Josef Stefan

Work

Stefan published nearly 80 scientific articles, mostly in the Bulletins of the Vienna Academy of Sciences. He is best known for originating Stefan's law in 1879, a physical power law stating that the total radiation from a black body is proportional to the fourth power of its thermodynamic temperature T:

${\displaystyle j^{\star }=\sigma T^4}$

He derived this law from the measurements of the French physicists Dulong and 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:

${\displaystyle j^{\star }={\int }_0^{\mathrm{\infty }}\left(\frac{d{j}^{\star }}{d\lambda }\right)d\lambda }$

With his law, Stefan determined the temperature of the Sun's surface, which he calculated to be 5,430 °C (9,810 °F). 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 fluids. 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 at the surface is now called the Stefan flow.

Very important are also his electromagnetic equations, defined in vector notation, and works in the kinetic theory of heat. Stefan was among the first physicists in Europe who fully understood Maxwell's electromagnetic theory and one of the few outside England who expanded on it. He calculated inductivity of a 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 than in its interior.

In mathematics, the Stefan problems or Stefan's tasks with movable boundary are well known. The problem was first studied by Lamé and Clapeyron in 1831. Stefan solved the problem when he was calculating how quickly a layer of ice on water grows (Stefan's equation).

Eponymous terms

Several concepts in physics and mathematics are named after Joseph Stefan:

• Stefan–Boltzmann law
• Stefan–Boltzmann constant σ
• Stefan adhesion
• Stefan problem
• Stefan's equation
• Stefan's formula
• Stefan flow
• Stefan number
• Stefan tube
• Maxwell–Stefan diffusion

The Jožef Stefan Institute, Slovenia's premier scientific establishment, is also named after him, and also:

• Stefan (crater) on the Moon