Stefan-Boltzmann Law

The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body per unit time is directly proportional to the fourth power of the black body's absolute temperature. Austrian physicist Josef Stefan established the relationship experimentally in 1879, and his student Ludwig Boltzmann derived it theoretically in 1884 from thermodynamic principles, giving the law its combined name. The relationship explains why a hotter object radiates disproportionately more energy than a cooler one, since doubling an object's absolute temperature increases its radiated power sixteenfold, and it is applied throughout astrophysics to estimate the luminosity of stars from their surface temperature and radius, as well as in engineering calculations of radiative heat transfer. The law was later shown to follow as a specific consequence of Max Planck's more general 1900 law of black-body radiation, once Planck's formula is integrated over all wavelengths.