
Now, a quote attributed to Galileo brings the article by Resnick (you have to find and read it) and Agassiz’s unique teaching methods together. “We cannot not teach people anything; we can only help them discover it within themselves.”
I assume readers come to PSI to learn. The articles I write are information which could never be published in any peer-reviewed scientific journal with which I am familiar. I could summarize the proceeding information as a learner must do the work, a teacher can only supply information. What the learner does with the information is solely up to the learner. And a learner should not expect to be given knowledge in gift wrapped neat ‘packets’ of information.
The possible paradox of the de Saussure device (https://principia-scientific.com/paradox-three-apparently-different-systems-produce-one-observed-temperature/) is an opportunity to illustrate this qualitative reasoning process, referred to by Resnick, as I understand it. This article was the second about the de Saussure device I had written; the first was (https://principia-scientific.com/the-horace-de-saussure-hot-box/). Which is another reason for this article for I consider my previous explanation of how energy was transferred from the device’s interior to its environment to have been incorrect. 
I begin by reviewing what Horace de Saussure did. First he saw that glass windows let sunlight into closed space like a room or a carriage and warmed the space. Because he saw others of that time (around 1767) using lenses to concentrate sunlight and achieve great temperatures, he wondered to what temperature a device, like the box he constructed with glass panes, could ‘trap’ the sunlight. He reported he began with five glass panes.
Now, if it is not obvious, I must note that Horace was an experimentalist. So he apparently was not satisfied with only the result achieved in the case of using five glass panes. He apparently began to reduce the number of panes because the device which achieved the greatest temperature had three panes. I can imagine, but do not know, that as he began to take away a pane and test the device again that he found the temperature of its interior increased until he took off the third pane and found that the greatest temperature achieved decreased. It is reported that he began to increase the insulation of the box’s bottom and walls to achieve even a greater temperature with the three pane device.
Horace began his experimentation to find the maximum temperature to which his device’s interior could be heated. He had a purpose and I must identify what my purpose is in analyzing his device and its results. My primary purpose is to try to determine if the maximum temperature achieved is related to the intensity of the solar radiation upon the device or if the fact that this temperature is approximately that of the two other seemingly related systems’ maximum temperatures is merely a coincidence.
I continue my qualitative analysis by formally inventorying what I know and what I do not know; along with my commentary of what I considered Horace knew and what he could not have known. This I do to illustrate that one does not need to know much to become an experimentalist. It just takes doing. And along the way you might find the need to change some factors, as Horace did.
The device is a well-insulated box with three separated glass panes through which solar radiation can be transmitted to its interior. The first factor is that not all the solar radiation incident upon the device is transmitted to its interior because glass absorbs a portion of the radiation’s IR portion. This is evidenced by the observation that the upper surface of the top glass pane becomes hot to the touch. (Horace likely observed this many times.) The second factor is that it is known that glass strongly absorbs, is opaque, to the long-wave IR radiation that is emitted by the interior surface which is warmed to a reported 230oF. (Horace did not know this.) The third factor is the physical principle that a good absorber is a good reflector because the radiation cannot penetrate a significant distance into the glass (opaque matter). (Horace did not know this.)
But we know it does penetrate far enough to be absorbed and to warm the surface. (A repeat which cannot be repeated enough because it is seldom considered even when known. And it has become an issue of contention even though it is the idea of a Nobel Prize winning physicist). The fourth factor is that a portion of light (solar radiation) is observed (and understood) to be reflected when the light transmitted through the boundary between two mediums having different refractive indexes. (Horace could have observed this.)
A major consequence of these factors is that only a portion of the incident solar radiation is actually transmitted into the device’s interior where it could be absorbed and converted into sensible heat (increased temperature). It seems that only a portion of the incident solar radiation is capable of heating the device’s interior to its maximum temperature is the paradox. It is this fact (maximum temperature) which seemed to lead to the conclusion that the device ‘traps’ the converted energy of the absorbed solar radiation. Because, as already noted, we now know that glass is opaque to the longwave IR radiation from the very hot surface of the interior, it might seem obvious we know everything about the device that needs to be known. However, an unanswered question, if the device seemingly traps some energy, why can it not trap more energy and its interior temperature increase beyond that observed?
So the paradox, which needs to be explained, is how does energy escape (be transferred) ‘naturally’ from the interior? Or, what limits the temperature to which this absorbed radiation increases the temperature? The obvious answer is that at some point, since there is an observed maximum temperature, the energy ‘in’ must be matched by the energy ‘out’. But this obvious answer begs the question: How?
It seems obvious that Horace observed a lower maximum temperature when there were five glass panes. It seems we can conclude that when he removed first pane, he observed a greater maximum temperature. Now before going forward, I see there is one critical bit of information that I have not previously considered. Horace reported he pointed his device toward the sun and even wiggled it a bit so that for short times the sunlight was incident upon the device’s side walls as well as its bottom. From this I conclude that Horace had at some time noticed that the maximum temperature decreased if the device was not pointed toward the sun.
This observation would simply confirm that the device’s maximum temperature was (is) limited by the intensity of the solar radiation incident upon its top glass pane. So before I really have begun my qualitative analysis it seems I have achieve the primary purpose of my analysis. However, I have not begun to correct my previous error relative to how the trapped energy in the interior may be continuously transferred to the environment once the maximum temperature is achieved.
Given the reflection of solar radiation from the surfaces of a glass pane, we understand a probable reason the maximum temperature of the device was less when there were five, or four, panes was this reflection reduced the intensity of the solar radiation being transmitted to the device’s interior. And if the maximum temperature decreased from that of three panes, when the third pane was removed, it seems we must understand that more energy was ‘leaking’ from the interior than before because we must also accept, given the two panes, that more energy should have been transmitted into the interior.
Now, that Horace reported he wiggled the device a bit to ‘illuminate’ the side walls as well as the bottom, seems to force the conclusion that this wiggle evidently did not decrease the maximum temperature he was observing and possibly sometimes increased the temperature a little. From my experience with my modified Suomi, Staley, Kuhn (SSK) net radiometer, I consider that when I ‘wiggle’ it a bit and its interior temperature increases a little, that I have better pointed it directly toward the sun.
And I have observed, with my modified SSK radiometer, if I continuously point it directly toward the sun, there is a considerable period near midday when the observed maximum temperature is constant within reasonable observational error. Hence, when I previously wrote without any comment that ‘the trapped energy in the interior may be continuously transferred to the environment once the maximum temperature is achieved, there is an observation which supports this consideration. Such a steady-state condition makes the de Saussure device’s analysis simpler.
As should an assumption that the primary leak of energy from the interior is (without going into the reasoning) through the three glass panes. A question, which sometimes comes up, is: when there is this steady state condition due to the fact that solar radiation is being continuingly absorbed, is this absorbed radiation still being converted to sensible heat? My answer is, of course, it is. This, because without this conversion continuously occurring, the temperature of the interior would immediately begin to decrease as energy continued to leak from the interior. The balance is that the conversion matches the leak.
Previously I did not consider the radiation process to be part of the energy leak. Which I now consider to be an error, a big error. The reason I had previously entertained this error began with the fact that the only possible energy transfer mechanism through a glass pane was thermal conduction. It is now more difficult to understand why I previously dismissed the possibility of transfer by radiation. However, I now consider the problem was I had not clearly understood (defined) the situation which existed in the device’s interior.
Which was that the solar radiation which penetrated to the device’s interior was being primarily absorbed by the interior’s bottom (which was opaque to both solar radiation and the long wavelength IR radiation which would be eventually emitted from the bottom’s surface) where the absorbed portion was converted into sensible heat. Previously, I had ignored that any solar radiation not absorbed must have been ‘reflected’ from the bottom surface toward the other surfaces of the interior. One of which was the bottom surface of the bottom glass pane through which the solar radiation has previously been transmitted. Of course, a portion of this ‘outgoing’ solar radiation must be reflected back into the interior just as the ‘incoming’ solar radiation had reflected back toward space from the surfaces of the glass panes.
The image of the device’s interior, which I am constructing in my mind, is one of multiple reflections of not only the solar radiation’s photons but also of photons of the long wavelength IR radiation being continually emitted from all surfaces of the interior according to Stefan-Boltzmann (S-B) radiation relationship. Because these long wavelength IR radiation photons cannot be transmitted through the opaque (to it) glass panes, they must be either absorbed or reflected from the bottom surface of the bottom pane. And the bottom surface of the bottom pane must be also emitting photons toward the other surfaces of the interior as they do likewise toward each other.
Now, I expect this qualitative reasoning of an invisible ‘world’ is unfamiliar to many but the world which the chemist studies is filled with invisible atoms and molecules. And if one has no or little experience with trying to imagine what is occurring in this invisible world, I am sure that much of the previous reasoning could appear rambling and confusing. But I am quite certain that a reason I made my previous error is that I did not begin to qualitatively reason and methodically write what I have just written.
So I see that the trapping mechanism of the de Saussure device is a one-way mirror (the glass pane) which basically transmits solar radiation in one direction and reflects the radiation emitted by the interior’s surface in the other direction. Notice that I, to simplify, ignore absorption of radiation by the pane’s surfaces. For, at a first approximation the surfaces of the pane can be ‘heated’ the gas molecules which I also ignore to simplify.
Now, as the number of photons moving at (near) the speed of light builds up, the temperature of the bottom surface of the bottom glass panes increases to the maximum temperature observed by Horace. For, at this temperature the transfer of energy through the bottom glass pane matches the energy being continuously transmitted into the interior near midday as the device is pointed toward the sun. And this thermal conduction requires there be a cooler temperature on the top side of the bottom pane. And the top side of the bottom pane emits radiation toward the bottom side of the middle pane. Which reflects this emission back toward the top surface of the bottom pane.
If it helps to imagine a ping-pong match, do it. But possibly easier is to image that a lesser number of photons are being trapped in the space between the bottom and middle pane because the temperature of this space is less than that of the interior. By now, I see the same thing occurring in the transfer of energy by thermal conduction through the middle pane as occurred through the bottom pane. And I see that the temperature of the space between the middle pane and the top pane must be less than that between the bottom pane and the middle pane. And finally, as the last step in the continuous transfer of energy from the interior to the atmosphere in contact with the top surface of the top pane, I see the temperature difference between the bottom surface and the top surface of each pane must be the same for all three panes.
Now, I have read there are devices which seem capable of measuring the temperature of the top surface of the top pane without contacting the surface. If this possible, the difference between the interior temperature and the ‘exterior’ temperature divided by 3 should be the temperature difference between the two sides of each pane. But if it is not possible to measure the temperature of the exterior surface without influencing its temperature, it should be possible to measure the temperatures of the two spaces between the glass panes just as the temperature of the interior space was measured. And the difference between these two temperatures are the temperature difference between the two surfaces of the middle pane.
Finally, since we know the exterior temperature, one way or another, we should be able calculate the emission of this top surface of the top pane using the S-B radiation relationship because if the emissivity of any surface has been measured, it should be that of a glass surface. And this calculated emission must be the energy of the solar radiation which is continuously absorbed by the interior surfaces of the de Saussure device.
Now, all that needs to be done is to do the experiment to see if the actually observed values fit what has been qualitatively reasoned. For this is a simple experiment an ‘amateur’ scientist with only moderate interest should be capable of performing. And I can propose one further experiment not yet considered to my knowledge. How would a doubling of the thickness of the glass panes influence the maximum temperature of the interior? Qualitatively reason about it, make an ‘educated’ prediction, and test it by experiment. Another experiment I can imagine is, once a continuous maximum temperature is achieved (actually this is what the first experiment tests; can a steady-state interior temperature be achieved?), cool the exterior surface by misting it with water and observe what happens. Some people find such simple experimentation more interesting than debating other people’s ideas. Try it; you might like it!
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