Talk:Stefan–Boltzmann law

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Contents 1 Old talk 2 calcul Earth temperature 2.1 Gray Body Temperature 3 Correct value of constant ? 4 Tyndall's measurements 5 Diagram request 6 Examples - Temperature of the sun

[edit] Old talk

It would be nice to give a different derivation of the intergal J in the appendix than the one in the article Planck's law of black body radiation. I suggest to do a contour integration of the function over the contour from zero to R and then to R + 2πi, 2πi + ε, then a clockwise quarter circle with radius ε and center 2πi to 2πi − iε and then back to zero. Count Iblis 13:30, 4 September 2006 (UTC)

I've just finished this. Count Iblis 23:14, 4 September 2006 (UTC)

[edit] calcul Earth temperature

- The title of this section is misleading: the calcul is just plain wrong for calculating the physical Earth tempearture, it only calculates the effective temperature of Earth (otherwise it assumes than a grey bodyœ absorber (albedo 0.3) is a black body emitter (effective temperature calculated)!) To have the physical temperature, fourth root of temperature has to be extracted before integrating over the surface, not after!

- would be nice to explain that the coefficient 1/(square root(2)) is a geometrical factor coming from the earth being spherical

once I learn about Latex, I ll make the changes —Preceding unsigned comment added by Goretesque (talk • contribs) 00:25, 28 October 2007 (UTC)

I think what it says about albedo is wrong, as is what you say. The albedo should not affect the equilibrium temperature, since it affects absorption and emission in the same proportion (assuming it's constant with wavelength, which it really isn't). Dicklyon 00:29, 28 October 2007 (UTC)

Do you mean that if two objects in space have all characteristic the same (size, orbit around sun, etc), but the albedo, they should be at same temperature ? are you speaking about effective temperature or physical? Goretesque 14:03, 28 October 2007 (UTC)

More than that. They don't have to be the same size, just the same distance from the sun, as long as the albedo is not wavelength dependent. In that case, effective temperature and physical temperature are not different, are they? In reality, the picture is made much more complicated by albedo varying with wavelength, which is what greenhouse gases contribute to. Dicklyon 16:19, 28 October 2007 (UTC)

Ok, I begin to understand what you are telling me:

- I made a mistake between size and shape! you are right, size of planet has no influence on effective temperature. However, shape will have some for objects, as the effective temperature depends on the amount of energy received (cross section of the object) compare to the surface over which this energy is spread. From planet, one can say it is always a disc spread over a sphere.

- however, from the definition of effective temperature (), if the distance from the star of a planet with albedo of 0 and a planet with albedo 0.5, then you can easily see that effective temperatures are different. This formula is what is used in the article (by replacing L with the value for Sun, and taking the albedo into account at the end) to calculate the "temperature of Earth". In fact it is the calcul of the "effective temperature of Earth", that is the temperature of a black body irradiating as much as Earth.

- by definition, the effective temperature T_eff and the physical temperature T_phys of a grey body can never be the same. The only case this could happen, is for a perfectly homogen grey body, that is a grey body with the exact same temperature on every points of its surface (that is a planet with the same temperature on tropics and on poles!). Taking into account only radiation, then the physical temperature of the surface is lower than the effective temperature.

- from this you can deduce that, in case of Earth, comparing T_eff 255 K and the actual measured temperature T_meas 288 K, is no sense for evaluating greenhouse effect. T_phys (much lower than T_eff) and T_meas have to be compared to get it, and it will be much more than 33 K.

- but all that reasoning is for a non rotating, not oblique, planet. Calculation become much more complicated in case of obliquely rotating globe (I am even not sure it is possible to calculate it)

- and finally, up to now, one considered a average albedo for Earth, did not consider oceans/earth coverage, did not take into account the internal heat, and one consider the system in thermal equilibrium! (and I am sure, I am forgetting some other factors)

conclusion: it is impossible to calculate T_phys for Earth; therefore impossible to evaluate a meaningful greenhouse effect, even a correct approximation Goretesque 23:07, 28 October 2007 (UTC)

- I think it should be pointed out that the 255K temperature is derived from 279K by multiplying by 0.7 ^ 1/4 . But I agree with Dicklyon that this ignores Kirchhoff . This implies that an ice age would catastrophically end with the earth a snow ball with a temperature about 156K . Surely there is experimental data on the temperature of gray body as a function of its albedo . Bob Armstrong (talk) 15:22, 15 January 2008 (UTC)

[edit] Gray Body Temperature

I've thought about this during the day , and believe I can clarify the argument that by Kirchoff's Law the temperature of a sphere of uniform albedo does not depend on that albedo . Assuming a gray body in earth orbit , at equilibrium
( ( SB * Te ^ 4 ) * e ) = ( a * ( K * SB * Ts ^ 4 ) )
where SB is the Stefan-Boltzmann constant , Te and Ts the temperatures of the sphere in earth orbit and sun , K the constant depending on geometry derived at Temperature relation between a planet and its star and e and a are the emissivity and the absorptivity of the sphere . By Kirchoff at equilibrium , e = a . Thus , for a ≠ 0 , e and a drop out and mean temperature of the sphere depends only on the surface temperature of the sun . Of course there is a singularity at absorptivity = 0 , or Albedo = 1 which means the internal temperature of a totally reflecting sphere would be disconnected from the space around it .

The idea that the temperature of an object can depend on its albedo , in particular the 4th root of its albedo , leads to absurdities such as the following : If the inner chamber of a vacuum bottle were coated with magnesium oxide with an albedo of about .9 then on the basis of a 4th root relationship , one would expect it's interior to settle at about 0.56 the temperature of the room the bottle is in , say about -100 centigrade . --Bob Armstrong (talk) 23:35, 15 January 2008 (UTC)

You read it wrong. It said the "effective temperature" would depend on the albedo, and that's true; review the definition. But I fixed it to be more clear. Dicklyon (talk) 01:30, 16 January 2008 (UTC)

- Seems to me effective temperature doesn't mean much for a passively heated body . Seen from the outside , its albedo will restore to its radiance exactly the amount reduced by its reduced emissivity . I actually would question why the section is about that rather irrelevant number rather than the actual predicted physical mean temperature for the planet . The most fundamental point is that by Kirchoff , the temperature of a radiantly heated gray body will be no different that of a black body . Clearly the notion that its temperature is reduced by the 4th root of , or for that matter any other function of , the albedo leads to an absurdity . In fact , I believe , tho not stated in the Wikipedia entry , Kirchoff applies frequency-wise , so this should be generalizable to any colored body . In fact , it must be because anything else leads to the absurdity that you can make an energy sink or source just by painting an object .

The bottom line is , there is no discrepancy between the Stefan-Boltzmann temperature measured in earth orbit and the measured temperature of the planet needing to be "explained" by some greenhouse effect . ( In this regard , I find it interesting that the Wikipedia article on the greenhouse effect has no equations quantifying it , nor have I been able to find any elsewhere . ) Bob Armstrong (talk) 00:50, 17 January 2008 (UTC)

It's not clear what you mean by "the Stefan-Boltzmann temperature measured in earth orbit". In any case, the point seems clear, that when the albedo varies with wavelength the equilibrium temperature is affected by that; we call it the greenhouse effect. I added another ref about it, including specific pages. Dicklyon (talk) 02:10, 17 January 2008 (UTC)

- By SB temperature I mean the temperature calculated as in the article from total radiant flux . That figure of 279K , incidentally , needs to be increased by 3k to 281k for the contribution from all other directions in space . This is getting mighty close to measurement error in mean solar and earth temperatures . I looked at both your references and they have the simply wrong ( by the arguments above ) assertion that the calculated mean temperature of the earth should be 255K . I see no derivation of the "greenhouse effect" in either of these references other than taking the difference between this mistaken number and the observed value which in fact agrees with notion that you can't make something cold just by painting it white . I think the idea that Venus , with the highest albedo of any inner planet can stay more than 2 times its SB temperature ( more that 3 times its "effective" temperature ) due to greenhouse heat trapping strains credulity . It violates very fundamental notions to claim you can make heat go up hill . I think it appropriate to mention that I did a "Mr Wizard" style experiment with black and white ping-pong balls at 2500M in the Colorado sun and observed very little if any difference in their asymptotic temperatures . By the logic that the "natural" temperature of the earth should be 255K , the white ball should have been freezing . The YouTube video of the experiment and a lot more on this topic is at my climate and energy page . These arguments combined with the total failure of global temperature to track CO2 over the last decade make the whole notion of anthropogenic global warming very suspect to say the least . ( Note , I clearly have more work to do to prove the case to colored balls , but it is hard to comprehend how some colored ball could chill if a white ball doesn't . ) , Bob Armstrong (talk) 19:33, 17 January 2008 (UTC)

I'm sorry, but you've totally lost me. Did you follow the links and read about where it mentioned greenhouse effect? It has no relation to your strawman idea of a "natural" temperature; they specifically talk about a "natural" greenhouse effect. Is your rant based on some reaction to this term? Dicklyon (talk) 19:37, 17 January 2008 (UTC)

- No , it's based totally on the fact that claiming the temperature of the earth should be reduced by the 4th root of 1 - its albedo is simply wrong . Both articles you cite use the difference between 279K and the reduced 255K as their total justification for a greenhouse effect . Bob Armstrong (talk) 22:37, 17 January 2008 (UTC)

To clarify for those reading, Mr. Armstrong is a global warming denier. He believes that the temperature of a body depends solely on the intensity of the radiation incident on the body, and that therefore changes in the composition of the earth's atmosphere cannot alter the surface temperature of the earth, so the idea that increased CO2 in the atmosphere could alter the earth's temperature must be wrong. He's attempting to get this page rejiggered to fit his ideas. (I've been having an entertaining discussion with him on a mailing list on this topic.) Pmetzger (talk) 01:41, 18 January 2008 (UTC)

Yes, I see. That sort of half explains his inability to read and understand what the article says, even though it is unrelated to the topic of human-caused modifications to the greenhouse effect. I suppose it means that asking again for him to review the references is pointless. Dicklyon (talk) 03:24, 18 January 2008 (UTC)

- That I deny there exists such a phenomenon as the "greenhouse" effect is to state the obvious . It is the reason why I deny its existence that must be dealt with . Note : it's very clear that a "greenhouse" effect greatly moderates the variance of planetary temperature ; the issue is whether it can change the mean . Here are the points of contention :

• Does or does not the article state that the mean temperature of the earth would be the calculated black body value 279k but that value is reduced to 255k by multiplying it by 0.91 , the 4th root of earth's presumed absorptivity , 0.7 ? The article may call this an "effective" temperature using a term applied to the observed radiation versus internal temperature of gray bodies , but thereafter the article uses it as the predicted actual temperature .

No, it does not. Read it again. The effective temperature is not a real temperature, and is not used as such. The real temperature requires a calculation that also involves emissivity. If that were the same as absorptivity, over the wavelengths that matter, then the real temperature calculated would be the 279 K number, not the 255 K number which would be the "effective temperature" at that cited albedo. The 279 K, the effective temperature in the blackbody assumption case, would be the same as the "real" temperature in any gray-body case, but that's still a hypothetical theoretical, not an actual. Dicklyon (talk) 02:13, 19 January 2008 (UTC)

- Yet you immediately use it in a calculation of greenhouse effect ! Bob Armstrong (talk) 23:42, 21 January 2008 (UTC)

• Does not this same logic lead to the prediction that a ball coated with magnesium oxide with an albedo of about 0.9 will come , in a similar 279k radiant environment , to an equilibrium temperature of about 0.56 of that or about 157K ? Is this not patent nonsense ?

Yes, that's patent nonsense, and not what the article says or implies. The ball would come to an "effective temperature" of 157K, perhaps, under the definition that it would emit the same radiant power as a blackbody of that temperature. If you don't acknowledge the definitions of the terms being used, you can't reason about the meaning. Dicklyon (talk) 02:13, 19 January 2008 (UTC)

- That's got the notion of "effective temperature" confused . By the equation for j^* at the top of the page , the "effective temperature" of a 279K body with an emissivity of 0.1 will be 157K . That's the amount of energy it will be radiating as seen from the outside . The "effective temperature" of a 157K body with a 0.1 emissivity would be about 88K . Bob Armstrong (talk) 23:42, 21 January 2008 (UTC)

• Is not the discrepancy between the measured earth temperature and this hypothesized 255K calculated temperature used as the total evidence for a "greenhouse" effect both in the article and in its references ?

I don't think so. The actual difference in albedo between the visible wavelengths where the earth absorbs and the long wavelengths where it radiates is probably not huge, so the greenhouse effect is perhaps only a few degrees. It's still a notable difference, and still easy to reason about. Dicklyon (talk) 02:13, 19 January 2008 (UTC)

- Here you are treating your calculated "effective temperature" as real . Otherwise there is nothing to explain . This still boils down to the idea that simply changing the color of a radiantly heated ball will change its temperature . Bob Armstrong (talk) 23:42, 21 January 2008 (UTC)

Explain these points , particularly the second one , and I'll be a convert . Alternatively show me any experiment in which simply painting a sphere changes its equilibrium temperature at all , much less as radically as by the 4th root of the albedo . Show me what the flaw is in my simple application of Kirchoff's law , ( ( SB * Te ^ 4 ) * e ) = ( a * ( K * SB * Ts ^ 4 ) ) . I sure wish I could lay my hands on the boy's science book where I first learned back in the 1950s that white and black rocks in the desert sun end up the same temperature .

It's very easy to find cases where painting a sphere (or a car) will change its temperature at equilibrium in sunlight. Black cars get hotter inside than white cars, usually, because they have similar emissivities in the long wavelengths, and very different absorptivities in the solar wavelengths. Dicklyon (talk) 02:13, 19 January 2008 (UTC)

- oh ? I had a white Porsche and it got hot as the devil sitting in the sun . And , my white and black ping-pong balls didn't show any difference . And , as I mentioned , it's very hard to shake the arguments I learned from boys' science books 50 years ago . Bob Armstrong (talk) 23:42, 21 January 2008 (UTC)

Additionally , I would appreciate a pointer to any derivation of the "greenhouse effect" with the same level of rigor as the derivation of Stefan-Boltzmann rather than simply based on the claim made here that a white ball will be colder than a black ball exposed to the same radiant flux .

Did you try reading that ref yet? It wasn't a long drawn-out derivation, but it was certainly not the trivialization of your strawman, either. Dicklyon (talk) 02:13, 19 January 2008 (UTC)

- I saw no derivation other than taking the difference between the observed temperature and the "effective temperature" . Bob Armstrong (talk) 23:42, 21 January 2008 (UTC)

Sorry if it sounds like a rant , but answer those first 2 bullets and you'll win me over . Bob Armstrong (talk) 01:47, 19 January 2008 (UTC)

Good, I'll take the win. Dicklyon (talk) 02:13, 19 January 2008 (UTC)

- Obviously I don't cede it . In fact , the article leaves me reminded of Steven Colbert's comments on people making reality simply by posting it on Wikipedia . For the nonce , I would suggest people stick with the more conservative statement of the physics on the Black body page . Bob Armstrong (talk) 23:42, 21 January 2008 (UTC)

That page does also mention greenhouse effect, but in the lengthy example it only works the blackbody case, and doesn't deal with albedo even, much less wavelength-dependent albedo. It doesn't say anything that contradicts the current page. I agree that the presentation would probably be improved if we got rid of the concept of "effective temperature," which is confusing and obviously misleading you in your attempt to apply logic to it. Dicklyon (talk) 02:01, 22 January 2008 (UTC)

I don't think the problem is with the explanation, which seems fine to me. I think that the problem in this case is with the particular reader having a conclusion they wish to be true in advance of reading the article. Pmetzger (talk) 12:57, 22 January 2008 (UTC)

Yes on the latter, but maybe also the former. The "effective temperature" is certainly a confusing concept when it's far from the actual temperature, like when the albedo is high. Shouldn't we re-express it without that? Dicklyon (talk) 21:44, 22 January 2008 (UTC)

Hrm. I don't have a good textbook handy with me, but I'd recommend we stick to the terminology in common physics texts, whatever that might happen to be. --Pmetzger (talk) 19:46, 28 January 2008 (UTC)

Some sources do use effective temperature of the Earth; the ones we have cited now in the article do not. We should probably cite one that does, since we start that way. Dicklyon (talk) 00:30, 29 January 2008 (UTC)

[edit] Correct value of constant ?

Any ideea why some sources give a different value for the constant? e.g.: "Stefan-Boltzmann Law This is the relationship between luminosity (L), radius (R) and temperature (T): L = (7.125 x 10-7) R2 T4 Units: L - watts, R - meters, T - degrees Kelvin" (See: http://science.howstuffworks.com/star3.htm) or "Stefan-Boltzmann Law - This is the relationship between luminosity (L), radius (R) and temperature (T): L = (7.125 x 10-7) R2 T4. Units: L - watts, R - meters, T - degrees Kelvin" (http://www.nameastargift.com/astronomydictionary/index.html) Units look ok. Why such a difference (maybe I am missing someting?) -Paul- (talk) 01:03, 9 February 2008 (UTC)

The one in the article is smaller than those by a factor of exactly 4*pi, so it's probably the power per steradian instead of the total power. In other words, someone got it wrong, I bet. Here's a book with an explanation that should help straighten it out. Dicklyon (talk) 06:23, 9 February 2008 (UTC)

[edit] Tyndall's measurements

I've been doing some checkings how Stefan experimentally derived the law. Here it is just briefly mentioned that he deduced it on the basis of experimental measurements made by John Tyndall. Stefan in fact never knew for Tyndall's measurements directly, but he learned of them from Wülner's textbook on thermodynamics, where Wülner in his 2nd and 3rd editions had included Tyndall's data. He also arranged temperatures to Tyndall's colours of radiated light, which were a little bit arbitrary. As Tyndall he refered to Draper's measurements. Stefan read about Tyndall's data in Wülner's textbook and fortunately correctly changed two temperatures into absolute scale. The questions is - to which Draper do both, Tyndall and Wülner, refer? My source says that Henry Draper in 1847 tried to establish experimentally at which temperature warmed body starts to radiate. He didn't succeed but he found out that energy density is increasing rapidly (exponently) and not strait proportional to temperature. Stefan read about Draper's measurement from his article in 1878. I guess Henry Draper can't be the right person, since in 1847 he was 10 years old, and I assume that it was his father John Draper. Tyndall also refers to Draper all over simply as Dr. Draper, and John Draper was also a physician. --xJaM (talk) 01:31, 5 March 2008 (UTC)

Yes, John Crepeau from the University of Idaho in his article Josef Stefan: His life and legacy in the thermal sciences cites John Draper's article from 1878 Scientific Memoirs: Being Experimental Contributions to a Knowledge of Radiant Energy, so this is the right source and John Draper the right person. --xJaM (talk) 17:49, 5 March 2008 (UTC)

[edit] Diagram request

A graph plotting power vs. temperature would be helpful to visualize the implications of the law. -- Beland (talk) 00:39, 6 March 2008 (UTC)

[edit] Examples - Temperature of the sun

Would someone please make clear what a "lamella" is? Its not a word in common usage, nor does it appear with a physical description in Wikipedia. A lamella isn't even described, for the context it is used here, in the Oxford English Dictionary! I assume that in plane English it is "a very thin plate of metal". —Preceding unsigned comment added by 88.106.45.45 (talk) 11:42, 13 March 2008 (UTC)

Lamella is meant to be a thin, usually oblong plate. It was a translation from Slovene. --xJaM (talk) 14:49, 17 March 2008 (UTC)