Black-Body Radiation
A black body is the perfect absorber — it takes in every photon that strikes it, no reflection, no transmission, only appetite. That appetite comes with a tax. When a thing warms up, it cannot keep the energy forever, so it lets it escape as thermal radiation: light emitted purely because of temperature.
What makes a black body special is that its glow depends only on temperature, nothing else. The material, the shape, the size — none of it matters. Two identical cavities at the same temperature radiate the same spectrum, whether one is made of iron and the other of glass. The spectrum itself is universal.
The total power radiated per unit surface area follows the Stefan-Boltzmann law, proportional to the fourth power of absolute temperature. Double the temperature and you get sixteen times the power. This is not a rough approximation — it is exact for an ideal black body. The proportionality constant, σ, has been measured to extraordinary precision and is known to more significant figures than most fundamental constants.
The spectrum has a characteristic shape. It rises from zero at zero frequency, peaks at some wavelength, and falls off exponentially toward the high-frequency end. The peak wavelength shifts inversely with temperature, which is why hot objects glow red, then yellow, then white, then blue as they get hotter. The Sun, at roughly 5800 kelvin, peaks in the visible range. A human body at 310 kelvin peaks far in the infrared, where night-vision cameras see perfectly.
The emissivity of a real material tells you how close it comes to a black body. A perfect black body has emissivity one. Real things are worse. Polished metals can have emissivity below 0.1. Lampblack, the coating on old photomicrographs, gets down near 0.96. Engineering practice treats many surfaces as gray bodies — constant emissivity across all wavelengths — which is approximately correct for rough calculations but fails spectacularly when precision matters.
Black-body radiation played the decisive role in the birth of quantum mechanics. Classical physics predicted that a black body should radiate infinite power at short wavelengths — the ultraviolet catastrophe. The fix required abandoning the classical assumption that energy is continuously divisible. Max Planck's resolution in 1900 introduced the constant h, now known as Planck's constant, which sets the fundamental grain size of energy exchange.
The concept matters beyond historical interest. Cosmology gives us the most perfect black body in the universe: the cosmic microwave background, a relic from 380,000 years after the Big Bang. At 2.725 kelvin, its spectrum matches the black-body curve so precisely that any deviation would have been detectable — and none exists. Infrared thermometers, pyrometers, and stellar classification all rest on black-body physics. The calibration of temperature itself owes a debt to this phenomenon.
A cavity with a small hole is the experimental realization of a black body. Radiation entering the hole bounces around inside, being absorbed with each reflection, with negligible chance of re-emergence. The light leaking out through the hole has the black-body spectrum corresponding to the cavity temperature. This is not a theoretical abstraction — it is the laboratory device that generated the data forcing physics to change.