Blackbody radiation
A blackbody is an ideal absorber and emitter of electromagnetic radiation. Its spectrum is not a single colour or wavelength: it is a continuous distribution whose shape depends only on temperature. Heating the body does two things at once—the whole spectrum grows stronger, and its peak moves toward shorter wavelengths.
A blackbody is a model, not a black-painted object
An ideal blackbody absorbs all incident electromagnetic radiation, whatever its wavelength or direction. At thermal equilibrium it also provides the reference spectrum for thermal emission. A small hole in an opaque cavity is a useful physical approximation: radiation entering the hole is reflected many times and is very unlikely to escape again.
The word black describes perfect absorption, not the colour seen when the object is hot. A sufficiently hot blackbody can glow red, white or bluish because it emits strongly in the visible range.
Temperature reshapes the entire spectrum
At every finite temperature, a blackbody emits over a broad range of wavelengths. The curve has one maximum when spectral power is plotted per unit wavelength. As temperature rises, the curve becomes higher at every wavelength and the maximum shifts left, toward shorter wavelengths.
Wien's displacement law: λmaxT = b
b ≈ 2.898 × 10−3 m·K. Use absolute temperature in kelvins.
Wien's law describes the wavelength at the peak of the spectrum when it is expressed per unit wavelength. It does not mean that the body emits only at λmax.
Explore the temperature
Move the temperature and compare two predictions at once. The peak wavelength comes from Wien's law; the total emitted power per square metre follows the Stefan–Boltzmann law.
Total thermal emission rises as T⁴
M = σT4
For an ideal blackbody, M is the total radiant power emitted per unit surface area and σ = 5.670 × 10−8 W m−2 K−4.
The fourth power makes temperature extremely influential. If two black surfaces have the same area and one has twice the absolute temperature, it emits 24 = 16 times as much total power per unit area. Real surfaces are often described by an emissivity ε less than 1, but the ideal blackbody corresponds to ε = 1.
This expression describes emitted radiation. For net radiative heat exchange with surroundings, radiation arriving from the surroundings must also be considered.
Why classical physics failed—and Planck's idea worked
Classical models could not reproduce the measured blackbody spectrum at short wavelengths. Planck obtained the correct spectral shape by treating energy exchange between matter and electromagnetic modes as quantized, in amounts related to frequency by E = hf.
The full Planck distribution predicts the broad spectrum, its temperature dependence and, as consequences, the Wien and Stefan–Boltzmann laws. The historical importance is therefore deeper than fitting one curve: blackbody radiation was one of the observations that forced physics toward quantum ideas.
Worked examples
1. Peak wavelength of a Sun-like surface
Estimate λmax for T = 5800 K.
Solution
λmax = b/T = (2.898 × 10−3)/5800 = 5.00 × 10−7 m = 500 nm. The wavelength peak lies in the visible range.
2. A room-temperature object
Find the peak wavelength for T = 300 K.
Solution
λmax = (2.898 × 10−3)/300 = 9.66 × 10−6 m = 9.66 μm. That is infrared, which is why an object can radiate thermally without visibly glowing.
3. Doubling absolute temperature
Two ideal blackbody surfaces have equal area. Surface B is at twice the Kelvin temperature of surface A. Compare their total emitted powers.
Solution
PB/PA = (2T)4/T4 = 24 = 16. At the same time, Wien's law predicts that B's peak wavelength is half that of A.