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The greenhouse effect and the 2nd law of thermodynamics

What the science says...

Select a level... Basic Intermediate

The 2nd law of thermodynamics is consistent with the greenhouse effect which is directly observed.

Climate Myth...

2nd law of thermodynamics contradicts greenhouse theory


"The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier 1824, Tyndall 1861, and Arrhenius 1896, and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist." (Gerhard Gerlich)


Skeptics sometimes claim that the explanation for global warming contradicts the second law of thermodynamics. But does it? To answer that, first, we need to know how global warming works. Then, we need to know what the second law of thermodynamics is, and how it applies to global warming. Global warming, in a nutshell, works like this:

The sun warms the Earth. The Earth and its atmosphere radiate heat away into space. They radiate most of the heat that is received from the sun, so the average temperature of the Earth stays more or less constant. Greenhouse gases trap some of the escaping heat closer to the Earth's surface, making it harder for it to shed that heat, so the Earth warms up in order to radiate the heat more effectively. So the greenhouse gases make the Earth warmer - like a blanket conserving body heat - and voila, you have global warming. See What is Global Warming and the Greenhouse Effect for a more detailed explanation.

The second law of thermodynamics has been stated in many ways. For us, Rudolf Clausius said it best:

"Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."

So if you put something hot next to something cold, the hot thing won't get hotter, and the cold thing won't get colder. That's so obvious that it hardly needs a scientist to say it, we know this from our daily lives. If you put an ice-cube into your drink, the drink doesn't boil!

The skeptic tells us that, because the air, including the greenhouse gasses, is cooler than the surface of the Earth, it cannot warm the Earth. If it did, they say, that means heat would have to flow from cold to hot, in apparent violation of the second law of thermodynamics.

So have climate scientists made an elementary mistake? Of course not! The skeptic is ignoring the fact that the Earth is being warmed by the sun, which makes all the difference.

To see why, consider that blanket that keeps you warm. If your skin feels cold, wrapping yourself in a blanket can make you warmer. Why? Because your body is generating heat, and that heat is escaping from your body into the environment. When you wrap yourself in a blanket, the loss of heat is reduced, some is retained at the surface of your body, and you warm up. You get warmer because the heat that your body is generating cannot escape as fast as before.

If you put the blanket on a tailors dummy, which does not generate heat, it will have no effect. The dummy will not spontaneously get warmer. That's obvious too!

Is using a blanket an accurate model for global warming by greenhouse gases? Certainly there are differences in how the heat is created and lost, and our body can produce varying amounts of heat, unlike the near-constant heat we receive from the sun. But as far as the second law of thermodynamics goes, where we are only talking about the flow of heat, the comparison is good. The second law says nothing about how the heat is produced, only about how it flows between things.

To summarise: Heat from the sun warms the Earth, as heat from your body keeps you warm. The Earth loses heat to space, and your body loses heat to the environment. Greenhouse gases slow down the rate of heat-loss from the surface of the Earth, like a blanket that slows down the rate at which your body loses heat. The result is the same in both cases, the surface of the Earth, or of your body, gets warmer.

So global warming does not violate the second law of thermodynamics. And if someone tells you otherwise, just remember that you're a warm human being, and certainly nobody's dummy.

Basic rebuttal written by Tony Wildish

Update July 2015:

Here is the relevant lecture-video from Denial101x - Making Sense of Climate Science Denial


Update October 2017:

Here is a walk-through explanation of the Greenhouse Effect for bunnies, by none other than Eli, over at Rabbit Run.

Last updated on 7 October 2017 by skeptickev. View Archives

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Further reading

  • Most textbooks on climate or atmospheric physics describe the greenhouse effect, and you can easily find these in a university library. Some examples include:
  • The Greenhouse Effect, part of a module on "Cycles of the Earth and Atmosphere" provided for teachers by the University Corporation for Atmospheric Research (UCAR).
  • What is the greenhouse effect?, part of a FAQ provided by the European Environment Agency.



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Comments 226 to 250 out of 1481:

  1. Re #223 KR You write:- "So, without the 333 W/m^2 backradiation, the surface of the Earth at current temperatures would still radiate upwards to space at net 356 W/m^2, not net 26 W/m^2. Don't you think this would have a cooling effect?" The real cooling effect of radiation is the 239W/m^2 leaving the top of Trenberth's diagram for deep space. The net 26W/m^2 due to GHGs is trivial in comparison with the 175W/m^2 total contributed by the sun (78W/m^2), water vapour (80W/m^2) and convection (17W/m^2).
  2. damorbel - Without greenhouse gases to radiate from the upper atmosphere, the 17 convection and 80 evaporative W/m^2 would quickly saturate and cycle back to the ground, reducing net transport to space via those pathways to zero, as it would have nowhere to go - the 169 emission from the atmosphere would be zilch without GHG's. And the 396 W/m^2 IR would go straight into space, rather than the 239 W/m^2 currently. Net would be 156-157 W/m^2 imbalance towards space, as opposed to the current 1 W/m^2 imbalance towards the ground. What do you think - would a negative balance of 156 W/m^2 have (as you seem to claim) no effect, or would it rather cool the earth about 150x faster than it's currently warming?
  3. Re #223 bis KR You write:- "the surface of the Earth at current temperatures would still radiate upwards to space at net 356 W/m^2," I have done detective work on this and it is based on "the Earth emitting like a black body", yet another piece of GHE folklore that has no foundation. It is very obvious that the Earth is not a black body radiator at any wavelength. A blackbody radiator would have an emissivity (e) of 1, whereas the Earth has an emissivity of 1-a, where 'a' is the albedo. Thus the Earth's emisivity is about 0.7, giving an equilibrium temperature of about 279K Yet another shocker for you to think about, the Earth's equilibrium temperature (279K) is completely independent from the albedo! In support of this you can look at the Trenberth diagram where you will find that the total power absorbed by the Earth from incoming Sunlight is 161+78 = 239W/m2, the same as the total outgoing 239W/m2 - even with a surface temperature of 288K! Pure blackbody radiators do not exist, they are a hypothetical concept introduced to distinguish absorption from reflection (or scattering - to use a better term).
  4. Here's an analogy to the greenhouse effect, that incorporates a few critical items: Imagine a reservoir behind a dam. There is a constant stream running into the dam (solar input), output pipes at the bottom of the dam (size = Earth area), with some fractional screens (emissivity) over them. Outflow rate is determined by area of the pipes, screen blockage, and primarily by water pressure/reservoir depth (temperature), which for the sake of discussion will scale with depth^4th. Flow = screen * constant * Area * depth^4 We'll start with the reservoir at a level where water pressure pushes an output flow through the pipes and screens equal to the amount coming in from the stream. Leaves block parts of the output screens (greenhouse gases), reducing output flow (cooling energy flow to space). The leaves increase the back-pressure at the output pipes (back-radiation). What happens? Well, output flow is now lower than input flow, and the reservoir level rises until increased pressure makes output flow equal to input again (temperature rises). That, in a nutshell, describes the greenhouse gas effect.
  5. Actually, damorbel, the surface IR emissions are measured observational data, as are the downward back-radiation numbers. You are quite simply incorrect. And greenhouse gases still reduce emissivity to space, sending just under 50% of the Earth emissions back down rather than to space.
  6. Re #227 KR You write:- "Without greenhouse gases to radiate from the upper atmosphere, the 17 convection and 80 evaporative W/m^2 would quickly saturate and cycle back to the ground, reducing net" This is not very sensible, is it? How can you write about "absence of GHGs" and "80 evaporative W/m^2" in the same breath - so to speak? The "80 evaporative W/m^2" comes from the oceans, you know! A completely passive atmosphere, let us say helium (and no water), would still have a temperature gradient due to compression by gravity and it would still circulate heat from the tropics to the poles, it may not be so efficient as water vapour and there would be no liquid water to perform the same circulation but a helium atmosphere would not be some sort of passive participant.
  7. Re #230 KR You write:- "Actually, damorbel, the surface IR emissions are measured observational data, as are the downward back-radiation numbers. You are quite simply incorrect." Measured or not, the net radiation is from the surface to the atmosphere, is that what you mean when you say "You are quite simply incorrect."?
  8. Emissivity of the ground is in the range of 0.96 to 0.99, with cloud albedo at 0.5 accounting for a combined emissivity (relative to a blackbody) of ~0.612. An effective emissivity change of 1.4% (from that same link, with a very simple climate model) will result in a 1°C temperature change. And greenhouse gases directly affect the emissivity of the Earth. As to your "helium atmosphere", total removal of greenhouse gases is a Gedankenexperiment. It's not intended to fully determine an end state, but rather serve as an illustration of how changing a parameter would cause a change from the current state, thus illustrating the importance of that parameter. Arguing about the endpoint of a Gedankenexperiment is quite simply a red herring.
  9. damorbel - You are incorrect when you state that IR from the Earth without GHG's (at current temperatures) would be anything but 396 W/m^2.
  10. damorbel - Also, you're incorrect in your statement about equilibrium temperature being unconnected to albedo. Even a simple climate model indicates about a 1°C temperature change for 3.3% change in albedo, 1.4% change in solar constant, or 1.4% in emissivity (for independent changes of a single value).
  11. damorbel, people have asked you, repeatedly, the simple and essential question "What happens to the photons from sources cooler than the target?" You have ignored those repeated questions, despite them being at the heart of the topic of this thread. Please answer my most recent version of that question: What happens to the photon named Greg?
  12. Re 236 Tom Dayton you wrote: "What happens to the photons from sources cooler than the target?" All bodies (that emit and absorb radiation) exchange photons all the time. The photons from a hotter body have more energy E (because E = h x v = Planck's constant times frequency) the cooler body emits lower energy photons because the peak emission frequency is, according to Wien's law, a direct function of temperature. Do not forget that all thermal bodies (those with an identifiable temperature - not monochromatic etc. like a laser) emit a broad spectrum of frequencies according to Planck's law. It is just that the hotter body emits photons with a higher energy and higher number of photons also. Whatever the configuration of the hot and cold bodies, the cold body will always absorb more photon energy (no. x E) from the hot body than the other way round. Betwen the surface the atmosphere and deep space it goes like this: the surface emits photons at 288K, these are absorbed somewhere in the troposphere, primarily by H2O & CO2 at, let us say at an average temperature of 255K. All the time the H2O & CO2 are emitting photons at 255K and absorbing photons from deep space at 2.7K, not very many and with very low energy (E = h x v ), so the balance is by far in favour of the energy going into deep space. If that was all, the H2O & CO2 in the troposphere would cool down PDQ but do not forget that these two gases are kept at the same temperature as the N2 & O2 also present in the atmosphere as well as absorbing photons from the surface. As well as absorbing surface photons and emitting photons to deep space, H2O & CO2 emit and absorb photons to and from each other. The extent to which this happens depends on where they are in the atmosphere; in the lower troposphere they exchange photons with the surface; since the surface and the lower troposphere have only a small difference of temperature the net energy exchange is small, a vast number of photons but, on average, a very small energy difference. Higher up the balance shifts from the surface exchange as the % H2O & CO2 intermediate between the emission/absorption altitude increases from zero. Even higher up in the atmosphere the gas density becomes so low and the chance of a photon being reabsorbed becomes correspondingly low. For thin atmospheres many photons emitted by H2O & CO2 do not get reabsorbed by adjacent H2O & CO2 molecules, some are reabsorbed by the surface but others are absorbed by deep space. Because it is the net transfer of photon energy between objects that determines the energy transfer you should realise that radiative transfer on Earth from the surface into the atmosphere is only about 26W/m^2, small in comparison with the 78W/m^2 put in directly by the Sun the 80 W/m^2 from evaporation and 17W/m^2 by convection (numbers from Trenberth's diagram). This is the heat that is transferred to the H2O & CO2 by O2 & N2 in the upper atmosphere for subsequent radiative transfer into deep space.
  13. Re 235 Tom Dayton you wrote: "Even a simple climate model indicates about a 1°C temperature change for 3.3% change in albedo" That is what is wrong with the climate models, they are based on the assumption that the Earth 'emits like a black body', an assumption I have seen many times. Not only is this assumption never justified it is self evidently incorrect because Earth reflects quite a portion of the incoming solar radiation, a portion that is called the albedo; so Earth can never be considered as 'a black body'! Worse still, this 'back body' assumption makes the planet's equilibrium temperature a function of its albedo which is simply not the case, there is nothing in modern physics that allows for such a conclusion. If you calculate the average temperature of any planet on the assumption that it is a black body then you will definitely get an erroneous temperature, unless of course it really is a black body. In the case of Earth this 'black body' assumption gives the average temperature as 255K when it should be 279K, a temperature that disposes with the GH effect entirely.
  14. Re 233 KR you wrote: "Emissivity of the ground is in the range of 0.96 to 0.99, with cloud albedo at 0.5 accounting for a combined emissivity (relative to a blackbody) of ~0.612" I could discuss the ground if you like but just think of the oceans which cover 70% of the planet. The oceans reflect light mostly by specular reflection but they do not reflect very much, that is why they generally look rather dark. Mostly the incoming sunlight energy is absorbed and causes evaporation of water, the heat from the Sun then goes into the atmosphere when condensation (rainfall!) takes place thus there is not much of a 'black body' factor in the transfer of heat from watery surfaces to the atmosphere. Water evaporation from land is also an important mechanism for heat transfer into the atmosphere. Including it as part of radiation from the surface like your truly amazing "Emissivity of the ground is in the range of 0.96 to 0.99" figures would appear to do, is definitely an odd way of calculating heat transfer. Even graphite and charcoal never get near these emissivities!
  15. damorbel #238 any body may behave like a blackbody in a frequency range and not in others. In particular, the earth surface is very near a blackbody in the IR range of interest.
  16. damorbel #224: "Sunlight travels from a cold region of the atmosphere to a warmer one... indisputable fact."? Just what it says. The stratosphere is between the Sun and the troposphere. The stratosphere is colder than the troposphere. Ergo, for sunlight to reach the troposphere (and us to be able to see it) it passes from a colder area to a warmer one. Also: "The sunlight that passes through the atmosphere is not affected by it." Nonsense. In the same post you went off on an inexplicable tangent about sunlight causing ozone formation. That alone proves that sunlight is affected by the atmosphere. Also: "Oh, and the temperature at the stratopause is not that low, just about freezing, 0C." First, the stratopause is the boundary between the stratosphere and the mesosphere. Second, it is the warmest point throughout the mesosphere and stratosphere. Third, 0C is still significantly colder than the ~15C average surface temperature. Also in #237: "Whatever the configuration of the hot and cold bodies, the cold body will always absorb more photon energy (no. x E) from the hot body than the other way round." True... but here you finally admit that the 'hotter' body is absorbing photon energy from the colder one. Ergo, the hotter body must have more photon energy with the colder body than without it. Take the colder body away and the hotter is emitting the same amount of energy but not receiving any... ergo, it has less energy and is colder than it would have been with the colder body there. In other words, yes more energy flows from the warm surface of the Earth to the cooler sky than vice versa, but the IR photon energy flowing from the greenhouse gases in the atmosphere down to the surface means the surface is warmer than it would be without those gases.
  17. #220 KR at 02:59 AM on 1 December, 2010 However, when you say that "...Earth is a system very far from thermodynamic equilibrium", I would like to point out that as far as we can tell (again from Trenberth 2009, although I'm sure there are slightly different estimates out there) the balance sheet is currently tipped only about 0.9 W/m^2 from dynamic equilibrium. If we can reduce or prevent further GHG emissions, we can reduce that imbalance, and the resulting shift in global temperatures. Thermodynamic equilibrium and steady state are very different concepts. Earth is not in thermodynamic equilibrium in any sense of the word, because its environment is not in thermal equilibrium. About one part in 184,801 of the skies around it has an effective temperature of 5777 K, while the rest is at 2.725 K. In first, second and third approximation there is only radiative coupling between Earth and its cosmic environment. In spite of the fact the Sun occupies only a tiny portion of the sky, due to the T4 dependence of thermal radiation flux, in excess of a hundred million times more radiative energy comes from it than from CMB (Cosmic Microwave Background). What you call dynamic equilibrium has nothing to do with thermal equilibrium proper, when entropy of the system is supposed to be at its maximum. Quite the contrary. The overall entropy content of the climate system (which includes at least the atmosphere and hydrosphere of Earth, probably the biosphere as well) is kept at the smallest possible value by continuously getting rid of the entropy produced inside the system (OLR has a much higher entropy flux than ASR). This low entropy state can only be maintained by working as hard as possible, that is, producing entropy at the highest possible rate (then radiating it away into outer space as soon as possible). This is what MEPP (Maximum Entropy Production Principle) is about. Obviously an energy balance has to hold in the long run and on average, otherwise sooner or later the system would enter some absolutely crazy state (contrary to observations). But this balance is best described by the concept of steady state, not as a dynamic equilibrium, because it's only too easy to mix up the latter one with thermal equilibrium. It is easy to show that whenever the climate system is in a MEP state, increasing the opacity of the atmosphere in thermal IR (that's what so called GHGs do) decreases rate of entropy production if all else is held unchanged. At the same time entropy content of the system goes up. That's what is described as warming, because warmer stuff has higher entropy in general. BTW, if the climate system were in some suboptimal state by having less IR opacity in the atmosphere than required by MEPP, adding GHGs would increase overall entropy production and decrease entropy content, hence temperature. Saying the addition of some more GHG causes warming is equivalent to insist current IR opacity is already at or above the value implied by MEPP. The fictitious value of 0.9 ± 0.15 W/m2 TOA energy flux imbalance from Trenberth 2009 has nothing to do with reality. What is actually measured by ERBE and CERES satellites, is 6.4 W/m2 (which is obviously wrong beyond repair). Therefore they apply all kinds of adjustments to the measured dataset so as to match computational model projections and this is how they arrive at the value which was assumed to be the correct one from start. The logic behind this exploit surely makes one's head spinning. J. Climate, 2008, 21, 2297–2312. doi: 10.1175/2007JCLI1935.1 The Annual Cycle of the Energy Budget. Part I: Global Mean and Land–Ocean Exchanges. Fasullo, John T., Kevin E. Trenberth J. Climate, 2008, 21, 2313–2325. doi: 10.1175/2007JCLI1936.1 The Annual Cycle of the Energy Budget. Part II: Meridional Structures and Poleward Transports. Fasullo, John T., Kevin E. Trenberth The only measurement having a chance to shed some light on the true value of energy imbalance at TOA is ARGO Ocean Heat Content data, and only after mid 2003, not before (because OHC measuring network before that date was far too sparse, with serious undersampling as a result). An energy imbalance of 0.9 W/m2 is equivalent to a heat accumulation rate of 1.45×1022 J/annum. In seven years (between mid 2003 and mid 2010) it would be more than 10×1022 J. The NOAA/NODC figure above shows somewhat less than zero J went into the upper 700 m of oceans, so more than 1023 J had to go somewhere else. But there is no place on Earth where such a huge quantity could possibly hide, therefore it is not hiding anywhere, but has left the terrestrial climate system by crossing TOA (as outgoing thermal radiation). In other words, there is no energy imbalance whatsoever, Trenberth's speculations are falsified along with the computational climate model calculations they were based on (which means Trenberth's famous "missing heat" is nowhere to be found at the moment, but it used to be in the oceans earlier, unobserved by the much less reliable XBT/MBT system, making steep parts of the NOAA/NODC OHC graph wanting). Present climate is as close to a steady state as it can possibly be. It is as simple as that. And now back to theory. The most lucid point to have is that Earth is not getting any heat from the Sun, just short wave EM radiation. This radiation is turned into heat when and if it is absorbed by either the atmosphere or the surface (accompanied by a huge increase in entropy). Concerning the effect of GHG addition, the "if all else is held unchanged" clause above is an all-important one. Of course there is no one there to hold things unchanged as some more CO2 is added to the atmosphere, making it more opaque in a restricted thermal IR band. The real climate system has an astronomical number of degrees of freedom (vastly more than any computational climate model can possibly have), so it can adjust itself in any number of ways if a single parameter (like IR opacity in the 14-16 μm band) is changing. If CO2 addition has decreased entropy production rate initially (that is, if the system was close to a MEP state), it will readjust itself to increase its entropy production rate if possible, but under no circumstances would readjustment decrease entropy production rate further. That is, there is a strong tendency to counteract climatic effects of CO2, but MEPP would not allow any change which would amplify it. And indeed, that's what is observed. In the 7 years considered atmospheric carbon dioxide content went up from 376 ppmv to 390 ppmv, which is 5.3% of the radiative effect of a CO2 doubling. Yet, it has induced neither "radiative imbalance" nor "heat accumulation" in the system, as it is indicated by actual measurements (as opposed to computational models).
  18. Berényi - You are correct, I should have used the term "steady-state", rather than "thermodynamic equilibrium". However - the essential I extract from your post is your statement that "...there is a strong tendency to counteract climatic effects of CO2, but MEPP would not allow any change which would amplify it". In other words, you claim that there is only negative feedback, not positive feedback to a CO2 forcing. Sorry to say, the data proves this not to be the case. Feedback is positive, your assertion is quite simply not supportable. MEPP is either not a correct description or it does not have the effects you claim. You have been pointed to before, and have failed to address this issue with your MEPP claims. You keep saying that "degrees of freedom will override climate forcings to maintain the status quo", and that is observationally, patently not the case. As to your claim that the last 7 years disprove CO2 forcing, that would be cherry-picking - if this holds for 20-30 years, and acquires statistical significance, then we have something worth discussing.
  19. In my previous post, "degrees of freedom will override climate forcings to maintain the status quo" is not a quote, but rather my interpretation of a number of postings on this subject. My apologies - I don't mean to put words into other peoples mouths.
  20. damorbel, like CBDunkerson (his last three paragraphs), I am pleased to see your agreement that photons from a cooler source are indeed absorbed by a warmer target. So you agree that the greenhouse gas effect does not violate the second law of thermodynamics, which is the topic of this thread, right?
  21. #243 KR at 01:46 AM on 2 December, 2010 that would be cherry-picking If OHC is supposed to be the true indicator of global warming and we have only seven years of reliable OHC data, then it is not cherry-picking to use what we have, is it? What is more (and it is independent of MEPP), even if we assume heat is accumulating in the climate system on an annual rate of 1.45×1022 J, it takes more than 300 years to warm the ocean up by 1°C. It is clearly inconsistent with a 2+°C warming by the end of this century.
  22. Re #245 Tom Dayton, you wrote:- " I am pleased to see your agreement that photons from a cooler source are indeed absorbed by a warmer target" Tom they would be absorbed by any 'target'. But do you agree that they are absorbed by adjacent CO2 (H2O, CH4 etc.) more or less at the altitude where they are emitted? Or do they make it to the Earth's surface as 'backradiation', as in Trenberth's diagram? Further, do you think the cold photons raise the surface temperature 33K from 255K to 288K? And finally, what would be the average surface temperature without the H2O & CO2 etc.?
  23. damorbel #247: "Tom they would be absorbed by any 'target'." That's a yes. Ergo, global warming theory does not violate the second law of thermodynamics. Now you are just quibbling about the magnitude of the effect. Which, as various people have pointed out, is a measured fact. Heck, Fourier made a pretty good stab at estimating it nearly two hundred years ago when he discovered the temperature discrepancy and first proposed what we now call the greenhouse effect as a possible explanation.
  24. Re #240 Riccardo you wrote:- "any body may behave like a blackbody in a frequency range and not in others. In particular, the earth surface is very near a blackbody in the IR range of interest." Not so. IR is just a colour the same as red, yellow, green etc. and there is an albedo (reflection) in the IR also. The IR emissions from H20, CO2 etc. do not follow the smooth black body emission spectrum, instead the spectrum is highly irregular meaning that, for substantial parts of Earth's emission spectrum there is no radiation from the GHGs. Now you could argue that radiation from Earth 'fills in the gaps' but you will also have to explain why the material that reflects the sunlight to give Earth an albedo doesn't also reflect radiation originating in coming from Earth. There is no real 'one way' reflection effect, what you have for the ladies changing room is a cunning lighting effect that gives the impression of a 'one way' mirror. The cause of Earth's 30% albedo also causes a reflection of 30% (inwards) of the radiation coming out from the planet. That is why the temperature of a planet like Earth is independent of the albedo.
  25. Re #248 CBDunkerson you wrote:- "damorbel #247: "Tom they would be absorbed by any 'target'." That's a yes. Ergo, global warming theory does not violate the second law of thermodynamics." You are going too fast. Since emitting (GH) gases absorb also there is no chance that any imbalance in thermal energy transfer will arise as described by 'back radiation' (i.e. W/m^2, J/s/m^2) as claimed by Trenberth. Not just 'insufficient' to cause 33K increase in surface temperature but none at all., the thermal energy transfer is going from the surface to the troposphere, cooling the surface as it goes. You must realise that with a full transparent atmosphere (no GHGs) the cooling radiation would all come from the surface, so what's the big deal? The surface would have just the same temperature it has now.

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