Arguments
The greenhouse effect and the 2nd law of thermodynamics
What the science says...
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The 2nd law of thermodynamics is consistent with the greenhouse effect which is directly observed. |
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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
#1436 "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."
This is what I find distressing about SkS: many people here get on their high horses in defense of science — yet show they cannot even read well enough to do it. At no time did I say the 2nd Law is actually violated. On the contrary: I explained many times that I see only an appearance of violation, and that I know from the derivation of Kirchoff's and Stefan-Boltzmann radiation laws that it is not violated.
Why, I repeated this so many times that a moderator accused me of "excessive repetition". But what else am I to do with responses that either misread what I wrote or ignore what I already said?
MattJ wrote "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."
No, the version given in the article is perfectly adequate as the greenhouse effect does not require "some other change, connected therewith, occurring at the same time" because the back-radiation is already compensated by the upwelling IR from the surface. The definition given in the article is also merely a rephrasing of the version given in the foot note. It isn't wrong, the difference between the two definitions is irrelevant in this particular case, so insisting on it is ridiculous pedantry.
""Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."
is an equivalent statement to
"Heat cannot of itself pass from a colder to a warmer body"
which appears in Clausius' textbook. Note this phrase is translated from Clausius as the footnote gives the German wording of "of itself". "Spontaneously" is a perfectly reasonable synonym for "of itself" in this context, and the "generally" refers to the possibility of there being "some other change...", which happens not to be relevant in this case.
Please stop digging.
MattJ "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."
Given that Clausius did not appear to have published anything himself in English, to suggest that the article presents anything as his words is utter nonsense.
There is also the point that the statement in the book may not be the only one he made, if anyone can track down the translations of his papers, or the translation of the second edition of his textbook, you may well find them there.
MattJ wrote "At no time did I say the 2nd Law is actually violated. ", no, but you were claiming that there must be "some other change" that prevents the violation. This is not the case, as the translation of Clausius' text book explains very clearly (the interchange is "compensated"). That was the point I was getting to with the thought example that you consistently avoided engaging with.
Re #1434 "Dikran Marsupial at 04:51 AM on 15 August, 2014
"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!"
But how can you be amazed at it? You yourself have never answered the "simple direct question" I put to you to keep you from wandering down the wrong way and disproving what I never said instead of actually addressing the real issue.
The "simple, direct questions" I am referring to are from #1435, where I wrote: 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?
That is three simple questions you never answered. So you are in no position to complain.
MattJ I have already answered the question, backradiation does not "heat up" the surface any more than a blanket "heats up" the person beneath it. It causes it to be warmer than it would otherwise be, by reducing the rate at which heat is lost. The net transfer is still from warmer body to cooler body. Sadly this doesn't seem to fit within your comprehension of the problem, which appears to be because your comprehension of the second law is defficient, and sadly you have too much hubris to recognise this.
Just to be clear:
(i) there is indeed LWIR coming from the upper atmosphere, it is usually known as "backradiation"
(ii) The stratosphere is cooler than the ocean surface.
(iii) The part that I disagree with is the "heat up" bit, which is incorrect, "causes to be warmer than it would otherwise be" would be closer to being correct as the net transfer of heat is from the surface to the atmosphere. I have already explained this to you (using a blanket as a metaphor). It would be correct to say that upwelling IR from the surface "heats up" the upper atmosphere.
Re #1444
Thanks, Tom, for your long and thoughtful reply. You did clarify several points well. But that integral is hard to do for a climate system, isn't it? That is why I am groping for a simpler way to explain it. Using a completely different form of the 2nd law and observing entropy increasing in each step of the process still seems the best way to go rather than take the article's approach.
Then to the skeptic who still object, "but you have heat going from cooler to hotter", we can say, "but entropy did increase, so there is no violation".
The problem with this approach is that it requires explaining to the layman what entropy is and how to track it and estimate it. Then there is still the problem that the idea that the second law says only and exactly "heat never travels from colder to hotter" is quite entrenched in the minds of many. I have encountered many, for example, who seem to have engineering thermodynamics backgrounds who still have this entrenched.
"Then to the skeptic who still object, "but you have heat going from cooler to hotter", we can say, "but entropy did increase, so there is no violation".
or alternatively, you could just show them the pages in Clausius' book where it is carefully explained that this is O.K. as it is "compensated" by a greater flow of heat in the other direction. There is then no need to mention entropy.
MattJ - What I find most frustrating in these discussions are exactly statements like "you have heat going from cooler to hotter".
"Heating" in colloquial usage is an increase in net energy causing an increase in temperature. Energy goes from cool objects to warm objects (in fact, to all objects within the radiative view of that cool object), not heat, not by the common use of that term.
Energy goes from cooler to warmer objects, which add to the sum of energy going into that warm object, an increase of incoming energy - and hence the object must warm to radiate energy equal to incoming.
But the net flow of energy, heat, is still from the warm object to the cool one. Adding a cool object simply reduces that net energy transfer.
To be more precise, a cooler object will cause a warmer object (or one of any temperature) to increase in temperature if that cooler object adds >0 energy, if the cool object radiates/conducts/convects more energy than an absolute zero background. The starting point is an contribution of zero, anything warmer than that will add incoming energy to an object in view, increasing the input.
For some reason the fact that any radiating object represents a positive contribution to incoming energy gets somehow overlooked in these discussions.
@1446
Thank you, Dikran, for that excellent find! Sure, a footnote several times the length of the text may be intimidating, but that one was well worth reading And his formulation in that footnote, "...the warmer body never receives more heat from the colder one that it imparts to it." Is particularly good for silencing the skeptic's objection. Now the cold CO2 can impart heat to the warmer thin ocean layer as long as the latter gives more heat back.
I wish modern texts had footnotes that explained the meaning of the various terms as well as that one did. But that is an old-fashioned practice, rarely duplicated now. They try to do the same with sidebars with only mixed results.
MattJ@1460 does that mean you now agree with me on my interpretation of the second law of thermodynamics only applying to the net transfer of heat, and hence there is no need to introduce the "other changes" clause?
BTW, the translation of the second edition suggests the footnote may not be an addition by the translator as the corresponding material is in the text of the second edition (translated by somebody else).
MattJ @1450
Unfortunately the word "generally" is there to cover Spontaneous endothermic reactions, These are reactions driven by a large increase in entropy, which can overcome a loss of enthalpy (and hence heat), and ensure that the change in Gibb free energy is still negative. This, of course, is to modify Clausius's words to cover the modern understanding of the second law of thermodynamics, which is only rigourously expressed mathematically (as Tom did @1441).
Thus Clausius's formulation of the 2nd law is actually incomplete as we now understand it. The author of the OP could either quote him directly and expose himself to the criticism that it was incomplete, or add the word "generally" to deal (albeit rather vaguely) with our current understanding.
I would also point out that you are (now) misrepresenting post 955, which does not object to the word "generally".
Dikran @1453, while I still disagree that it is a cause of confusion, I do have to agree with Matt that the form of the 2nd law given in the article is not a quotation of Clausius, and is portrayed as such. If it was a paraphrase, it should not have been enclosed in inverted commas and should not have been indented (but may be higlighted in italics). By including quotation marks and indentation, the OP (whether intentional or not) has marked the statement as a quotation of Clausius, or (as it is in English) a fairly literal translation of Clausius. Further, if it is intended as a translation, it should be identical to the translation of the apparent source given for the quote, ie, the wikipedia article linked in the sentence introducing the quote.
As it happens, I have found a reproduction of the original Clausius article in german. From that it can be clearly seen that footnote was not included in that article, and hence it cannot be attributed to Clausius. On the other hand, Clausius did read and approve the proofs (footnote on page vii of the English translation). Therefore Clausius not only endorsed the translation of the principle given in that book, and quoted by wikipedia, but he also endorsed the explanation of the second law as given in that footnote. (He may even have written it, but we do not have proof of that and hence cannot attribute it to him.)
Turning to the actual words of Clausius,they were:
Google translate renders that as:
From that it appears that the rendition from the English version, and as given by wikipedia is fairly literal:
Given that, and the implied endorsement of the translation mentioned above, I think it is unreasonable to not take them as his words. The "quotation" in the original post, however, cannot be taken as anything but a loose paraphrase of those words, or a paraphrase of the English gloss from the footnote (which being originally published in English, requires no translation).
Given all this, the OP should be editted either to include the form of Clausius words as given in the English translation as quoted in wikipedia, or the text should be modified to indicate the law as actually given is a paraphrase, or the author's own phrasing of the law.
I do not consider this a minor matter as misquotation is academic misconduct, and therefore something SkS should never do except by accident, and in the later case the error should be corrected as soon as possible.
Dikran @1461, thankyou. In the second edition, Clausius attributes the formulation of the footnote in the first edition to himself (p78), and repeats much of the explanation from that footnote. In particular, he mentions the passage of heat from the colder to the hotter body, which is not prohibited, provided that a greater amount of heat flows in the opposite direction. His wording is:
He concludes by formulating the 2nd law as:
That means in editing the OP to correct the misquotation, the author may use the above formulation, or that from the footnote which is now acknowledged by Clausius as his own. They need only include a link to the source either instead of or in addition to the link to wikipedia.
I need only add that the formulation given in the OP is certainly a good paraphrase of the last formulation quoted from Clausius. Therefore there is nothing wrong with it except for the point that paraphrases should not be presented as quotations.
Tom thanks for the adiditonal details, it does seem that Clasuius adopted the footnote for his second edition, as I mentioned in a previous post, but you have certainly clarified it further.
"I do not consider this a minor matter as misquotation is academic misconduct"
This is too strong a statement as it is only misconduct if done deliberately, if there is no intent to decieve, it is just an error and is not misconduct. I agree that it should be change if it turns out not to be a reasonable translation of something Clausius actually wrote, however this has not yet been established. It may be that his did write something along these lines in another work. Performing a google search suggests this exact wording does occur in other academic papers and books, so I doubt SkS are the first to make this error, if that is what it is. I am making enquiries...
However, in the light of my finding, I think it may be better just to rewrite the basic rebuttal from scratch as there is now a much more straightforward refutation of the myth based on Clausius' own understanding of his second law.
Dikran @1465, following up I have found the major revision of the wikipedia page on thermodynamics which eliminated the form of the statement quoted in the OP above, and replaced it with another version, which has since in turn been replaced. The original replacement took place on Oct 11th, 2010, with prior versions of the article having the quote in the OP. Evidently, therefore, the OP took its quote from the wikipedia page to which it linked. If it is a misquote, it is then entirely inadvertent as regards SkS. The original version on wikipedia may also explain the frequent occurence of that version on the web.
With regards to books, google books shows just five books containing that version of the quote. Of those, it shows the relevant contents of just three recent (2011 to 2013) textbooks, the former on "The Energy Problem", and the seond on thermodynamics, and the third being Farmer and Cook (2013). The earlier books are one from 2010 by Lawrence Soloman discussing "The Deniers", and one from 1992 by Richard Lindzen. Unfortunately without the text it is not possible to determine whether Lindzen attributes the version of the 2nd Law to Clausius, or whether he presents it as a quote.
Of the five, the most interesting is Stein and Powers (2011), which attributes the quote to "Rudolf Clausius' paper in 1850" (p27). In fact Clausius' talk to the Academy of Berlin in 150 was published in two parts in Pogendorff's Annalen, the first starting on page 368, and the second on page 500. These were translated in 1851, and included as the first memoir in the first edition of the "Mechanical Theory of Heat".
The closest formulation I can find in Clausius 1850 occurs on page 45 of the English first edition of "Mechanical Theory", and page 503 in the Annalen. In English it reads:
The relevant principle is, of course, stated in the second part of the sentence. While the quote given in the OP is a good, if abbreviate, paraphrase of that sentence, it is also clearly not direct quotation. Interestingly, in the "Mechanical Theory" a footnote dates 1864 again glosses the principle stated in the body of the text as "... heat cannot of itself pass from a colder to a warmer body". That, or the alternative formulation, ie, that "A passage of heat from a colder to a hotter body cannot take place without compensation" have the strongest claim to represent Clausius' true formulation of the 2nd law (ie, the one he was happiest with on reflection).
Moving on: With misquotation, as with plagiarism, academic misconduct can exist in the absence of intent. That is why there are fairly strict academic rules about methods of quotation, which are always relaxed outside of strict academic contexts (and apparently always in the physical sciences). The strict rules are there to prevent inadvertent misquotation. One of those rules is that when you quote somebody indirectly by quoting somebody else quoting them you clearly indicate that so that any error can be attributed to the source that made the error. If you do not so attribute, you are considered as guilty of any error as if you yourself had made it.
In this case, however, clearly SkS misquoted here inadvertently by copying somebody elses "error". Further, they linked to their source and in a way that made it transperent that it was their source. At least, it made it transperent until the text of wikipedia was edited. Consequently no fault lies with the authors of the OP. Of course, that does not mean the text should not be updated with a correct quotation of an original source (or possibly rewritten in light of the other interesting material uncovered by this excercise.
Cheers Tom, I suspect you are right on the source, good detective work!
@1446
Dikran- Thanks for finding the link. I do need to point out, however, that when I right-clicked on the link labeled "Google Books", I got a broken URL. It was not hard to edit though: once I removed everything before "books.google.co", it worked (people using other browsers might have to insert/omit "http://" or "www.").
Now that I have read that note, I consider it more reasonable than I did before, to consider using his alternative statement of the same law "an uncompensated transmission of heat from a colder to a warmer body can never occur" and allow considering the sun's input of energy as such 'compensation'.
It still sounds odd to consider the sun's energy input 'compensation', we would not normally use the term that way nowadays, but as I read the footnote, I see he is using the term 'compensation' that generally. For he does say it expresses the same idea as "by itself", and we all agree that the heat transfer from colder CO2 to warmer ocean thin surface layer is ultimately driven by the energy input from the sun, it is not "taking place 'by itself'".
This has been a longer detour into the historical development of thermodynamics than any of us hoped for, but it does throw light on why the meme Science of Doom calls "the imaginary second law" is so persistent. Few thermodynamics courses at any level, even college level physics and engineering, are willing to take the time for such detours and show where misunderstandings of older thermodynamics terms and concepts still trip people up.
@1466 & @1464
That is, as Dikran said, good detective work. But I am still amazed that you can claim, "I need only add that the formulation given in the OP is certainly a good paraphrase of the last formulation quoted from Clausius. Therefore there is nothing wrong with it except for the point that paraphrases should not be presented as quotations."
That 'formulation' still has the disastrous interpolation, 'generally'. That weakens the law to the point of total uselessness. It accomplishes nothing and destroys everything. Even just ripping out that one word would improve the original article by a lot.
Remove that one word! That is all I ask! (though, I would also like direct quotes to be real direct quotes...)
I should also point out that at no time did I accuse SkS of dishonesty for making this mistaken statement of the law. But I cannot see it as anything other than negligence that it has gone uncorrected for so long, even after comment #955 pointed it out way back in 2011.
@1452
""Spontaneously" is a perfectly reasonable synonym for "of itself" in this context, and the "generally" refers to the possibility of there being "some other change...", which happens not to be relevant in this case.
Please stop digging."
I am genuinely surpised at your interpretation of the word 'generally'. I would have thought English is nor your native language. Either that, or you are the one who is 'digging' and engaging in pedantry.
No, the only reasonble interpretation of the word 'generally' here is to make the whole sentence a generalization, which may have exceptions. But this in turn weakens the law to the point of uselessness, which is exactly why Clausius did not use the word 'generally' in <b>any</b> of his formulations. Not even in the footnote you provided. Nor is it used in any of the valid restatements of the law, both old and modern.
I generally disagree with you, MattJ, but only because I'm trying to get this thread to 1500 comments. At that point, it will be taken out back and shot (and buried in an unpublished location).
MattJ @1468-70:
1) We have established that Clausius' first statement of the 2nd Law, as translated into English was:
That was glossed by Clausius as:
The original purported quotation sourced from wikipedia and appearing in the OP is:
It mashes the two together, taking glossing "general deportment of heat" from the body of the text as generally, and glossing "of itself" in the footnote as "spontaneiously". Both glosses are transparently reasonable, ie, they fairly present the information content of the phrases they gloss. Presented as a summary of Clausius' first statement of the principle (rather than a direct quotation), it is therefore wholly unobjectionable. If you have a problem with the use of the word "generally", take it up with Clausius.
2) As already noted, I would prefer the use of either of the two more considered forms of Clausius statement, and as direct quotations. The word "generally" does not appear in either, so that should satisfy you.
3) As shown in my post @1444, the heat transfer processes between surface and atmosphere are not changed by the absence or presence of sunlight in the short term. Therefore they do not involve one of the changes which are irreversible except by supplying the heat deficit from warm to cold of which Clausius was talking about in the footnotes.
It is compensated by the direct flow of a greater quantity of heat from the warmer surface to the cooler atmosphere. That is the other case of "compensation" that Clausius discusses and does not involve the Sun in any way except in replenishing the heat thus lost by the surface. Discussing the Sun as compensating the supposed reverse flow of heat merely confuses the issue for not such net reverse flow occurs, and hence no such compensatory role is called for. (As stated initially, this case is quite different to that of refrigerators, where a compensatory change in pressure of the coolant is required.)
DSL, I don't know about burrying it, but a strong case for locking this thread can be made, and would be supported by every SkS commentator. Notifications of any errors in future edits could be made by email, and if somebody realy thinks they have a strong case for violation of the 2nd law, they can email a copy of a blog post as well, which can be published with or without reply should they be able to convince an "editor" and "two referrees" from the SkS team that that should be worthwhile.
Surely everything that is worth saying on this thread has already been said repeatedly.
MattJ wrote "I am genuinely surpised at your interpretation of the word 'generally'. I would have thought English is nor your native language. Either that, or you are the one who is 'digging' and engaging in pedantry."
As it happens, English is my first language (my second being MATLAB). In the context of the quote the word "generally" indicates that there are exceptions to the rule as stated, see e.g. the third definition given here):
What could those exceptions be? Rather obviously the exceptions are the cases where there are "some other changes...".
This doesn't weaken the second law at all, it is just a statement of only the general case of the second law, where the exception is not relevant (such as the case for the greenhouse effect, where no "some other change" need be introduced to explain what we observe).
The problem appears to be that you are unaware of a (perhaps idomatic English) usage of "generally", not that there is something badly wrong with the quote. As it happens, I am working on rewriting the article, and I shall use quotations from the translations of Clausius' book.
Now I asked: "MattJ@1460 does that mean you now agree with me on my interpretation of the second law of thermodynamics only applying to the net transfer of heat, and hence there is no need to introduce the "other changes" clause?"
but you appear to have ignored yet another of my questions.
MattJ wrote "For he does say it expresses the same idea as "by itself", and we all agree that the heat transfer from colder CO2 to warmer ocean thin surface layer is ultimately driven by the energy input from the sun, it is not "taking place 'by itself'".
I think you still have not quite understood. While the original source of the heat is the sun, the upper atmosphere is warmed by outboud IR radiation emitted by the surface. Thus the interchange of heat between the surface and the upper atmosphere (no need to mention the sun at all) involves a greater transfer of heat from the surface to the atmosphere than vice versa.
It would be more accurate to say that the backradiation is not compensated by energy from the sun, but that it is directly compensated by outbound IR from the surface.