Stefan–Boltzmann lawlaw

Imagine a stove: the stronger you heat it, the more heat it radiates — that's intuitive. But the Stefan–Boltzmann law says that the radiated power increases not just a lot, but as the fourth power of temperature! That is, if you heat an iron from 300°C to 600°C (twice as hot on the absolute scale), it will radiate 16 times more heat. Analogy: it's like having a garden hose — you turn the tap slightly, and the water pressure increases dramatically. So it is with light and heat from a heated body.

The Stefan–Boltzmann law was established empirically by Josef Stefan in 1879 from the analysis of experiments by Dulong and Petit, and five years later Ludwig Boltzmann gave a theoretical derivation from thermodynamics and Maxwell's electromagnetic theory, linking radiation pressure to energy density. The essence is simple: the total energy emitted by a unit area of a black body per unit time is proportional to the fourth power of its absolute temperature. This power-law dependence works throughout the Universe — from a candle flame to giant stars.

Stefan–Boltzmann law: the total radiant exitance (integrated flux of radiation per unit area) of a black body is j = σ T^4, where σ ≈ 5.67×10⁻⁸ W/(m²·K⁴) is the Stefan–Boltzmann constant. The law was empirically found by J. Stefan in 1879 and theoretically justified by L. Boltzmann in 1884 based on classical thermodynamics and electrodynamics, using the relationship between radiation pressure and energy density. In modern physics, the law is derived from Planck's distribution by integrating over all frequencies, which automatically gives an expression for σ in terms of fundamental constants.