Arguments
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)
At a glance
Although this topic may have a highly technical feel to it, thermodynamics is a big part of all our everyday lives. So while you are reading, do remember that there are glossary entries available for all thinly underlined terms - just hover your mouse cursor over them for the entry to appear.
Thermodynamics is the branch of physics that describes how energy interacts within systems. That interaction determines, for example, how we stay cosy or freeze to death. You wear less clothing in very hot weather and layer-up or add extra blankets to your bed when it's cold because such things control how energy interacts with your own body and therefore your degree of comfort and, in extreme cases, safety.
The human body and its surroundings and energy transfer between them make up one such system with which we are all familiar. But let's go a lot bigger here and think about heat energy and its transfer between the Sun, Earth's land/ocean surfaces, the atmosphere and the cosmos.
Sunshine hits the top of our atmosphere and some of it makes it down to the surface, where it heats up the ground and the oceans alike. These in turn give off heat in the form of invisible but warming infra-red radiation. But you can see the effects of that radiation - think of the heat-shimmer you see over a tarmac road-surface on a hot sunny day.
A proportion of that radiation goes back up through the atmosphere and escapes to space. But another proportion of it is absorbed by greenhouse gas molecules, such as water vapour, carbon dioxide and methane. Heating up themselves, those molecules then re-emit that heat energy in all directions including downwards. Due to the greenhouse effect, the total loss of that outgoing radiation is avoided and the cooling of Earth's surface is thereby inhibited. Without that extra blanket, Earth's average temperature would be more than thirty degrees Celsius cooler than is currently the case.
That's all in accordance with the laws of Thermodynamics. The First Law of Thermodynamics states that the total energy of an isolated system is constant - while energy can be transformed from one form to another it can be neither created nor destroyed. The Second Law does not state that the only flow of energy is from hot to cold - but instead that the net sum of the energy flows will be from hot to cold. That qualifier term, 'net', is the important one here. The Earth alone is not a "closed system", but is part of a constant, net energy flow from the Sun, to Earth and back out to space. Greenhouse gases simply inhibit part of that net flow, by returning some of the outgoing energy back towards Earth's surface.
The myth that the greenhouse effect is contrary to the second law of thermodynamics is mostly based on a very long 2009 paper by two German scientists (not climate scientists), Gerlich and Tscheuschner (G&T). In its title, the paper claimed to take down the theory that heat being trapped by our atmosphere keeps us warm. That's a huge claim to make – akin to stating there is no gravity.
The G&T paper has been the subject of many detailed rebuttals over the years since its publication. That's because one thing that makes the scientific community sit up and take notice is when something making big claims is published but which is so blatantly incorrect. To fully deal with every mistake contained in the paper, this rebuttal would have to be thousands of words long. A shorter riposte, posted in a discussion on the topic at the Quora website, was as follows: “...I might add that if G&T were correct they used dozens of rambling pages to prove that blankets can’t keep you warm at night."
If the Second Law of Thermodynamics is true - something we can safely assume – then, “blankets can’t keep you warm at night”, must be false. And - as you'll know from your own experiences - that is of course the case!
Please use this form to provide feedback about this new "At a glance" section. Read a more technical version below or dig deeper via the tabs above!
Further details
Among the junk-science themes promoted by climate science deniers is the claim that the explanation for global warming contradicts the second law of thermodynamics. Does it? Of course not (Halpern et al. 2010), but let's explore. Firstly, we need to know how thermal energy transfer works with particular regard to Earth's atmosphere. Then, we need to know what the second law of thermodynamics is, and how it applies to global warming.
Thermal energy is transferred through systems in five main ways: conduction, convection, advection, latent heat and, last but not least, radiation. We'll take them one by one.
Conduction is important in some solids – think of how a cold metal spoon placed in a pot of boiling water can become too hot to touch. In many fluids and gases, conduction is much less important. There are a few exceptions, such as mercury, a metal whose melting point is so low it exists as a liquid above -38 degrees Celsius, making it a handy temperature-marker in thermometers. But air's thermal conductivity is so low we can more or less count it out from this discussion.
Convection
Figure 1: Severe thunderstorm developing over the Welsh countryside one evening in August 2020. This excellent example of convection had strong enough updraughts to produce hail up to 2.5 cm in diameter. (Source: John Mason)
Hot air rises – that's why hot air balloons work, because warm air is less dense than its colder surroundings, making the artificially heated air in the balloon more buoyant and thereby creating a convective current. The same principle applies in nature: convection is the upward transfer of heat in a fluid or a gas.
Convection is highly important in Earth's atmosphere and especially in its lower part, where most of our weather goes on. On a nice day, convection may be noticed as birds soar and spiral upwards on thermals, gaining height with the help of that rising warm air-current. On other days, mass-ascent of warm, moist air can result in any type of convective weather from showers to severe thunderstorms with their attendant hazards. In the most extreme examples like supercells, that convective ascent or updraught can reach speeds getting on for a hundred miles per hour. Such powerful convective currents can keep hailstones held high in the storm-cloud for long enough to grow to golfball size or larger.
Advection
Advection is the quasi-horizontal transport of a fluid or gas with its attendant properties. Here are a couple of examples. In the Northern Hemisphere, southerly winds bring mild to warm air from the tropics northwards. During the rapid transition from a cold spell to a warm southerly over Europe in early December 2022, the temperatures over parts of the UK leapt from around -10C to +14C in one weekend, due to warm air advection. Advection can also lead to certain specific phenomena such as sea-fogs – when warm air inland is transported over the surrounding cold seas, causing rapid condensation of water vapour near the air-sea interface.
Figure 2: Advection fog completely obscures Cardigan Bay, off the west coast of Wales, on an April afternoon in 2015, Air warmed over the land was advected seawards, where its moisture promptly condensed over the much colder sea surface.
Latent heat
Latent heat is the thermal energy released or absorbed during a substance's transition from solid to liquid, liquid to vapour or vice-versa. To fuse, or melt, a solid or to boil a liquid, it is necessary to add thermal energy to a system, whereas when a vapour condenses or a liquid freezes, energy is released. The amount of energy involved varies from one substance to another: to melt iron you need a furnace but with an ice cube you only need to leave it at room-temperature for a while. Such variations from one substance to another are expressed as specific latent heats of fusion or vapourisation, measured in amount of energy (KiloJoules) per kilogram. In the case of Earth's atmosphere, the only substance of major importance with regard to latent heat is water, because at the range of temperatures present, it's the only component that is both abundant and constantly transitioning between solid, liquid and vapour phases.
Radiation
Radiation is the transfer of energy as electromagnetic rays, emitted by any heated surface. Electromagnetic radiation runs from long-wave - radio waves, microwaves, infra-red (IR), through the visible-light spectrum, down to short-wave – ultra-violet (UV), x-rays and gamma-rays. Although you cannot see IR radiation, you can feel it warming you when you sit by a fire. Indeed, the visible part of the spectrum used to be called “luminous heat” and the invisible IR radiation “non-luminous heat”, back in the 1800s when such things were slowly being figured-out.
Sunshine is an example of radiation. Unlike conduction and convection, radiation has the distinction of being able to travel from its source straight through the vacuum of space. Thus, Solar radiation travels through that vacuum for some 150 million kilometres, to reach our planet at a near-constant rate. Some Solar radiation, especially short-wave UV light, is absorbed by our atmosphere. Some is reflected straight back to space by cloud-tops. The rest makes it all the way down to the ground, where it is reflected from lighter surfaces or absorbed by darker ones. That's why black tarmac road surfaces can heat up until they melt on a bright summer's day.
Figure 3: Heat haze above a warmed road-surface, Lincoln Way in San Francisco, California. May 2007. Image: Wikimedia Commons.
Energy balance
What has all of the above got to do with global warming? Well, through its radiation-flux, the Sun heats the atmosphere, the surfaces of land and oceans. The surfaces heated by solar radiation in turn emit infrared radiation, some of which can escape directly into space, but some of which is absorbed by the greenhouse gases in the atmosphere, mostly carbon dioxide, water vapour, and methane. Greenhouse gases not only slow down the loss of energy from the surface, but also re-radiate that energy, some of which is directed back down towards the surface, increasing the surface temperature and increasing how much energy is radiated from the surface. Overall, this process leads to a state where the surface is warmer than it would be in the absence of an atmosphere with greenhouse gases. On average, the amount of energy radiated back into space matches the amount of energy being received from the Sun, but there's a slight imbalance that we'll come to.
If this system was severely out of balance either way, the planet would have either frozen or overheated millions of years ago. Instead the planet's climate is (or at least was) stable, broadly speaking. Its temperatures generally stay within bounds that allow life to thrive. It's all about energy balance. Figure 4 shows the numbers.
Figure 4: Schematic representation of the global mean energy budget of the Earth (upper panel), and its equivalent without considerations of cloud effects (lower panel). Numbers indicate best estimates for the magnitudes of the globally averaged energy balance components in W m–2 together with their uncertainty ranges in parentheses (5–95% confidence range), representing climate conditions at the beginning of the 21st century. Figure adapted for IPCC AR6 WG1 Chapter 7, from Wild et al. (2015).
While the flow in and out of our atmosphere from or to space is essentially the same, the atmosphere is inhibiting the cooling of the Earth, storing that energy mostly near its surface. If it were simply a case of sunshine straight in, infra-red straight back out, which would occur if the atmosphere was transparent to infra-red (it isn't) – or indeed if there was no atmosphere, Earth would have a similar temperature-range to the essentially airless Moon. On the Lunar equator, daytime heating can raise the temperature to a searing 120OC, but unimpeded radiative cooling means that at night, it gets down to around -130OC. No atmosphere as such, no greenhouse effect.
Clearly, the concentrations of greenhouse gases determine their energy storage capacity and therefore the greenhouse effect's strength. This is particularly the case for those gases that are non-condensing at atmospheric temperatures. Of those non-condensing gases, carbon dioxide is the most important. Because it only exists as vapour, the main way it is removed is as a weak solution of carbonic acid in rainwater – indeed the old name for carbon dioxide was 'carbonic acid gas'. That means once it's up there, it has a long 'atmospheric residency', meaning it takes a long time to be removed.
Earth’s temperature can be stable over long periods of time, but to make that possible, incoming energy and outgoing energy have to be exactly the same, in a state of balance known as ‘radiative equilibrium’. That equilibrium can be disturbed by changing the forcing caused by any components of the system. Thus, for example, as the concentration of carbon dioxide has fluctuated over geological time, mostly on gradual time-scales but in some cases abruptly, so has the planet's energy storage capacity. Such fluctuations have in turn determined Earth's climate state, Hothouse or Icehouse – the latter defined as having Polar ice-caps present, of whatever size. Currently, Earth’s energy budget imbalance averages out at just under +1 watt per square metre - that’s global warming.
That's all in accordance with the laws of Thermodynamics. The First Law of Thermodynamics states that the total energy of an isolated system is constant - while energy can be transformed from one component to another it can be neither created nor destroyed. Self-evidently, the "isolated" part of the law must require that the sun and the cosmos be included. They are both components of the system: without the Sun as the prime energy generator, Earth would be frozen and lifeless; with the Sun but without Earth's emitted energy dispersing out into space, the planet would cook, Just thinking about Earth's surface and atmosphere in isolation is to ignore two of this system's most important components.
The Second Law of Thermodynamics does not state that the only flow of energy is from hot to cold - but instead that the net sum of the energy flows will be from hot to cold. To reiterate, the qualifier term, 'net', is the important one here. In the case of the Earth-Sun system, it is again necessary to consider all of the components and their interactions: the sunshine, the warmed surface giving off IR radiation into the cooler atmosphere, the greenhouse gases re-emitting that radiation in all directions and finally the radiation emitted from the top of our atmosphere, to disperse out into the cold depths of space. That energy is not destroyed – it just disperses in all directions into the cold vastness out there. Some of it even heads towards the Sun too - since infra-red radiation has no way of determining that it is heading towards a much hotter body than the Earth,
Earth’s energy budget makes sure that all portions of the system are accounted for and this is routinely done in climate models. No violations exist. Greenhouse gases return some of the energy back towards Earth's surface but the net flow is still out into space. John Tyndall, in a lecture to the Royal Institution in 1859, recognised this. He said:
As long as carbon emissions continue to rise, so will that planetary energy imbalance. Therefore, the only way to take the situation back towards stability is to reduce those emissions.
Update June 2023:
For additional links to relevant blog posts, please look at the "Further Reading" box, below.
Last updated on 29 June 2023 by John Mason. View Archives
I want to post here my admiration of the persistence of those who have kept up with almost 1000 posts rebutting a rather obviously flawed argument, that starts from failing to observe that you can’t apply the 2nd law of thermodynamics unless you have a closed system. There is a continuous influx of energy from the sun, so the ground and atmosphere aren’t a closed system. Case closed.
If Gerlich really is physics professor at an apparently good university who has real students, they should demand a refund if this is the quality of his understanding.
BTW there are a few dead links in the Notes:
This is a good post, but I would like to believe that a lot of the thrashing in the discussions attached to it could have been avoided if Skeptical Science would edit the article to make the correction already suggested by post#955: the citation of the Clausius formulation of the Second Law is incorrect.
Far better would be to use Clausius's own translation of his statement of the law: "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time."
One of the immediate advantages of this formulation is that it immediately enables us to put the burden on the "believers in the imaginary Second Law" to show that there are no "other changes" that allow the transfer of heat from the cold atmophere to the warm earth.
Certainly, the 'generally' of the version currently in the article is terribly confusing. What is 'generally' supposed to mean in the statement of a physical law? Would Newton ever have said "to each and every action there is generally an equal and opposite reaction"? Of course not.
At least when Clausis said "other changes", we know he was speaking in the context of heat engines, so we know he meant changes in thermodynamic state, whether of the heat engine or in the surrounding environment. We do not know anything of the sort for 'generally'.
Alternatively, several great physicists of more recent times, so in reference to the more complete theory of thermodynamics they themselves developed, have given formulations that might even prove more useful, e.g.:
Wolfgang Pauli: Clausius says that heat conduction is an irreversible
process — a process is called irreversible if the initial state
cannot be reached from the final state without compensation
Enrico Fermi: it is impossible to have a process whose SOLE effect is
the transfer of heat from a colder to a hotter body
Richard Feynman: Carnot asserted that at constant temperature it is
impossible to extract heat out of its source and turn it into work,
without producing other changes in the given system or its surrounding
environment.
Please consider these also, but at the very least, correct the Clausius quote: it can only cause unnecessary confusion, as people are still referring to this article.
MattJ I think you are missing the key point which is that the net transfer of heat is from the warmer surface to the cooler atmosphere, so the second law of thermodynamics holds whether there is "some other change" or not. If you lie under a blanket, the blanket keeps you warmer than you would otherwise be, even though the blanket (and the air beneath it) is cooler than you are. This does not require "some other change" in the blanket (or air beneath it) and does not contravene the second law of thermodynamics.
Dikran-
No, I am not missing that point. I am addressing the point you implicitly get wrong when you say (in #1428) that "the second law of thermodynamics holds whether there is 'some other change' or not".
The clause "whether there is 'some other change' or not" is invalid. The Second Law holds, period. But the Second Law does not say that heat, whether 'net' or not (it does not make the distinction) can never flow from colder to hotter.
It does no good to quote the Second Law incorrectly, and then say, "it does not contravene the second law of thermodynamics". As long as you allow the "imaginary second law" to maintain a hold on the reader's mind, especially on the 'skeptical' reader, he will still keep coming back to the imaginary form and say, "but, but, heat cannot flow from cooler to hotter", even after you explain to him that you are really talking about "net transfer of heat from the warmer surface to the cooler atmosphere", since you are still requiring radiating CO2 molecules in a -20C stratosphere to heat up an ocean layer that is on average above +20C (these numbers are off the top of my head and approximate, but you get the idea: the source of the radiation is much colder than the warmed sea surface: it is still a violation of the "imaginary second law", but not of the law as Clausius really stated it).
But if you understand that the second law forbids heat transfer from colder to hotter only as the sole result of a thermodynamic process, then the "imaginary second law" loses its hold, since now the skeptic has to show there is no other result before he can claim "it violates the second law". He can't do that, since the laws of heat radiation invoked to explain backradiation warming of the ocean are derived in accordance with Clausius's statement of the 2nd law.
[Rob P] - allcaps edited. If you must place emphasis on a word or text use the bold format.
MattJ wrote "since you are still requiring radiating CO2 molecules in a -20C stratosphere to heat up an ocean layer that is on average above +20C"
This is incorrect, this is not what is required for the enhanced greenhouse effect to cause the surface to be warmer than it would be in the absence of greenhouse gasses in the atmosphere. Nor does a blanket that is slightly cooler "heat up" a warmer body that is under the blanket. You need to understand the problem first, before seeing how the second law applies.
Consider two black body objects A and B, in a vacuum, where object A is marginally warmer than object B. Do you agree that object B will emit IR photons that will be absorbed by A? "Yes" or "No". If "No" please explain why.
Dirkan-
Please read what I actually wrote and respond to that instead of rebutting a climate-denial argument I never used or supported. I am not talking about nor implying that "a blanket heat up a warmer body that is under the blanket". Unlike certain denialists, I understand that the heat transfers in the blanket example are all from higher temperature to lower, so that there is no need to invoke the "without some other change" clause in Clausius's statement of it. Nor do I doubt that in your black body example, both objects emit photons absorbed by the other.
I thought I made that clear when I said that " it [radiative heat transfer from cooler to hotter] is still a violation of the "imaginary second law", but not of the law as Clausius really stated it".
Rather, the point I am trying to make is that different from that. Actually, I am trying to make three points: 1) the statement of the Second Law attributed to Clausius in the article is incorrect: it is not what Clausius said, nor is it even correct 2) you simply cannot build a correct scientific explanation/argument on an incorrect version of one of the fundamental laws 3) partly because of this mis-statement, the article has <b>not</b> explained why the cold CO2 in the stratosphere can transfer heat to the warmer earth and ocean surface without violating the Second Law.
There was a good article on ScienceOfDoom that I always have trouble findiing when I look for it, it did explain why this transfer can take place — but only by referring to Kirchoff's Law and the Stefan-Boltzmann Law, pointing out that since these law were themselves derived from the Second Law, the results must be consistent with it.
This approach is sound, it is correct, but it is awfully indirect. And it too relied on getting the statement of the Second Law correct, which this Skeptical Science article does NOT do.
That is why I say that as a bare minimum, the article should correct the Clausisus quote and state the Second Law correctly. But it would be so much better if in addition to this, it can directly state what the "some other change" is when cold GHGs manage to transfer heat to the warmer thin surface layer of the ocean.
MattJ wrote"Please read what I actually wrote"
I did, you wrote "since you are still requiring radiating CO2 molecules in a -20C stratosphere to heat up an ocean layer that is on average above +20C" and I pointed out that is not the case. A blanket is just a useful metaphor I introduced to illustrate why that is not necessarily the case. Now it seems the fastest way to reach agreement is by consideration of the thought experiment.
Now you agree that body B emits photons that are absorbed by A. Do you agree that this photon takes away some energy from B and adds it to A? yes or no, if no, explain why.
Dikran-
Yes, you did "point out that is not the case", but then you immediately switched to talking about something else, the several heat transfers that <b>are</b> in the direction of decreasing temperature, without addressing the real issue. That is why I asked you to "read what I actually wrote".
Nor are you addressing the issue by asking about photons. The question is not "do photons take energy away from B and add it to A". The question is how this can happen without violating the Second Law. You should have not even asked the question not only for this reason, but because I already made it clear that I do undestand that the energy transfer you refer to is real. But simply acknowledging that it takes place does not address the issue: how can it take place without violating the Second Law?
MattJ wrote "but then you immediately switched to talking about something else" no, as I said it was a metaphor to help you to understand the issue. It is a shame that you did not engage with it.
"Nor are you addressing the issue by asking about photons" you assume you understand the point I was making, which evidently you do not. The fact that you refuse to answer the question suggests to me that you are not willing to have your argument put to the test, and therefore should not be surprised if you are not taken seriously.
As it happens, for radiative transfer, it is exactly what happens to the photons and energy they carry that is important.
I am always amazed how rare it is in discussions of climate change for people to be willing to answer simple direct questions and will go to such great lengths to avoid doing so!
Dikran-
Also, simply answering "since you are still requiring radiating CO2 molecules in a -20C stratosphere to heat up an ocean layer that is on average above +20C" with "I pointed out this is not the case is not helpful. Which part of it do you disagree with? Are you going to claim there is no LWIR coming from the stratosphere? Or that the stratosphere is warmer than the ocean surface? Even if the backradiation were mostly coming from the troposphere, it would still be going from cooler to warmer, yet transfering heat to the warmer ocean surface. The only difference is that the temperature difference is not as dramatic. But it is still there, and with the inconvenient sign.
Now glancing back through the comments on this article, I noticed some tried to explain this by saying that the Second Law applies only to a closed system, or to "net heat". But Clausius never made a distinction between 'heat' and "net heat". And in the statement of the Second Law itself, he does not state any restriction to "closed systems" (but since he was speaking in the context of heat engines, one can make a case for that). So one must either prove that Clausius's statement either appies only to closed systems, generalizes to "net heat" or use a more modern form of the Second Law that is already known to apply to "net heat". Or take the Science of Doom approach, which as I already mentioned, works, but is awfully indirect; it is difficult to use in discussion with laymen or skeptics because of the long winding path through Kirchoff and Stefan-Boltzmann.
But this Skeptical Science article takes none of these routes; it doesn't even get the statement of the Second Law correct. That is a serious shortcoming.
[JH] You are now skating on the thin ice of escessive repetition which is prohibited by the SkS Comments Policy. Please read the policy and adhere to it.
Dikran Marsupial @1434.
You might find the comment @1435 a bit odd as you are, I think, confused by the comment @1433. The implication you make from the beginning of the final paragraph is contrary to the less ambiguous statements later in that paragraph. "...I already made it clear that I do undestand that the energy transfer you refer to is real. But simply acknowledging that it takes place does not address the issue: how can it take place without violating the Second Law?"
MattJ is saying that photons do really pass from B to A but in so doing the 2nd Law of Thermodynamics is violated and this phenomenon thus requires explanation.
Goodness!! It appears the 2nd Law of Thermodynamics is breached!!!
MA Roger, the point I was heading towards was that if photons from B that are abosorbed by A do transfer heat energy from a cooler object to a warmer one, then for MattJ's interpretation of the second law to be obeyed, there must be "some other change, connected therewith, occurring at the same time" and I was going to ask what it was.
Of course if you adopt the modern statistical intepretation, there is no need to find the "some other change" as the second law only applies to the net transfer of heat, and there is no problem. The reason why we don't need to explain why it doesn't violate the second law of thermodynamics is because it is not precluded by more modern interpretations of the second law in the first place.
I suspect the problem is that Clausius would have been easily able to measure temperatures of objects (and hence the net transfer), but how would he be able to detect the fact that the radiation is bi-directional between the objects? Not too surprising then that he didn't make the distinction between transfer of heat and net transfer.
The funny thing is the Science of Doom page gives exactly the same definition of Clausius' second law as the SkS page does.
Anyway, MattJ has exhausted my patience, some people are fundamentally unable to see any point of view other than their own, and being unwilling to engage in a thought experiment designed to highlight where the disagreement lies suggests that they don't want to see any point of view other than their own. This is a pity, as if MattJ were right, it would be the most efficient way of demonstrating it.
MattJ's original request:
is adequetly met by the word "spontaneously" in the OP version.
In this I think you are naive; G&T's misformulation was too attractive for climate change deniers to resist, and they have continued to try and make it stick no matter how the 2nd Law was formulated.
My own observation on the ensuing exchanges is that MattJ appears terribly confused about the distinction between energy and heat transfer; he should get that straight first.
MattJ, the exceptions that Clausius allows for with his clause "without some other change, connected therewith, occurring at the same time" covers situations such as those found in refridgerators, in which heat is pumped from a colder interior to a warmer exterior, but only at the expense of pumping additional heat from a still warmer furnace (via power generation) to drive the process with a net increase in entropy for the entire process. What you are missing is that the "warming" of the Earth by greenhouse gases is not analogous to that case. Rather, it is analogous to the far simpler case of decreasing the efficiency of heat transfer outwards from a body warmed by a still warmer source. Therefore, the exception is not involved. Including a more explicit statement of the exception (more explicit because it is mentioned in the OP as noted by Phil) would therefore in no way help decrease scientific confusion about the greenhouse effect and thermodynamics. Rather, trying to explain the greenhouse effect by analogy to refrigerators will increase that confusion.
Hi, Tom-
Thanks for your reply. For sure, Clausius was including such systems as you describe as "without some other change, connected therewith, occuring at the same time". He was even thinking primarily if not entirely of such systems. But how can we be sure that those are the only such changes he had in mind? I had the impression, based on discussions of the Second Law and its various forms in thermodynamics texts by Fermi, Feynman, Pauli and others, that the law, even in Clausius's form of it, covers a more general class of 'changes'. Thus, for example, Pauli paraphrases it as being equivalent to saying "heat conduction is irreversible". But the concepts of irreversibility and reversibility are more general than providing heat or work from outside, as in your refrigerator example. If when you go around the cycle, some thermodynamic variable must be different from the beginning when you get back, the process is irreversible, a change has occurred. It is not just the two thermodynamic variable heat and work that are under consideration.
I also have to point out that I am not assuming "that the 'warming' of the Earth by greenhouse gases is analogous to the refrigerator case." Rather, I am pointing out that even when you say that it is based on "the far simpler case of decreasing the efficiency of heat transfer outwards from a body warmed by a still warmer source", you are still leaving something out.
That is, sure, once one understands that backwave radiation occurs resulting in IR being absorbed and turned into heat, yes, the hottest point is the sun itself, and all the other surfaces heat moves to are colder than that. But there is still the case of the cold atmosphere transfering heat to the warm surface to accomplish that "decrease of efficiency of transfer". Explaining that event's consistency with the Second Law is what is left out.
Let me try to put that another way: sure in the overall system, all the heat comes from the sun with the heat/temperature of the earth depending on both how quickly heat comes in and how quickly it goes out, so that slowing the rate of outflow raises the temperature. But to explain how this happens involves explaining how the hotter ocean surface can be heated by the cooler atmosphere, an <b>apparent</b> violation of the Second Law: this article 'explains' it only be getting the Second Law wrong, so that it really hasn't explained anything relevant.
If you really think Clausius' statement was meant to apply only in the context of heat engines and closed cycles, then it is useless to use his statement of the Second Law in this article, since, as you yourself point out, the analogy of a refrigerator (a heat engine of a particular sort) and the climate system is not very good, and can be quite misleading. The article should then use a completely different formulation, one that has been proved to generalize to the climate system, such as "in an isolated system, entropy is non-decreasing". But this particular option has its own difficulties, I think I understand why the author chose not to use it.
Finally, concerning Phil's point. Yes, it was mentioned, but only later, and the author did not even seem to notice that he was contradicting himself, putting an unnecessary burden on the reader to resolve the contradiction, all still without a clear and correct statement of the law. Good expository prose does not do this: you get the statement exactly right the first time, and then explain as necessary the technical or otherwise surprising sense of the expressions used. Or you use a special case as a stepping stone to the final, full generalization. But even the appearance of self-contradiction defeats the purpose of the article — and creates a lot of room for the quibbling and carping we saw in 1400 posts.
Not to mention there is still this crippling problem of the word 'generally' being used in the alleged statement of Clausius' form: no law of physics has such weasel words as 'generally', that makes the 'law' useless for generalization. No wonder Clausius himself never said that!
MattJ @1440:
But the cold atmosphere does not warm the warmer ocean, and nor is their any apparent violation of the second law. The second law, stated mathematically is that for a closed system:
ΔS ≥ ∫δQ/T
where S is the entropy, δQ is the incremental transfer of heat, and T is the temperature.
Therefore to determine the entropy change we need to integrate over all incremental heat transfers. In the case of the relationship between atmosphere and surface under the greenhouse effect, we need to integrate over all energy transfers between atmosphere and surface. From the Fasullo and Trenberth, we have this summary of those transfers:
Summing over all such transfers, we find that 356+80+17 = 453 W/M^2 is transfered from the surface to the atmosphere, while only 333 W/m^2 is transfered trom the atmosphere to the surface. Integrated over all energy transfers from between surface and atmosphere, that is a net transfer of +120 W/m^2 from the warmer surface to the cooler atmosphere. That transfer involves in increase in entropy proportional to the inverse of the reduction of temperature involved, ie, proportional ratio of surface to atmospheric temperatures.
There is only an "appearance" of a violation of the 2nd law because people insist on considering the back radiation in complete isolation, ie, not as part of a system of transfers including those from the surface to the atmosphere. If you intergrate all such transfers, as is required by the 2nd law, there is transparently no violation of the 2nd law involved.
And there's your answer as to why the greenhouse effect doesn't violate the 2nd Law, Matt. You have to include the Sun's continuing contribution of energy. If you don't everything else seems to violate the 2nd Law.
Re 1441: Not that awful Trenberth diagram again! Sure, I know the diagram is correct, but people who are climate scientists simply have no idea how confusing it is to people who are not familiar with it. It looks like lots of things should add up that don't.
But you say one has to do the integration — but then you don't do it. You are doing a sum of watt/m2, which is not even the right units for entropy. Nor are you doing the sum over a cycle/process, which is what the expression you gave for delta S requires.
But rather than ask for that integration, what I think you really need, so what I will ask for is a clarification of the grounds of your assertion that "But the cold atmosphere does not warm the warmer ocean, and nor is their any apparent violation of the second law." That there is an apparent violation is pretty clear, since lots of people find it apparent. But more important: when you say, "the cold atmosphere does not warm the warmer ocean" what do you think happens to the IR photons from CO2 high in the cold stratosphere when they meet the surface of the earth or of the ocean? Aren't they almost entirely absorbed? And once absorbed, isn't all their energy converted to heat? How could these steps be anything other than "the cold atmosphere warming the warm ocean?
At this point, I think Robert Murphy is a lot closer to answering my question. I have suspected it has a lot to do with the low entropy energy input from the sun driving the whole process, but even this leaves unanswered questions.
In particular, if we follow a more modern statement than Clausius's (an idea I have been mentioning for a while), then the increasing wavelength of each of these stages of radiative transfer each shows an increase in entropy, so that entropy is non-decreasing, as the second law requires. It is even still non-decreasing in the case of cold stratosphereic CO2 adding heat energy to the thin but warmer surface layer on the ocean.
It is much harder to make the same argument from Clausius's form, especially when the author does not even state his form correctly. Clausius NEVER said "Heat <b>generally</b> cannot flow spontaneously".
MattJ @1443, the formula for the Clausius inequality is:
That only applies to cyclical processes, and is integrated over the cycle. You will notice the variant integration symbol used to indicate that fact.
The formula, ΔS ≥ ∫δQ/T, which I gave above is for any closed system, and uses a conventional integration. That is, it sums over all energy transfers in the region under consideration, and for the time under consideration.
The Fasullo and Trenberth diagram provides us with total average energy flows per unit time. From that we can integrate over area and time if we want to, but the result will be the same as simply summing over the power flows in showing that the 2nd law is not violated by the exchange of energy between surface and atmosphere.
Importantly for this discussion, this is shown without bringing in extraneous factors like the energy input from the Sun, or the energy outflow to space. In fact, we can model a genuinely closed surface/atmosphere system and the principles involved in the energy exchanges will be the same. The actual values integrated will not be, for the energy flows will change over time as the surface and atmosphere equalize in temperature. Such a process would involve every means of energy exchange that actually exists in the atmosphere, including back radiation, and would result in a net increase in entropy. Further, the surface would cool over time while the atmosphere warms over time. It follows that back radiation does not violate the 2nd law of thermodynamics, and that neither does it warm the surface.
We can extend this model by opening it to space, and compare to situations, ie, one with an atmosphere containing greenhouse gases, and one without. If we do so we can show that the surface in the case with the atmosphere will cool slower than the surface without an atmosphere. However, it will still cool so there will be no question of any violation of the 2nd law of thermodynamics or the atmosphere warming the surface.
Finally, we can add in the Sun and find an equilibrium situation. In that case, the surface equilibrium will be warmer with the atmosphere than without. That, however, is because the slower rate of cooling for a given surface temperature with an atmosphere requires a warmer surface temperature for the outgoing radiation to match in energy the incoming energy from the Sun. Thus, in this case, it is true to say that the surface is warmer than it would have been without the greenhouse gases, but it is the Sun that warms the surface, not atmosphere.
We might say colloquially that the greenhouse gases warmed the surface, just as we might say colloquially that a blanket warms us at night. In both cases, however, it is strictly inaccurate. A blanket will not "warm" a cold stone, and greenhouse gases will not "warm" in the absense of the incoming solar radiation because they do not warm at all, they merely slow the loss of heat.
You comment:
No. I do not mistake the net flow of heat with the individual flows of energy. Nor am I unaware that in the superior formulation of statistical thermdynamics the 2nd law holds only on average, and that the shorter the time interval the higher the probability that it is violated for that short term. Thus, there are IR photons from the atmosphere that strike the ocean and transfer energy, but there are more IR photons from the ocean that do the reverse so that the the net heat flow is from ocean to atmosphere (and hence it is the ocean warming the atmosphere rather than the reverse).
Finally:
The wavelength of IR radiation exchanged between atmosphere and surface is approximately the same for any specific atmospheric component, but the difference in wavelength between incoming SW radiation and outgoing IR radiation does indeed show the process to involve an increase in entropy, and to not violate the 2nd law of thermodynamics.
MattJ:
I'm sorry, but I cannot understand this point; the OP correctly formulates the 2nd Law using the word "spontaneously" to indicate that exceptions to the flow of heat require "work". It does so in the 3rd paragraph, not "only later". I would suggest that you actually re-read the OP.
I would re-iterate the my point, that you seem to be having great trouble distinguished heat from energy flows. Dikran tried to help you with this, but you refused to let him, Tom is having another attempt; but fundamentally your remarks show that you know less about the physics of the greenhouse effect than you think you do.
O.K., well I thought I'd go and look up Clausius' statement, and I found a translation of his works here:
"The Mechanical Theory of Heat, with its Application to the Steam Engine, and to the Physical Properties of Bodies", by R. Clausius, Translated by John Tyndall, Edited by T Archer Hurst, 1867 (available via Google books)
Yes, it was indeed that John Tyndall!
Clausius' statement of the second law mentioned by MattJ can be found on page 117, and has an interesting footnote, which I have reproduced below:
The footnote makes it very clear that I was wrong in that Tyndall, and I presume also Clausius (as he has an author's preface published in the volume) were well aware that there is a bidirectional transfer of heat between two bodies of different temperatures:
However, it is in complete agreement with what I wrote about the second law applying only to the net flow of heat,
and thus the greenhouse effect does not violate the second law of thermodynamics because the surface imparts more radiation to the upper trophosphere than in receives in back radiation. In Tyndall's terms it is fully compensated.
Update: It seems unclear whether the translation was by Tyndall or Hirst, or possibly a bit of both as Tyndall translated the original papers and apparently worked with Hirst. Tyndall certainly wrote the introduction. However the central point remains as Clausius obviously approved the translation.
Very interesting. This formulation makes the G&T paper completely moot. Their entire demonstration relies on faulty interpretation of the law.
PhilippeChantreau indeed, but it is still able to generate a thread of 1448 comments! ;o)
I really don't understand why there is so much skeptic [sic] interest in the very weakest skeptic [sic] arguments, such as this one, and the idea that the rise in CO2 is natural, where in both cases a bit of common sense is all that is required.
Re #1448 Dikran says, "I really don't understand why there is so much skeptic [sic] interest in the very weakest skeptic [sic] arguments, such as this one, and the idea that the rise in CO2 is natural, where in both cases a bit of common sense is all that is required."
Well, look at how long it took for you to recognize that I was right, my quote of Clausius is correct (in #1446), the author's version is not. That alone should show you that it does take more than just "common sense". When you put forth an alleged scientific explanation that can't even quote the Second Law correctly, you should expect enough dispute to generate a 1448 comment thread. By starting out with such a blunder, you make the weak skeptic's argument look much stronger than it actually is.
Re #1445
No, Phil, he does NOT "get it right". Nor am I the first to point out this error. It was pointed out long ago (#955), yet nothing was done about it.
What the article actually says is: "Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."
Do you see the difference now between what you said and what the article actually says? If, as you say, he had only used the word 'spontaneously', you would be correct. But he also put in the word 'generally', making it useless as a physical law.
But there is another problem which I also pointed out: the wording, despite what the article claims, is NOT even from Clausius. Yet the article presents this as his own words.