Planck's Law - Introduction

Introduction

Planck's law describes how much energy objects radiate, and more specifically how much energy of each frequency is radiated. It quantifies how objects at low temperatures radiate very little, hot objects glow a dull red and emit a perceptible amount of heat, and very hot objects (such as the sun) are dazzlingly bright yellow or blue-white. The law gives the power radiated normally from a unit area of the radiator into unit solid angle within a frequency band of unit width centered on frequency ν. As such the spectral radiance B_ν(T) has units of W·m−2·sr−1·Hz−1 when stated in SI units.

This nominal meaning is however inaccurate because the radiation varies with both angle and frequency. It is made precise by shrinking unit area, unit solid angle, and unit bandwidth to their infinitesimal counterparts dA, dΩ, and dν. The infinitesimal power radiated normally from a surface element dA into solid angle dΩ within a band of width dν is then given by B_ν(T) dA dΩ dν. The total radiated power over any region is obtained by integration over that region with respect to those three quantities.

Much as the thermodynamics of ordinary gases composed of molecules can be understood using statistical mechanics, Planck's law can be derived by viewing the radiation as a gas of massless bosons (such as photons) in thermal equilibrium. If the temperature is changed, photons are created or annihilated in the right numbers and with the right energies to fill the cavity with a Planck distribution at the new temperature, and the pressure and energy density of a photon gas at equilibrium are entirely determined by the temperature. This is unlike the case for material gases, for which the pressure and energy density depend on the total number of particles and their properties, such as mass. In this way the Planck distribution arises as a limit of the Bose–Einstein distribution, the energy distribution describing bosons in thermodynamic equilibrium.

Radiation will obey Planck's law inside a cavity with opaque walls held at some fixed temperature, or near the surface of a black body. The radiation is isotropic, homogeneous, unpolarized, and incoherent, and the Planck distribution is the unique distribution for electromagnetic radiation in thermodynamic equilibrium. Uniqueness means that at a given temperature, all sealed cavities will contain the same spectrum of radiation, regardless of the material their walls are composed of.