Editing Josef Stefan (section)

==Work==
Stefan published nearly 80 scientific articles, mostly in the Bulletins of the Vienna Academy of Sciences.<ref>{{Cite journal|title=Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien in WikiSource|url=https://de.wikisource.org/wiki/Sitzungsberichte_der_Kaiserlichen_Akademie_der_Wissenschaften_in_Wien_%E2%80%93_mathematisch-naturwissenschaftliche_Classe/Inhalt|volume=e.g. Bd. 027, 1857}}</ref> He is best known for originating [[Stefan's law]] in 1879, a [[physical law|physical]] [[power law]] stating that the total [[radiation]] from a [[black body]] is proportional to the fourth power of its [[thermodynamic temperature]] ''T'':

:<math> j^{\star} = \sigma T^{4}</math>

He derived this law from the measurements of the French physicists [[Pierre Louis Dulong|Dulong]] and [[Alexis Thérèse Petit|Petit]]. As both incident radiation and blackbody emission are always equal, this equation applies equally to the temperature of any ideal body subject to incident radiation across its surface. In 1884, the law was extended to apply to grey-body emissions by Stefan's student [[Ludwig Boltzmann]] and hence is known as [[Stefan–Boltzmann law]]. Boltzmann treated a [[heat engine]] with light as a working matter. This law is the only physical law of nature named after a Slovene physicist. Today, the law is derived from [[Planck's law]] of black-body radiation:

:<math> j^{\star} = \int_{0}^{\infty} \left( {dj^{\star}\over d\lambda} \right) d\lambda </math>

With his law, Stefan determined the temperature of the [[Photosphere#Sun|Sun's surface]], which he calculated to be {{convert|5430|°C}}. This was the first sensible value for the temperature of the Sun.

Stefan provided the first measurements of the [[thermal conductivity]] of gases, treated [[evaporation]], and among others studied [[diffusion]], [[heat conduction]] in [[fluid]]s. For his treatise on [[optics]], the University of Vienna bestowed the [[Lieben Prize]] on him. Because of his early work in calculating evaporation and diffusion rates, flow from a droplet or particle that is induced by evaporation or [[sublimation (phase transition)|sublimation]] at the surface is now called the [[Stefan flow]].

Very important are also his [[Electromagnetism|electromagnetic]] equations, defined in [[vector (geometry)|vector]] notation, and works in the [[kinetic theory of gases|kinetic theory]] of heat. Stefan was among the first physicists in Europe who fully understood [[James Clerk Maxwell|Maxwell's]] [[electromagnetism|electromagnetic theory]] and one of the few outside England who expanded on it. He calculated [[inductance|inductivity]] of a [[inductor|coil]] with a quadratic cross-section, and he corrected Maxwell's miscalculation. He also researched a phenomenon called the [[skin effect]], where high-frequency [[electric current]] is greater on the surface of a [[Conductor (material)|conductor]] than in its interior.

In mathematics, the [[Stefan problem]]s or Stefan's tasks with movable boundary are well known. The problem was first studied by [[Gabriel Lamé|Lamé]] and [[Benoît Paul Émile Clapeyron|Clapeyron]] in 1831. Stefan solved the problem when he was calculating how quickly a layer of [[ice]] on water grows ([[Stefan's equation]]<ref>{{Cite book|last=Shumon Koga, Miroslav Krstic|title=Materials Phase Change PDE Control & Estimation|chapter=Phase Change Model: Stefan Problem|chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-58490-0_1|website=Materials Phase Change PDE Control & Estimation |series=Systems & Control: Foundations & Applications|year=2020|pages=1–13|publisher=Springer |doi=10.1007/978-3-030-58490-0_1|isbn=978-3-030-58490-0|s2cid=229250452 }}</ref>).