Physics
Stefan-Boltzmann Law
Quick fact
The Sun's surface temperature is about 5,500°C, and its total power output is 3.8×10²⁶ watts – a direct consequence of the Stefan-Boltzmann law.
Why this is interesting
Why does a hot piece of metal glow red, then white as it gets hotter? The answer lies in a simple yet powerful law that governs how all objects radiate energy.
Read the full explanation
Understanding Stefan-Boltzmann Law
Think of any object at a non-zero temperature: its atoms and molecules are in constant motion, and they emit electromagnetic radiation. The Stefan-Boltzmann law tells us exactly how much energy is radiated per unit area. It says that the power (energy per second) emitted is proportional to the fourth power of the object's absolute temperature (in kelvin). This means if you double the temperature, the radiated power increases by a factor of 16 – not just double. That's why a campfire feels so warm even at a distance: the fire's high temperature dramatically boosts the radiation. For a perfect emitter (a blackbody), the formula is P = σT⁴, where σ (sigma) is a constant. Real objects emit somewhat less, described by their emissivity factor.
A deeper explanation
The Stefan-Boltzmann law emerges from integrating Planck's law of blackbody radiation over all wavelengths. Planck's law gives the spectral radiance of a blackbody; summing over all wavelengths yields the total radiance, which is proportional to T⁴. This result was originally discovered experimentally by Josef Stefan and later derived theoretically by Ludwig Boltzmann using thermodynamic reasoning. The law is fundamental because it links a macroscopic property (temperature) directly to emitted energy without needing details about atomic structure. It governs everything from the glow of molten steel to the energy output of stars. In practice, the law is used with an emissivity factor (ε) for real surfaces: P = εσT⁴. Applications include designing radiators, measuring temperatures via infrared sensors, and calculating the Earth's energy balance—where it shows why a small temperature change can significantly alter the planet's heat budget.