Thermal Radiation and the Stefan-Boltzmann Law

Every body, whatever its temperature, emits thermal radiation: electromagnetic waves due to the agitation of its charges. At ordinary temperatures, this radiation is mostly infrared (invisible); it is what a thermal camera detects. The hotter a body is, the more it radiates — and at shorter wavelengths: a heated metal goes from dull red to white.

The power radiated by a surface follows the Stefan-Boltzmann law:

   P = σ · A · T⁴        (T in kelvins, σ = 5.67 x 10^-8 W/m²·K⁴)

The crucial point is the fourth power: temperature appears to the power 4. A small change in T changes the radiation enormously.

   if T doubles (x2)   ->  P is multiplied by 2⁴ = 16
   if T triples (x3)   ->  P is multiplied by 3⁴ = 81

This explosive dependence explains why very hot objects (stars, light bulb filaments) radiate colossal amounts of power, and why the equilibrium temperature of a planet depends so finely on the sunlight it receives. Careful: T is in kelvins, never in degrees Celsius — the law only makes sense on the absolute scale.

Every body emits, but every body also absorbs the radiation it receives. An object is in thermal equilibrium when it radiates as much as it absorbs. It is this balance between radiation received (from the Sun) and radiation emitted (into space) that sets the Earth's average temperature — and that the greenhouse effect upsets by trapping part of the infrared radiation emitted by the ground.