Thermal Radiation
Thermal radiation is electromagnetic radiation emitted by matter as a consequence of its temperature, produced by the thermal motion of charged particles. An ideal emitter, a black body, has a spectrum given by Planck's law and determined by temperature alone; its total emitted power per unit area is σT4 (Stefan–Boltzmann law) and its spectral peak lies at wavelength λmax = b/T (Wien's displacement law). Real surfaces emit a fraction ε (the emissivity) of the black-body value.
Curious
All objects constantly emit electromagnetic radiation, because the charged particles inside them jiggle with heat. At room temperature that radiation is invisible infrared, which is what thermal cameras detect. Heat something to about 800 K and it starts to glow dull red; hotter still, it glows orange, then yellow-white. The colour of a hot object tells you its temperature, which is how astronomers measure the surface temperatures of stars (see Hertzsprung-Russell Diagram).
Thermal radiation needs no medium, which is how the Sun warms Earth across empty space (see Heat Transfer). Explaining its spectrum required the birth of quantum theory in 1900 (see Max Planck).
Exploring
| Law | Statement | Year |
|---|---|---|
| Kirchhoff's law | Emissivity equals absorptivity at each wavelength (equilibrium) | 1859 |
| Stefan–Boltzmann law | Emitted power per area = εσT4 | 1879 / 1884 |
| Wien's displacement law | λmaxT = 2.898×10−3 m K | 1893 |
| Planck's law | Full spectrum of black-body radiation | 1900 |
Deep Dive
Planck's law. The spectral radiance is Bλ(T) = (2hc²/λ5)/(ehc/λkBT − 1). Classical equipartition (the Rayleigh–Jeans law) instead predicted radiance growing without limit at short wavelengths, the “ultraviolet catastrophe” (see Equipartition Theorem). Planck's assumption that oscillator energies come in units of hf removed the divergence; integrating his law gives the Stefan–Boltzmann constant σ = 2π5kB4/(15c²h³) = 5.670×10−8 W m−2 K−4, and differentiating it gives Wien's law.
Cosmic test. The COBE FIRAS instrument (1990) measured the cosmic microwave background spectrum as a black body at 2.725 K with deviations below about 50 parts per million, the most precise black-body spectrum ever recorded (see Cosmic Microwave Background). Stars are only approximate black bodies; their spectra show absorption lines and their “effective temperature” is defined through the Stefan–Boltzmann law (see Red Giants).
Greenhouse effect. Earth's surface emits mostly between about 5 and 50 μm, where water vapour and carbon dioxide absorb strongly; these gases re-emit infrared both upward and downward, raising the surface temperature above the 255 K radiative estimate. The physics of this effect is well established; projections of future warming depend on feedbacks, especially clouds, that carry larger uncertainties, as assessed by the IPCC.
Concept Relationship Map
Requires: temperature, electromagnetic waves
Enables: quantum theory (Planck), stellar temperatures, Earth's energy balance
Commonly confused with: radioactivity (unrelated nuclear process)
Sources
- Planck, M. (1901). Annalen der Physik, 309, 553–563.
- Mather, J.C., et al. (1994). “Measurement of the Cosmic Microwave Background Spectrum by the COBE FIRAS Instrument.” The Astrophysical Journal, 420, 439–444.
- Prša, A., et al. (2016). “Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3.” The Astronomical Journal, 152, 41.