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: : 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: : j^{\star} = \int_{0}^{\infty} \left( {dj^{\star}\over d\lambda} \right) d\lambda With his law, Stefan determined the temperature of the
Sun's surface, which he calculated to be . 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 ==