Talk:Kirchhoff's law of thermal radiation

message: 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)
replies: text: 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)
replies: text: 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)

text: 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)
thread_title: Query

message: 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)
thread_title:  The Kirchoff's "Equation" ? 

message: 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)
replies: text:  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)
thread_title:  Thermal blankets 

message: I can't make up my mind if the explanation given in radiant barrier#Reflectivity and emissivity misrepresent Kirchoff's law or not. Does it? EverGreg (talk) 17:13, 11 July 2009 (UTC)
replies: text: 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#Reflectivity and emissivity.  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#Reflectivity and emissivity 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)
thread_title:  [[Radiant barrier]] 

message: 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)
thread_title:  Absorption efficiency greater than one 

message: This link Kirchhoff's Law review is to a site run by a fruitcake, his remark about the 'tragedy' of Kirchhoff's misunderstanding is comparable to the same author's view about the 'Sun being made out of liquid iron' http://www.ptep-online.com/index_files/2007/PP-08-12.PDF 
I intend to strike the link out unless this view of Kirchhoff's work can be shown to be correct(!)--Damorbel (talk) 16:21, 19 August 2010 (UTC)
replies: text: "It is ill-advised to use personal attacks.." Please accept my apologies, I can offer no excuses for my remarks and would like to withdraw them. --Damorbel (talk) 13:04, 24 August 2010 (UTC)
replies: text: Pierre-Marie Robitaille, in this document  you write "Kirchhoff’s law can take on several formulations, which stem from the equivalence between the coeffcients of emission, ε, and absorption, α, at thermal equilibrium" which means, if I understand you correctly, that these coefficients will only be equal at thermal equilibrium (my emphasis), i.e. they are somehow dependent on temperature. My understanding is that these coefficients being a function of temperature does not form part of Kirchhoff's thesis. Would you care to contradict me?--Damorbel (talk) 15:49, 25 August 2010 (UTC)

text: There appears to be a problem here. 71.79.101.111 you are infact anonymous and you have no connection with Pierre-Marie Robitaille, yes? So you are 1/ misrepresenting yourself by remaining anonymous and 2/misrepresenting the views of Pierre-Marie Robitaille by putting your own views attached to his name. I ask you to clarify exactly what you are doing, please. --Damorbel (talk) 07:43, 30 August 2010 (UTC)
thread_title:  External links 

message: 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)
thread_title: Physics for Kirchhoff's law and Planck's law

message: 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)
thread_title:  absorptivity depends on the actual present state of the body, not merely on its elementary character 

message: 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)
thread_title:  A black surface? 

message: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Ambiguity or confusion 

message: 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)
replies: text: 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)
replies: text: 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)

text: 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)
thread_title:  fluctuation-dissipation 

message: 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.Kangro, H. (1970/1976).
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.Kangro, H. (1970/1976). 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 . 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."<Hermann, p. 12.> 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 .Chjoaygame (talk) 01:52, 9 March 2016 (UTC)
thread_title:  assuming