Talk:Kirchhoff's law of thermal radiation

Query
In line 2 of the article, it says that Kirchoff's law was proved in 1861. Laws of nature are not something that one can prove or disprove. My understanding is that what Kirchoff formulated with regard to black body radiation was actually a theorem and not a physical law. So shouldn't this article be entitled Kirchoff's theorem instead of its current title? -- Metacomet 00:54, 16 December 2005 (UTC)


 * There isn't as sharp a distinction between "law" and "theorem" as you seem to think. For example, Kirchhoff's voltage "law" is really just a consequence of Maxwell's equations, as is Lenz's "law" and Snell's "law".  There are lots of things called "laws" that are really just theorems proved from more basic descriptions of physical law, which in turn can be derived from other more basic derivations, etcetera.  (Partly, the naming is a historical question of which came first, but I don't think there is a general rule.)  Regarding the article title, you have to stick with common usage as it is.  —Steven G. Johnson 01:03, 16 December 2005 (UTC)


 * That said, the concept of "proof" is probably one to be avoided in science, where the general idea is that hypotheses are either supported or refuted through evidence. In this case, yes - the mathematical proof rests on the assumption of the underlying physical theory of thermodynamics being correct. So it's not really a proven theory, as much as a logical deduction from the best current model of physics. --JB Gnome (talk) 04:29, 24 November 2010 (UTC)

The last line of this article, about the reflectivity of emergency blankets sounds plausible,except the reflectivity/emissivity of a substance is wavelength dependent, so just because something is reflective in the visible portion of the spectrum does not mean it will be the same in the long wave thermal region. Perhaps it is true in this case, but I don't believe that it logically follows.


 * Metals generally become better reflectors at longer wavelengths, so a metal that is a good reflector at optical wavelengths is also almost certainly going to be reflective at infrared wavelengths. In practice, I seem to recall that these blankets use Aluminum, a graph of whose reflectivity is given at Optical coating.  True, the text is a bit vague (it just says "reflective material" and doesn't specify a wavelength or a metal), and could be improved.  —Steven G. Johnson 19:47, 5 January 2006 (UTC)

The Kirchoff's "Equation" ?
I have tried to search for this equation (approximation for liquid-gas transition):

$${(\frac{\partial{\mathcal{H}_{fg}}}{\partial {T}})}= \mathcal{C}_{P_{g}} - \mathcal{C}_{P_{f}}$$

and the equation (approximation for solid-liquid transition):

$${(\frac{\partial {\frac{\mathcal{H}_{sf}}{T}}}{\partial T})} = \frac{\mathcal{C}_{P_{f}} - \mathcal{C}_{P_{s}}}{T}$$

They are called Kirchoff's equations. I think there should be a disambiguation page for these.

--Musically ut 06:42, 27 November 2006 (UTC)

Thermal blankets
It is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation. I'm not convinced that this is a good example. I think they work mainly because of their reflectivity, bouncing radiation back to the body inside, and absorbing little to be conducted to the outer surface where the losses will be mainly down to convection and conduction rather than radiation? Derek Andrews (talk) 11:00, 4 May 2009 (UTC)


 * But that's exactly why it's a good example! Since their reflectivity is high, their absorptivity is low, which means their emissitivity is low too.--JB Gnome (talk) 04:32, 24 November 2010 (UTC)

Radiant barrier
I can't make up my mind if the explanation given in radiant barrier misrepresent Kirchoff's law or not. Does it? EverGreg (talk) 17:13, 11 July 2009 (UTC)
 * I would say it was more accurate than what is presented in this article as Kirchoff's law. When neither medium at an interface absorbs radiation, what is emitted is simply that which is not reflected (back into the interior of the emitter), whence they sum to 1, as per radiant barrier.  Absorption obeys Beer's law; it is irrelevant for sufficiently thin layers, and for thicker layers it doesn't invalidate Kirchoff's law but simply complicates it, provided both directions treat it symmetrically, which this article does not.  Just now I linked radiant barrier to this article in the expectation that at some point someone would fix the latter, which I'm happy to do if there are no objections.  --Vaughan Pratt (talk) 03:56, 28 November 2009 (UTC)

Absorption efficiency greater than one
According to "Absorption and Scattering by Small Particles" by Bohren and Huffman, pp. 125-126, the absorption efficiency can be greater than one in some circumstances, when the a particle is smaller than or comparable to the wavelength.


 * Eh, this is just a Mie resonance, in which the scattering cross-section can exceed the geometric cross-section. It's not a contradiction of Kirchhoff's law (which is for infinite surfaces), and you can only make it seem so by playing games with the ambiguity of the definition of "incident power" for finite objects.  (Essentially, because of diffraction a finite object can absorb energy even from portions of the incident wave that don't strike the object directly; the light "bends into" the object.)  — Steven G. Johnson (talk) 15:13, 10 August 2009 (UTC)

Physics for Kirchhoff's law and Planck's law
My present understanding is that the coefficients of absorption and emission are governed by the state of the material including its radiative content and environment. The Einstein theory with A and B coefficients is helpful here. The A and B coefficients are determined simply by the quantum mechanics of the molecules, but different coefficients apply to their different states of excitation. The emissivity and absorptivity are governed jointly by the A and B coefficients and by the states of the molecules and radiation. In thermodynamic equilibrium special relations hold between these factors. According to Milne 1928, we may expect a Planck distribution when there prevails "local thermodynamic equilibrium". According to Goody and Yung 1989, page 31, in a nutshell "We may, therefore, regard Planck's and Boltzmann's laws as interchangeable; conditions leading to one lead to the other, and vice versa." I suppose that this does not cover all problems of interest, but as far as it goes it seems right?Chjoaygame (talk) 09:50, 13 November 2011 (UTC)

reliable source
"This will be true even though the walls are perfectly reflecting due to the very small amount of interaction between the photons themselves."

I think this is important enough to call for a properly reliable source.Chjoaygame (talk) 09:16, 13 November 2011 (UTC)


 * A reliable source should not be too hard to find - check out http://www.extreme-light-infrastructure.eu/High-field_5_2.php which references Lifshitz. PAR (talk) 02:11, 27 December 2011 (UTC)


 * The source indicated just above (http://www.extreme-light-infrastructure.eu/High-field_5_2.php) makes no reference to Planck's law or to Kirchhoff's law. It concerns very intense radiation and high-energy and laser physics, which can be far from thermodynamic equilibrium, and far from the range of applicability of Kirchhoff's law, not the usual heat radiation that is the subject of Planck's law and Kirchhoff's law. It does not amount to a physical argument that photon-photon interactions will in general lead to a Planck distribution in a time-frame that is notable for an article on Kirchhoff's law. It is therefore not a suitable reliable source for the statement quoted above as placed in the article on Kirchhoff's law.


 * Rybicki and Lightman 2004 is cited as a reliable source for some purposes. On Planck's law, just prior to their discussion of Kirchhoff's law, they write on page 15: "Since photons are massless, they can be created and destroyed in arbitrary numbers by the walls of the container (for practical purposes, there is negligible self-interaction between photons).


 * Goody and Yung write about the atmosphere on page 21: "The possible processes non-linear in the light intensity have been fully explored." They go on to say that the exploration leads to the conclusion that "the deviations from Lambert's law on this account are completely negligible."


 * Looking through Chandrasekhar 1950, and through Mihalas and Mihalas 1984, and through the sections on thermal radiation in Loudon 2000 and in Mandel and Wolf 1995, I find no mention of photon-photon interactions. I think that these authors are likely to have been aware that in high-energy physics some phenomena of such kinds have been examined; these authors are respected and well-informed physicists. That they make no mention of photon-photon interactions in their discussion of thermal radiation is most likely an indication that they think that such interactions in that context are not notable, not even notable enough to deserve a caveat that they are neglible. It seems very unlikely on the other hand that they make no such mention because they are ignorant or careless.


 * The sentence in question is not part of the ordinary run of considerations of Kirchhoff's law. The ordinary run of considerations of Kirchhoff's law is about the interaction of light with matter, which is important for this purpose precisely because of the negligibility of photon-photon interactions if they even occur at all at the energies of usual concern for Kirchhoff's law.


 * The sentence in question may be very sophisticated and up-to-date for some contexts, and indicates that the editor is very learned.


 * Overall, this looks like a case that the sentence in question in context is not supported by appropriate reliable sources, or is considered to be non-notable in context, or even explicitly denied, by reliable sources.Chjoaygame (talk) 06:31, 28 December 2011 (UTC)

absorptivity depends on the actual present state of the body, not merely on its elementary character
The Einstein theory of A and B coefficients shows how absorptivity must depend on the actual present state of the body, not merely on its elementary characteristics. The absorptivity depends on the occupation numbers of the possible quantum levels of the atomic or molecular species. This was not understood even in the early days of the Planck law, but was pointed out by Einstein in papers of 1916, with a near-re-publication in 1917. A translation of the 1917 paper is to be found in The Old Quantum Theory by D. ter Haar (1967). If the state of the body is such that nearly all the atoms are in upper level quantum states, there is 'negative absorption'. 'Negative absorption' means that stimulated emission exceeds primary absorption. Thermodynamic analysis, to which Kirchhoff's law refers, must consider stimulated emission as a component of absorption because it is directly proportional to the radiation density. See for example The Quantum Theory of Light, third edition, Loudon, R. (2000), Oxford University Press, Oxford UK, ISBN 0–19–850177–3.

Kirchhoff's law strictly stated applies to thermodynamic equilibrium. There are conditions away from strict thermodynamic equilibrium in which Kirchhoff's law is an extremely good approximation, and local thermodynamic equilibrium is one such condition. See for example Foundations of Radiation Hydrodynamics, Mihalas, D. and Weibel-Mihalas, B., (1984), Oxford University Press, Oxford UK, ISBN 0–19–503437–6. There are, however, conditions far from thermodynamic equilibrium in which Kirchhoff's law does not apply, for example in a laser. Such conditions were hardly considered before 1916, and even at the time of the invention of the laser, there was scepticism. It is fundamental to Kirchhoff's law that in its strict statement it refers to thermodynamic equilibrium. Discussion of departure from thermodynamic equilibrium is a development of the law, but is not primary to it.Chjoaygame (talk) 23:32, 26 December 2011 (UTC)

Perfect black body
What is the difference between a black body and a "perfect black body"? If there is none, can we dispense with the phrase "perfect black body"? PAR (talk) 05:01, 27 December 2011 (UTC)
 * The need for further explanation (perfect....) may arise from a feeling that 'some blackbodies are blacker than others'. It may not be apparent to all, but the 'blackbody' concept cannot exist in the real world since its density would have to be zero, otherwise it would have a refractive index which would give rise to some kind of scattering, which of course is not allowed by the 'blackbody' concept.
 * I agree, an absence of 'perfect[ion]' would be an improvement. --Damorbel (talk) 11:25, 27 December 2011 (UTC)

Kirchhoff defines his own perfect black bodies
Kirchhoff's perfect black bodies were defined by Kirchhoff. They absorb all radiation that falls on them, right in an infinitely thin surface layer. They obey Lambert's cosine law in their emissions. They are theoretical fictions. In contrast, Planck's perfect black bodies do not have any absorption or emission at their interfaces, which are fictive mathematical surfaces, not infinitesimally thin material layers that can emit and absorb as do Kirchhoff's; but they are opaque to any radiation that might reach their interior through the interfaces; and the interfaces reflect none.Chjoaygame (talk) 13:07, 30 December 2011 (UTC)


 * Why are we emphasizing Kirchhoff's 19th-century definition rather than the modern definition? (Note that for the a semi-infinite body, a half-space, Planck's definition reduces simply to saying that absorptivity and emissivity are 1, since the "interior" is infinitely remote.  For any sufficiently large body, therefore, one can concentrate solely on the absorptivity.)  We do a disservice to readers by placing such emphasis on obsolete presentations, which might mislead the reader when there is a conflict with the modern understanding.  This is first and foremost a physics article.  Have a section on the history, sure, but don't make the 19th-century mindset central to the article and be clear on when it has been superseded. — Steven G. Johnson (talk) 14:15, 30 December 2011 (UTC)


 * According to Goody and Yung (1989) on page 64: "The treatment of Kirchhoff's laws is nowhere more explicit and readable than in Planck, M., 1913 ..." (translated in 1914). Planck discusses and more or less rejects Kirchhoff's definition of a perfectly black body. For the understanding of the processes, Planck's replacement version has significant merits, even today. I have de-emphasized Kirchhoff's version by moving it down the page.Chjoaygame (talk) 15:02, 30 December 2011 (UTC)


 * Note that the perfect black bodies of Planck don't occur in reality either; the article's current wording seems to imply that this objection only applies to Kirchhoff's definition. (Not that it is really a serious "objection"; there is nothing wrong with defining black bodies as a limiting case, any more than there is a problem in defining vacuum as a limiting case that is only ever approximated in reality. The real problem with Kirchhoff's definition as far as I can tell is that it is artificially limiting, because you don't have to absorb in an infinitesimal layer to radiate with a black body spectrum.)


 * I have no problem with referring to Planck. Just make it clear that Planck's definition is still the accepted one (citing a modern textbook or two as authorities), although it is worth double-checking to be sure that there aren't any recent further generalizations that have become widely accepted (none that I've heard of, but one should always be cautious in treating very old presentations as the last word on a subject).


 * To be frank, I'm not sure why Kirchhoff's black-body definition should be included at all. His limitation to absorbing everything in infinitesimal layers seems like a historical footnote, not something that had a big impact on the understanding of thermal radiation or anything of great interest to a reader trying to understand thermal radiation today.  And if we do include it, we have to explain how it is different from the modern understanding and why it is different (something the article fails to do now); without this explanation, including it at all is just an invitation for confusion.  (In any case, it is already mentioned in the black body article, whereas the topic of this article is mostly relevant to grey bodies.) — Steven G. Johnson (talk) 02:32, 31 December 2011 (UTC)


 * How do the great minds of physics do their work? Significant writers over a half-century objected to Kirchhoff's second derivation of his law of thermal radiation. I am thinking about possible derivations of it. I think it of interest to try to identify suitable premises.Chjoaygame (talk) 03:31, 31 December 2011 (UTC)

A black surface?
Since when has a blackbody had a surface? Surely a 'surface' requires a density change which would immediately cause reflection according to the Fresnel equations. The term 'blackbody' does not refer to an actual body, it merely describes the function of absorbing (and emitting). Real physical entities also have another function of scattering E.M. radiation which gives rise to refraction and reflection aswell as other optical effects. None of these effects can exist in isolation, they are all due to the (differing) interactions of E.M. radiation with matter, trying to specify blackbody effect in terms of a scattering effect ('a surface') is futile. --Damorbel (talk) 08:21, 2 January 2012 (UTC)

Ambiguity or confusion
Does this make sense to anybody without changing it in your mind first?

The absorptivity $$\alpha_\lambda$$ is the ratio of the energy absorbed by the wall to the energy incident on the wall, for a particular wavelength. This will be proportional to $$\alpha_\lambda E_{b \lambda}(\lambda,T)$$ where $$E_{b \lambda}(\lambda,T)$$ is the intensity of black body radiation at wavelength $$\lambda$$ and temperature $$T$$. The emissivity of the wall is defined as the ratio of emitted energy to the amount that would be radiated if the wall were a perfect black body. That will be $$\epsilon_\lambda E_{b \lambda}(\lambda,T)$$ where $$\epsilon_\lambda$$ is the emissivity at wavelength $$\lambda$$.

Also, 'intensity' is ambiguous. I didn't change it in case I'm missing something. 173.25.54.191 (talk) 04:39, 12 August 2013 (UTC)


 * To be very correct, the spectral absorptivity of an infinitesimal area element da is the ratio of the energy absorbed by the element to the energy incident, at a particular wavelength. The energy absorbed will be equal to \alpha_\lambda E_{b \lambda}(\lambda,T)\,da. Likewise the emitted energy will be \epsilon_\lambda E_{b \lambda}(\lambda,T)\,da where \epsilon_\lambda is the spectral emissivity. (Spectral means "as a function of wavelength or frequency.) If you omit the da, then they are proportional, not equal. As far as intensity goes, its the word I usually use. I'm not very good on the nomenclature, but there is a proper term, spectral radiance or irradiance, I think. PAR (talk) 06:36, 16 August 2013 (UTC)


 * I have made two slight wording changes that I hope may address the problem of making sense of it. As for 'intensity', I will leave that to others to consider.Chjoaygame (talk) 07:18, 16 August 2013 (UTC)

fluctuation-dissipation
It sounds like Kirchoff's law is an example of fluctuation-dissipation theorem. Is this the case? --Nanite (talk) 11:26, 6 September 2013 (UTC)


 * No. Kirchhoff's law of thermal radiation describes the mean radiation in matter as it is emitted and absorbed in thermodynamic equilibrium. It does not mention fluctuations.Chjoaygame (talk) 18:34, 6 September 2013 (UTC)


 * Ah, good point. I was imagining it as fluctuations over time in electric field or photon amplitude (mean zero) — analogous to Johnson noise — however you're right that the law deals with power and the analogy is perhaps a bit stretched. --Nanite (talk) 07:25, 7 September 2013 (UTC)


 * Actually, you are correct: there is a close relationship. Thermal radiation is produced by thermal fluctuations in the electromagnetic current densities in the materials, described by the fluctuation–dissipation theorem, and you can directly obtain the radiated power from these currents using the fluctuation–dissipation theorem.  Kirchhoff's law then follows if you apply reciprocity to these currents.  See, for example, here for a very direct calculation using a Langevin approach, or here for generalization to near-field thermal radiation. — Steven G. Johnson (talk) 01:42, 6 May 2021 (UTC)

assuming
Editor YohanN7 has posted a new edit. It changed this:


 * Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not precisely know the form or character of that universal function. It was eventually found precisely, in mathematical terms, by Planck in 1900.

into this:


 * Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not precisely know the form or character of that universal function. Attempts were made by Rayleigh and Jeans 1900 - 1905 to describe it in classical terms. It was eventually found precisely in mathematical terms by Planck in 1900, assuming quantized emission of radiation. This marks the advent of quantum mechanics.

It is puzzling that the commas were removed from "It was eventually found precisely, in mathematical terms, by Planck in 1900."

The insertion of the phrase "assuming quantized emission of radiation" is ambiguous. The discovery of the mathematical form was empirical. It led Planck to contrive a derivation that assumed quantized emission of radiation. The form was not discovered through the making of the assumption. The assumption was made through the empirical discovery of the form. The edit does not make this clear, and could be read to mean that the assumption, not the empirical work, was the source of the mathematical form.

It is not evident why the Rayleigh–Jeans efforts were inserted at a point before mention of Planck's discovery, yet Planck's discovery is then described as eventual. On p. xvi, Kangro (1970/1976) writes "With knowledge of RAYLEIGH's formula, yet impelled rather by the positive indication from the Reststrahl measurements in the long wavelength region, PLANCK constructed the new entropy function." A possibly different opinion is expressed by Armin Hermann < A translation of Frühgeschichte der Quantentheorie (1899–1913), Physik Verlag, Mosbach/Baden, 1969>. He writes on page 13: "These remarks by Planck prove that Rubens had pointed out to him the limiting case $λT → ∞$. At the time he proposed his radiation equation on October 19, 1900 he was not aware of Rayleigh's radiation law, which had appeared in the June 1900 issue of the Philosophical Magazine." I guess Kangro was better informed than Hermann on this matter, because Kangro had information from Hettner. Kangro says "yet impelled rather by the positive indication from the Reststrahl measurements in the long wavelength region". Planck later wrote about the developments prior to his discovery of his law: "The principal participants in these debates were Lummer, Pringsheim, Jahnke, Thiesen, Kurlbaum, and Rubens who proposed and discussed the most diverse equations." Planck did not believe in the equipartition postulate for this. Rayleigh knew that it failed in general, but observed in his June 1900 paper that it seemed to work to an extent in the limiting case $λT → ∞$.Chjoaygame (talk) 01:52, 9 March 2016 (UTC)

It is notable that over a decade or so, significant work, including by Planck, using classical physics, provided important piecemeal contributions to the construction of the Planck law. This work was intertwined with progressively improving observational technique. Rayleigh's 1900 contribution was not great.Chjoaygame (talk) 08:05, 9 March 2016 (UTC)