A Most Excellent Exposition

Everyone please read and widely share this most excellent exposition of the debunk of climate science and climate alarmism, produced by a reader and commentator. It also serves as excellent educational material for understanding the climate and heat transfer through the Earth’s atmosphere from the Sun, and would easily make excellent teaching material if we have any institutions left which are interested in teaching real critical thinking and real science and real mathematics.

I do not know who exactly actually produced this, but it was originally submitted via this comment. Whoever it is, they have done excellent work and this document should be shared widely by everyone, through all of your social media accounts and other avenues as possible. Send it to teachers you know, professors you know, institutions you know, etc:

https://climateofsophistry.files.wordpress.com/2019/10/lars-asks.pdf

 

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55 Responses to A Most Excellent Exposition

  1. George says:

    Yes, Joe, an EXCELLENT presentation!! WOW!! Laid out very well for the layman to grasp. Kudos to whomever made this!!!

  2. Joseph E Postma says:

    That document would make for a great small book on its own!

  3. Joseph E Postma says:

    For sure George. Whoever “Suit Yourself” is, from the comment submission, is one smart cookie.

    I’m reading it again more slowly this time…it’s impressing the heck out of me. We have a live-mind on our hands!

  4. … live mind, as opposed to the HIVE mind.

  5. boomie789 says:

  6. What we do here, we integrate the flux over all frequencies that gives the total flux and that’s equal to Sigma times the effective temperature to the fourth power.

    Now for my attempt at clarification (is this correct?):

    “Integrate” roughly means “add together”.

    Flux, however, occurs over different frequencies for different temperatures. A higher temperature has more flux and higher-energy flux at higher frequencies. So, when we “integrate” or “add together” those higher energy fluxes, we get the correct total flux distribution at the respective temperature that produces those fluxes in THAT distribution across frequencies.

    Simply adding fluxes, therefore, and trying to equate the sum to a temperature FAILS to account for the GREATER QUANTITY and GREATER ENERGY of flux happening at higher frequencies of greater temperatures.

    A certain watts-per-meter-squared, in order to correctly correspond to a temperature, MUST take account of the correct distribution of flux-amount and flux-quantity for the respective frequencies of that associated temperature. Otherwise the watts-per-meter-squared is false.

    Temperature determines the distribution of frequencies over which flux occurs. Flux does NOT determine the temperature. Even though there is an equation for the relationship between watts-per-meter and temperature, temperature must establish watts-per-meter on the other side of the equals sign, not the other way around.

    There has to be a temperature before there can be any watts-per-square-meter flowing. Temperature must precede the flux that it causes. There is no meaning in the idea of a flux that exists before a temperature that causes it.

    The temperature must exist first — a simple fact of causation, like water has to exist, before water can flow. Temperature CAUSES flux, and that’s why the equals sign in the SB law cannot be considered as dictating the watts-per-meter-squared.

  7. Rosco says:

    RK – you’ve got to remember spectral bands and also the inverse square law. The graph I produced show flux for temperature emissions from temperatures in the same spectral band – the temperatures I used all fall into the IR band.

    “Climate science” has no way of allowing for this reality – in fact they ignore it all together – reality I mean.

    The stupidity of the simplified model is that the solar radiation is totally different radiation to that emitted by ice at minus 18°C.

    At a distance a bit more than twice that of Earth to the Sun the solar radiation will have a value of 239.7 W/m2 but it will still be totally different radiation to that emitted by ice at minus 18°C.

    To just add them up as the simple model does is stupid beyond belief. The solar radiation at that distance will still be able to eject electrons from solar panels and generate electricity – something IR emitted by ice at minus 18°C will never accomplish.

  8. Ironically I have been laying out your work over the past few days and then up on my feed JF vs Joe shows up. I thought this should be interesting. Unfortunately he took you all over the place instead of beginning at the start of the problem (and of course you went off on your flat earth rant which doesn’t help the non believers (believe it or not)).
    You really need to being with the input swapped for output and WHY they the scientist do this. Which in turn leads to everything else. I sent in questions to prompt the conversation but JF as usual always ignores my questions.
    So after the show I decided to publish what I have done for you to use. Perhaps you could do a video going through it all.

  9. tom0mason says:

    A most excellent write up, very good.
    ~~~~~~~~~
    However from what I see the climate worriers wish to have there cake and eat it …
    The problem with all these climate worriers is that they wish to use an averaged figure for the earth’s temperature but then use this as an ‘instantaneous value’ or as an unaveraged thermal level, and for it’s effects on the planet.
    The average temperature of the planet does not, can not, give anyone more information about unaveraged temperature effects on the planet’s surface, or unaveraged temperature effects within the atmosphere. It’s an average and as such has lost all specificity both temporal and regional for effects on the planet.
    As I have outlined before —
    In two cases the average temperature was the same but —
    1. the poles warmed slightly as the tropics cooled slightly, – or –
    2. the poles cooled slightly and the tropics warmed slightly
    The climatic effects between the two are RADICALLY different.

    The heat of the sun has a large and direct effect on environment regions and for particular times (diurnally, seasonally, and with changes in orbital parameters), it warms areas nearer the tropics more than the poles.
    So called ‘back radiation’ has no observed effect on anything, it is pure (averaged) hokum.

  10. boomie789 says:

    I like that idea Suit Yourself.

    The irradance of the entire earth has been reflected back at itself. The irradance irradiates from all sides at once, so they reflect it back over the entire surface. Under the auspice of conservation of energy. When the sun actually has a focal point of energy. Where there is all the energy needed to drive the climate. 87.5C at the equator, dissipating towards the poles, over 24hrs.

    Then maybe go from here and explain the alarmist use flat earth physics, because they do.

  11. Joseph E Postma says:

    I chatted with the interviewer a little bit before things started. He says he is in hiding because of threats received from “leftists” and so although he is from Quebec, he couldn’t tell me where is located now. Typically that would be a “good thing” as far as the orientation of the personality which received such threats, meaning that they should be a rational climate skeptic. However, in addition to being in hiding he also seems as if he was “controlled”. He was reading his questions from a script it seemed, and was repeatedly attempting to make the sophistical arguments that alarmist leftists always do. At no point did he ever concede that I made a point, which I obviously did many times. For example when he challenged me about connecting this to flat Earth theory…and I simply showed the alarmist diagram which IS a flat Earth…no acknowledgement. Either purposeful, or it is still surprising how seemingly educated people cannot understand simple things.

  12. Joseph E Postma says:

    “The average temperature of the planet does not, can not, give anyone more information about unaveraged temperature effects on the planet’s surface, or unaveraged temperature effects within the atmosphere.”

    That’s an excellent sentence. Because of course it is the unaveraged temperatures, i.e., the real-world temperature differentials, which cause heat flow and as consequence create the climate and its variations.

  13. Joseph E Postma says:

    I mean I make it a binary choice, and I remain flabbergasted that people seem unable to comprehend the choice and to make it:

    A) Sunshine spread over the entire Earth’s surface at once as if the Earth is flat, where the Sun cannot create the climate, with an alternative greenhouse effect where the climate creates itself.

    B) Sunshine in real time on a round rotating Earth where the Sun creates the climate.

    Choose. Either answer completely and entirely and 100% obliterates the other. Binary choice, one or the other.

  14. boomie789 says:

    He is a white nationalist/race realist. I think his book is about dysgenics. That’s why he is in hiding. The left doesn’t support nations sovereignty. Which is odd, considering the effect “combating global warming” will have on western nations. You would think he would be more open to discrediting it.

    They’re are to many alarmist bricks in his foundation of knowledge. We need to remove each brick, one by one, and replace them before he can see.

    Like his misconceptions about the atmosphere and the properties of CO2. He has this brick wall of misinformation blocking you from getting through.

    I watched his interview today with some centrist fool, JF’s respect for modern science and academia is non-existent. A qoute “I shit on It”-JF.

    I hold out hope this guy could come around.

  15. Joseph E Postma says:

    Oh wow that’s interesting. OK great, good to know his position on academia.

    Well…I recall stating that choice to him during the interview – what do we need to do to get people to acknowledge and face that simple choice?!

  16. geran says:

    “Choose. Either answer completely and entirely and 100% obliterates the other.”

    One is obviously true, the other is obviously false. It should be an easy choice.

    What we are seeing, from the Warmists, is a combination of incompetence and dishonesty. Some are sincerely ignorant of the physics. But others openly try to pervert the laws of physics.

    They can understand arithmetic, so if the numbers work out, they tend to “believe”. TSI (incoming solar) after albedo is about 960 Watts/m^2. If you divide that by 4, the answer is 240 Watts/m^2. They can do that simple division, so they believe they understand the physics. It must be right because the arithmetic is right!

    But they can’t understand the physics. They can’t understand that 960 Watts/m^2 can raise the temperature of a flat BB plate, insulated on the back, to a temperature of 361 K (87.6 ºC, 189.6 ºF). While 240 Watts/m^2 could only raise the temperature of the same plate to 255 K (-18.1 ºC, -0.5 ºF).

    The difference in temperatures is drastic.

    240 Watts/m^2 can NOT heat the planet. An ice cube emits more flux!

    So they keep the hoax alive by eliminating the Sun, thereby in their heads, needing another heat source to get to Earth’s average temperature of 288 K. And they continue demonstrating their ignorance of physics by claiming CO2 is that “heat source”.

  17. boomie789 says:

    Focus on one incorrect brick at a time until it crumbles. Make him acknowledge his conception is incorrect. Then replace it with the truth. Don’t move on until he understands.

    Easier said than done. At best this is only possible with 50% of people. A mind is much easier to make than it is to change.

    He has the same conception as Roy Spencer with this blanket effect. He brought it up multiple times. CO2 holding in heat. Make that brick disappear, replace it with a dissipating atmosphere, like explained in other comments. Then move on to the next brick. Destroy his misconceptions, destroy his wall, then his mind will be able to understand.

    I hope that helps. It’s an art getting in people’s heads.

  18. boomie789 says:

    It’s also a flat earth under a frozen sun.

    If it were just a flat earth it would all be as hot as the equator is now.

  19. Joseph E Postma says:

    Exactly. It’s a flat Earth at twice the distance from the Sun!

  20. MP says:

    The name TSI assumes “tota”l solar irradiation. But it is not total, it covers only the visible spectrum. The TSI completely ignores the effect of the ultraviolet spectrum, the x-ray spectrum, and cosmic rays.

    Here is an excellent presentation about that

  21. MP says:

    Correction. UV is in the TSI. Electromagnetic particles, Electromagnetic fields, and x-rays are not in the TSI

  22. Pierre D. Bernier says:

    You guys in Alberta are lucky this week. You have Greta all to yourseves. Tell me ! Why is it that the oil industry as a whole doesn’t push back more then that ? I don’t understand, really ! I don’t !

  23. Pierre D. Bernier says:

    Would it be starting at last ?

  24. Extinction Rebellion zombies are now proud that many celebrities embracing their fake cause have signed an open letter that openly admits that they are all hypocrites, but it’s not their fault — they are victims of the fossil-fuel system, and their hypocrisy is not the main point of the “conversation”, but a distraction from what they are saying.

    How utterly, sophistically lame is THAT?! — Have you ever seen a bigger pile of bullshit? — hypocrites justifying their hypocrisy by claiming that it is a distraction from their hypocritical actions contradicting the very words they utter?!

    Can circular stupidity evolve any further? — I think not.

  25. Pierre D. Bernier says:

    Another wonderfull piece by Dr. Tim Ball

  26. Pierre D. Bernier says:

    A thought experiment just to see if I get this right.

    In my living room I have a table with a glass top 1m by 1m giving me a surface of exactly 1 square meter. At room temperature of 22 ºC (295 K), according to the Stefan-Bolztman law, this table top radiates ~429 W.

    From… https://en.wikipedia.org/wiki/Incandescent_light_bulb
    The uncoiled length of the tungsten filament in a bulb is usually 580 millimetres with a diameter is 0.046 millimetres.

    So, Circumference = 0.046mm * Pi = 0.1445 mm.
    Surface = 580mm * 0.1445 = 83.8 mm2.
    S = 83.8mm2 / 1000mm/m /1000mm/m = 83.8 * 10^-6 m2

    A 100 Watts bulb, assuming a 100% efficiency, will radiate 100W / 83.8 10^-6 m2 = 1.193 * 10^6 W/m2 for a temperature of 2142 K.

    What a difference the surface area makes. Less energy gives higher temperature. And they wonder why the Sun can create the climate !

    Now. The filament has a continuous energy source. It’s not going to cool down any time soon. The table has no internal energy source. After radiating some photons to the atmosphere, shouldn’t it cool down some bit, say 3K eventually ? Space is at 3K, a home for any radiation. The absolute sink hole. I know,, after cooling to 21.999999999 ºC, you have a temperature differential and the table top is going to pick up some heat back to 22 ºC from the environment.

    Did I get that right ? Something wrong somewhere ?

  27. geran says:

    It looks good, Pierre. Except, you forgot the funny part.

    The pseudoscience clowns would remind us that the glass table top emits from both sides, or 429 (2) = 858 Watts. So if you had two such tables, you could heat your room in winter with 1716 Watts, because they believe radiative fluxes add!

    Clowns are so funny!

  28. Pierre D. Bernier says:

    / radiative fluxes don’t add /
    That is exactly where I bug and wanted to get to. I have one foot dragging here.
    If I have 2 identical parabolic reflectors both pointing at the same place on a white screen. If i put a 150 W bulb in one reflector and a 75 W bulb in the other, won’t I have more light on the screen then if I have just the 150 W light bulb ? Won’t the fluxes add up ? If I do a spectral analysis of the light on the screen, wont I see 2 superimposed Planck curves ? Is it just because I have 2 real light sources here ?
    I’m spinning in the mud here !

  29. geran says:

    The 150W and 75W bulbs would emit different spectra. And yes, parts of one would overlap the other. But that does not result in a temperature increase.

    For example, if you turned on the 75W bulb first, it could warm a black body to some equilibrium temperature. If you then turned on the 150W bulb, the BB temp would increase, but the temp would not rise above the temperature of the 150W bulb by itself.

    Turning on the 150W bulb first, and then the 75W bulb, you would see no increase. The 75W bulb cannot increase the radiative effect of the 150W bulb.

    A simple analogy is a bowl of water at 80 degrees. Add an equal amount of water at 40 degrees. Does the extra water at 40 degrees raise the temperature of the mixture?

  30. Pierre D. Bernier says:

    geran
    I’m not sure the bowls of water is a good analogy because the result would be 2 bowl worth at 60 degrees water. Anyways, that’s beside the point. The screen does receive 225W therefore has to emit 225W. Say it’s a black velvet screen so as to minimize reflection (100% absorption). We have 2 choises…
    1) The wattage is re-emitted as a higher temperature of 225W with a single Planck curve or,
    2) At the temperature of the strongest bulb with 2 super-imposed Planck curves with a surface area equivalent to 225W.

    I’m still spinning.

  31. geran says:

    Pierre, the bowls of water ARE a good analogy. You proved it yourself. You realized that adding energy to a system with average higher energy could not raise the system temperature.

  32. If i put a 150 W bulb in one reflector and a 75 W bulb in the other, won’t I have more light on the screen then if I have just the 150 W light bulb ?

    Depending on how you angled the reflectors, I would say that you would have more surface area illuminated.

  33. Pierre D. Bernier says:

    / more surface area illuminated./
    Not sure if more surface but I do have 2 real light sources. Not one real and one imaginary. If Jupiter was to turn into a star tomorow, how would that affect the earth. We would have 2 real energy sources (Suns).
    Still spinning my wheels in the mud !

  34. geran says:

    Pierre, maybe you’re in the mud because you want to be.

    We’ve seen this game before.

  35. Pierre D. Bernier says:

    geran
    Maybe you’ve seen this game before but I haven’t. I don’t have time to read every single things. Plank’s law applies to a blackbody. Keyword “a” meaning one. One radiating blackbody ! If we happened to be living in a 2 stars system don’t tell me that things would be the same regarding the Earth. When I open 2 lamps in a room at night, the walls are brighter then if I light only one. Granted that part of it is just reflection.

    Rosco has clearly demonstrated that you cannot add 2 fluxes using the SB law because it does not give the same result that Plank’s law gives. I fully agree with that. That you cannot add 2 fluxes using the SB law proves just that, not that you cannot do it.

    I’m just trying to imagine what the emission pattern would be with 2 lights shining on a black screen. Is that to much to ask ? I’m not the type to just accept what I’m told without questioning. There is plenty of that on the warmist side and in the past under the church rule. I’m making a real effort to understand a physical phenomenon. If you don’t want to help, I’m fine with that. Just don’t answer. If the question has been discussed before on this site, or else where, then please point me to it.

  36. geran says:

    Pierre, the “game” I am referring to is played when someone demonstrates they do not understand the relevant physics, then when someone else tries to explain to them, they refuse to consider reality, as when you rejected the simple analogy of adding 40 degree water to 80 degree water. That analogy explains why a 75W bulb cannot radiatively raise the temperature of a surface over what a 150W bulb can do. Look at your own words:

    ”I’m not sure the bowls of water is a good analogy because the result would be 2 bowl worth at 60 degrees water. Anyways, that’s beside the point.”

    You refuse to accept the analogy, then claim it is “beside the point”, even though you realized that adding more energy resulted in lowering the temperature.

    Currently, the same game is being played by another individual. That individual is claiming geothermal warms Earth, not the Sun. Of course it follows that the individual must discard simple examples and analogies. Suspicious minds might consider that individual just wants to disrupt and confuse. What do you think?

    If someone were sincerely trying to understand, then they would be receptive to clear, easy-to-understand examples and analogies, rather than quickly discarding them. One cannot learn with a closed mind.

  37. Pierre D. Bernier says:

    I’m not saying that the wall should be warmer with the 75W bulb on. I’m asking where the fuck does it go ? What does the emmision spectra looks like ? Am I aloud to ask questions or should I obey the church blindly ? If not I’ll go somewhere else !!!

    I’m not trying to impose anything on anyone like that person you’re talking about, so please don’t insult me ! I’m just asking not imposing ! There is a BIG difference. So cool it down and if it doesn’t suit you don’t answer anymore !

  38. geran says:

    Pierre, if you’re sincerely trying to understand, do you now acknowledge that adding 40 degree water to 80 degree water is a good analogy?

  39. CD Marshall says:

    geran

    I’m curious about your bulb example. With a binary star system how would the energy flux work? Maybe this is a question for Joseph, but I initially assumed with a binary star system the energy would be doubled. Now I’m thinking my reasoning is incorrect. Two 100 watt bulbs doesn’t create a 200 watt bulb it just creates two 100 watt bulbs illuminating at 100 watts each if I am understanding this right.

  40. Pierre D. Bernier says:

    geran
    / do you now acknowledge that adding 40 degree water to 80 degree water is a good analogy? /
    I agree that 40C water wont heat 80C water. It would be ridiculous to think it would. But no, you have 2 equal volume buckets, one at 40 and the other at 80 which makes it a fixed energy closed system. Once you put them together it’s over. Done. The system is in equilibrium with the same total energy. Finished. Kaput !

    The light bulb analogy has constant continuous energy input in time. That energy has to be dissipated somehow which is not the case with the buckets and I honestly think that I should see that energy coming out somewhere somehow, otherwise the whole thing should burn down at some point in time. I’m not disputing that the 150W light bulb might fix the max temperature and the 75W bulb wont make a difference in the temperature of the screen. I just want to know where do I see that extra 75W go ? Through the wall Purely reflected. Combination ? I just want to see the emission spectra. That all !. What will the emission spectra look like ?

    It’s all too easy to say it’s as if it does not exist. If I accept that answer without understanding and asking questions then I’m no better then the alarmists and no, I’m not trying to make trouble..

  41. geran says:

    CD, the bulb example was really Pierre’s, but your question is worth answering.

    For clarification, assume we have a black body plate, in space, perfectly insulated on the back side. The front side faces the sun, at a distance of 1 AU, receiving 1365 Watts/m^2 constantly.

    The plate would quickly reach equilibrium temperature of 394 K.

    Now bring another sun in front of the plate, exactly like the first sun, and at the same distance. The plate would be receiving 1365 Watts/m^2 from both suns. But since it is already at the equilibrium temperature, it would not increase in temperature. Believing the fluxes add is one of the flaws in the GHE pseudoscience.

    The simple analogy is a big block of ice in a room. The ice is emitting about 300 Watts/m^2. If you add another identical block of ice, the temperature does not rise, even though both blocks are emitting 300 Watts/m^2. Even 10 blocks of ice (3000 Watts/m^2, to clowns) still won’t raise the temperature.

  42. geran says:

    Pierre, the easiest way to understand why the 75 W bulb cannot add to the 150 W is that the photons would be reflected. If you imagined a scenario where the photons could somehow be forced to be absorbed, they would cause a lowering of the average vibrations, thereby cooling the surface. But, it’s not possible to force low energy photons into a “hotter” surface without adding more energy, such as a laser does. And a laser would cause an increase in temperature.

  43. Pierre D. Bernier says:

    Geran
    Now you have answered my question clearly and to my satisfaction. Now I see the relation to your buckets of water. Now I see why the 75W is reflected directly from the surface and the 150W is absorbed and radiated back in IR.

    thx.

  44. Illumination and flux are not the same thing. Two light bulbs can add more illumination to a given room, simply because there’s more surface area of glowing bulb per surface area of room. The SIZE of the illuminating source has increased. The overall flux has not.

    A light bulb that is four feet long is going to illuminate a room differently than a light bulb that is one foot long.

  45. CD Marshall says:

    Geran,

    Thank you that was fascinating. Now if you don’t mind, applying a bi-nary to Earth for instance, how would that change the conservation of energy and/or heat flux? Would the ToA still be 1365 W/m^2?

    They said Jupiter almost became a star, that is not your normal bi-nary star system for Jupiter, even as a star, would be much smaller than the Sun. Now this is more like Pierre’s version of two different bulbs what would that effect be if Jupiter had become a smaller star? Being that Jupiter is 5.2 AU (4.2 from Earth?) from the Sun I doubt it would have any effect on the Earth as opposed to identical bi-nary twins.

    You said, “Now bring another sun in front of the plate, exactly like the first sun, and at the same distance. The plate would be receiving 1365 Watts/m^2 from both suns. But since it is already at the equilibrium temperature, it would not increase in temperature.”

    So the Earth would receive only 1365 W/m^2 from the two twin stars. Since Jupiter-Star is smaller 1365 would still the number that can be reached.

    Physics 101 confusion between energy, heat and temperature. Still wrapping my head around the differences.

  46. lifeisthermal says:

    Finally people are starting to understand that an energy balance must be done with heat source Power and not average energy per m^2. I´ve been saying this for years. Just look at any book on heat transfer and steady states, there it is.

  47. geran says:

    “Physics 101 confusion between energy, heat and temperature.”

    CD, to make it even more confusing, radiative physics is really not even taught in “101”. That’s why many people are so often confused by “flux”.

    And that’s why I try to keep the examples very simple. I used two suns on the same side of a flat blackbody plate, so as not to allow too many side issues. I use ice cubes a lot, for the same reason. Everyone can understand ice cubes. The point is, radiative fluxes do not add, except in very special cases. Even though fluxes have the same units, they are very different.

    A flux emitted from a cold surface consists of photons with average energy much less than those emitted from a hot surface. Photons can have different wavelengths, directions, and phases. That means that fluxes can be as very different. If you tried to add 5 oranges to 7 buckets of sand, do you get 12 oranges, or 12 buckets of sand, or 6 buckets of oranges, or 6 sandy oranges, or….

    Fluxes don’t add. They don’t subtract. And you can’t “divide-by-4”.

  48. geran says:

    PS Fluxes are not conserved.

    Energy is conserved, but flux is not conserved.

    That’s why trying to “balance” fluxes is pure pseudoscience.

  49. “Currently, the same game is being played by another individual. That individual is claiming geothermal warms Earth, not the Sun.”

    Apparently this “person” is now stalking posts over at PSI and trashing me…lol. They ALWAYS turn into stalkers.

  50. “I’m curious about your bulb example. With a binary star system how would the energy flux work? Maybe this is a question for Joseph, but I initially assumed with a binary star system the energy would be doubled. Now I’m thinking my reasoning is incorrect. Two 100 watt bulbs doesn’t create a 200 watt bulb it just creates two 100 watt bulbs illuminating at 100 watts each if I am understanding this right.”

    One does need to account for view factors. Recall that flux decreases as the inverse square law from a point source. Having two identical point sources now makes the view factor slightly closer to that of a wall of light. If you go to a complete infinite wall of source light, then there is NO inverse square law and no decrease in intensity of flux from the source wall. So, point sources can add up beside each other until the point at which the view toward the point sources is a wall – at that point, at any distance from the wall, the flux now doesn’t decrease in distance from the wall.

    Flux from point sources can add up via the view factor, until the point at which the flux from the point sources reaches a maximum of the flux at their source which occurs when there are infinite point sources forming a wall a light. So, infinite points of source locations, forming a wall of light, only produces the *finite* flux at any given point source location on the wall. It doesn’t add up to infinity even though there are infinite source locations on a wall…it only produces the flux at any given point location which then does not decrease in intensity with distance from the wall.

    Note that this scenario is with independent energy sources, not one source reflecting or recycling its own light such as to produce additional temperature as per the climate GHE scheme.

    So now if we extend this to two bulbs, which are point sources, of different power/flux/intensity, then we can extend that concept to an infinite wall with, say, some smoothly varying temperatures all over it. The flux intensity felt at any distance from the wall will then be something in between the maximum temperature location on the wall, and the minimum. So likewise, adding two different power bulbs will not produce more power than the hottest bulb, but something in between, similar to adding two bowls of water together of different temperature.

    With the one hot bulb, its flux intensity is reduced at a receiver at any distance given the inverse square law from point sources. Adding identical hot bulbs will in the infinite limit create a “bulb wall” and the result is that at any distance you will receive the full flux of the temperature of the filament itself! Adding cooler bulbs will do less good than this. But it is the view factor here which is changing and is important to consider, but also, given the limits, the addition of multiple sources never results in the flux adding to ABOVE the source flux *at the source surface itself*.

    And that latter is what the GHE is – the IR flux back-adds with itself to create greater intensity flux at the flux source.

  51. “The SIZE of the illuminating source has increased. The overall flux has not.”

    Yes, that is exactly it, the relevance of the view factor. You can keep on increasing the size of the illuminating source until it is an infinite wall, and at that point the flux is still only the flux directly at the surface of the source, because you’ve gotten rid of the inverse square law which is for point sources.

  52. Geran is basically getting things correct, but just needs to remember view factors, and the effect on inverse square law, etc. Pierre is asking a great question. But this is a subtle and careful problem and even in university education it is not covered extensively, although it is certainly in the textbooks. Adding two bulbs will not increase the source flux above the hottest bulb *at that bulbs surface*…however, one must also account for distance and view factors at distance recievers because the entire geometry of the situation is being changed when additional independent sources are added. Flux still do not add to produce higher temperature than the hottest source bulb filament itself…but, at distant receivers, the geometric topology of the space is being modified, and this has an effect on the inverse square law.

  53. geran says:

    Correct Joseph. I just try to keep my examples simple, as in always setting the view factor = 1.0.

    And your mention of the inverse square law is another example of why flux is not conserved. If the surface of a sphere (radius R) were emitting 240 W/m^2, then at a distance of 2R from the sphere’s center the flux would be 60 W/m^2.

    The energy leaving the “R” sphere would equal the energy arriving the “2R” sphere, but 240 W/m^2 ≠ 60 W/m^2.

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