StefanBoltzmannKonstante

The Stefan-Boltzmann constant, usually denoted by σ, is a physical constant that appears in the Stefan-Boltzmann law, relating the total radiant power emitted per unit area by a blackbody to its absolute temperature.

In the Stefan-Boltzmann law, the emissive power M of a blackbody is M = σ T^4, where T is the absolute temperature. The constant has units of W m^-2 K^-4 and a CODATA value of approximately 5.670374419 × 10^-8 W m^-2 K^-4. It can also be expressed in terms of fundamental constants as σ = (2 π^5 k_B^4) / (15 h^3 c^2), linking thermal radiation to quantum and relativistic constants.

The constant is named after Josef Stefan, who proposed the empirical law in 1879, and Ludwig Boltzmann, who provided a theoretical basis from thermodynamics and kinetic theory. Planck's radiation law later allowed a microscopic derivation of σ from Planck's constant h, Boltzmann's constant k_B, and c, the speed of light.

Applications of the Stefan-Boltzmann constant include estimating the total energy radiated by stars and planetary bodies, modeling radiative heat transfer in engineering, and serving as a key parameter in climate science and astrophysics.

The constant is related to the radiation constant a by a = 4σ/c, which appears in the expression for the energy density of blackbody radiation u = a T^4. Together with σ, these relations underpin classical blackbody theory and the Planck distribution.