Talk:Stefan–Boltzmann constant

Merging out-of-place information at the bottom of the article (below references) into the article
We need an expert to interpret the interesting commentary left behind by a certain "old journalist" at the bottom of the article, and to help integrate that information into the article. Hyxl4161 (talk) 15:05, 18 March 2020 (UTC)
 * I agree with you that the merge would be a good idea. For the time being I've proposed the author to move that content from the article to this talk page. I hope they will reply soon. Regards, - Gryllida (talk) 03:28, 28 April 2020 (UTC)
 * Hi and, I have for now removed his edit as it was not relevant to the page. Most of the information was unsourced and talk about the "history" and "derivation" was already covered on the page Stefan–Boltzmann law. I believe the expert tag should be removed now.   ΤheQ Editor   Talk? 01:21, 8 May 2020 (UTC)

How about we describe this in terms a stupid person could understand?
Or at least define your terms--what the hell are W, m, and K in this context? —Preceding unsigned comment added by 216.56.28.38 (talk) 23:11, 8 February 2010 (UTC) \


 * I'm not sure how you would like us to make this particular page any more easy to understand. The units of W, m, and K are standard SI units for Watt, meter and Kelvin, respectively.  If you didn't know this, you could have clicked on the link to SI, given right there in the preface to the constant expressed in SI units.  If your confusion is with how the constant was derived, the article provides a link to Stefan-Boltzmann Law, which provides the underpinning calculations and theories for the constant.  If you believe something is not clear on that entry, then perhaps you should bring up what you specifically find confusing in that talk page.  --151.173.12.253 (talk) 16:39, 11 February 2010 (UTC)

Emission in a non-vacuum
I have here an article (Rabl, 1976 Comparison of solar collectors, Solar Energy (18) 93-111) which states that emitters emit n² as much radiation when immersed in a medium of refractive index n. This article goes on to state that the definition of the Stefan-Boltzmann 'constant' is


 * $$\sigma = \frac{2 \pi^2 n^2 k^4}{15 c_o^2 h^2}$$

How can we reconcile the present article with that asserted 'fact'? Jdpipe (talk) 02:10, 16 June 2011 (UTC)


 * We can't reconcile, because the formula above doesn't have the right units. If you checked that before posting your comment, you would see that what you wrote doesn't make sense. I mean, you should have done that, but that's, OK. And the article states (yes I checked it), in fact, that:


 * $$\sigma = \frac{2 \pi^5 n^2 k^4}{15 c_o^2 h^3}$$


 * And that agrees with what is written in this wikipedia article (in the case of $$ n \approx 1 $$). Of course your mistake is explained by the fact that it's really difficult to read some numbers in the article.


 * I'm sorry if my reply seems rude - if that happened, I ask your apologies. 143.107.78.234 (talk) 19:39, 18 July 2011 (UTC)

Error?
Withdrawn. I missed the bar on the h-bar. Joemarasco (talk) 21:12, 1 September 2016 (UTC) Joemarasco (talk) 19:53, 4 September 2016 (UTC)

Clarification for the unsourced value "prior to 20 May 2019"
Unless I'm mistaken, CODATA publishes the constants every four years, making 2018 the most recent. The wording suggests that there was a change in 2019, but I couldn't find any source to back this up. The expression for the stefan-boltzmann constant most likely was a reference to the 2014 CODATA paper [here]. But is it even necessary to include this? Other articles such as for the Planck constant do not even mention 2014 data.  ΤheQ Editor  Talk? 01:14, 8 May 2020 (UTC)


 * The change in 2019 was the redefinition of the SI base units, which became effective as of 20 May 2019. The consequence here is that the Stefan-Boltzmann constant is now expressible as an exact value in terms of the fixed constants k, h, and c.  CODATA typically publishes all of the latest best values of the physical constants during the calendar year after those values have been determined; which, in this latest case, coincides with the effective date of the revised SI.  I'll look into (at least for now) linking the relevant date.  DWIII (talk) 00:59, 9 June 2020 (UTC)
 * Following this up, I plugged the 2019 values for h, k, and c into the formula organized as 2*pi/15*h*((pi*k/h)^2/c)^2 (thereby avoiding excessively large or small numbers) and evaluated it with unix bc set to 99 digits of precision. The first 40 places after the decimal were 0.0000000567037441918442945397099673188923..., confirming the "exact" value ending in 419... given in the article.  Wikipedia doesn't require a source for numbers obtained by straightforward calculation.  Vaughan Pratt (talk) 00:35, 14 October 2020 (UTC)
 * Incidentally those who like to do mental arithmetic will find multiplying by 5.67 easier when approximated as 5 + 2/3. For example at T = 300 K, T^4/10⁸ = 81, 5*81 = 405, and 2/3*81 = 54 for a total of 405 + 54 = 459 W/m2, a hair less than the more accurate value 459.300... Vaughan Pratt (talk) 00:44, 14 October 2020 (UTC)

Where that $$\pi^4/15$$ comes from
Since this article is mostly just a list of constants, I looked up where that "15" (or "60") comes from... So, when you integrate over all wavelengths

$$f=\int\limits_{0}^{\infty}F_\lambda\, d\lambda$$

where $$d\lambda = -[hc/kT] y^{-2} dy $$

You'll eventually get to an integral like this: $$f=\int\limits_{0}^{\infty} \frac{y^3}{e^y -1}\, dy = \frac{\pi^4}{15} \approx 6.49394 $$

... which is exactly $$\pi^4/15$$ Try it out on Wolfram Alpha... [Integrate[y^3/(-1 + E^y), {y, 0, Infinity}]

This is where I'm getting this from: http://www.hanksville.org/courseware/bb/SBLaw.html — Preceding unsigned comment added by 192.184.203.108 (talk) 09:42, 20 March 2022 (UTC)