What a blackbody is
A blackbody is an ideal object that absorbs all the radiation that falls on it and emits thermal radiation that depends only on its temperature. Stars, glowing metal, the filament of an old light bulb and even your own skin behave approximately like blackbodies.
Two laws describe that radiation.
Wien’s displacement law
The wavelength at which a blackbody emits the most is inversely proportional to its absolute temperature:
λmax = 2,897,771.955 nm·K ÷ T
Hotter objects peak at shorter wavelengths, which is why heated metal glows red, then orange, then white as it heats up. In frequency terms, the peak is at about 5.879 × 10¹⁰ Hz per kelvin; this frequency peak is not at the same place in the spectrum as the wavelength peak, because the two spectra are plotted per unit of different quantities.
Stefan-Boltzmann law
The power radiated per square meter of surface is:
M = ε × σ × T⁴
with σ = 5.670374419 × 10⁻⁸ W/m²·K⁴ and ε the emissivity, 1 for a perfect blackbody. Because of the fourth power, doubling the absolute temperature multiplies the radiated power by 16.
Worked example: the Sun
The Sun’s surface is about 5,778 K:
| Result | Value |
|---|---|
| Peak wavelength | 501.5 nm, green light |
| Power per square meter | 63.2 million W/m² |
| Peak frequency | about 339.7 THz (3.40 × 10¹⁴ Hz) |
Even though it peaks in green, the Sun looks white, because it emits strongly across the whole visible range.
Other examples
| Object | Temperature | Peak wavelength |
|---|---|---|
| Human skin | about 307 K (34 °C) | about 9.4 µm, infrared |
| Earth’s surface | about 288 K | about 10 µm |
| Incandescent filament | about 2,700 K | about 1,070 nm, near infrared |
| Hot blue star | 20,000 K | about 145 nm, ultraviolet |
Thermal cameras work in the 8 to 14 µm band precisely because objects near room temperature radiate most there.
Emissivity
Real surfaces radiate less than a blackbody at the same temperature. Typical emissivities are about 0.95 for matte black paint, 0.98 for skin and below 0.1 for polished aluminum. This is why shiny surfaces fool infrared thermometers.
Tips
- Enter temperatures in kelvin, Celsius or Fahrenheit; the laws themselves always use kelvin.
- The radiated power is the gross emission. The net heat loss of an object also depends on what it receives from its surroundings.