Stefan–Boltzmann Law

Astrophysics · 1879

Equation: F = σT⁴; L = 4πR²σT⁴ for a sphere of radius R
Field: Astrophysics
Named After: Josef Stefan · Ludwig Boltzmann
Year: 1879

Symbols

F the power radiated per unit area by a black body · σ the Stefan–Boltzmann constant · T absolute temperature · R the radius of the star · L its luminosity, the same law over the whole sphere · a real surface radiates εF, with emissivity ε below 1 — about 0.8 for oxidised steel

Significance

Power radiated per unit area goes as the fourth power of temperature, so a modestly hotter body blazes enormously brighter — and over a sphere it gives a star's brightness from its size and temperature alone, which is how astronomers weigh a stellar output across light-years. Two cautions travel with it. The T of a star is an effective temperature: the temperature of the black body that would radiate the same, not a reading from anywhere in particular. And nothing real is a black body — multiply by emissivity, which is where the same equation stops being about stars and starts being about why a steel bar at 1,200 °C sheds a quarter of a megawatt from every square metre and cools while you look at it.