All objects emit energy in an amount that depends on their temperature, as described by
the Stefan-Boltzmann law:
E = εσK4 W/m2
where E is radiated energy in units of W/m2, ε is the emissivity of the object (a
dimensionless quantity with a value
between 0 and 1),
K is temperature in Kelvins (add 273.15 to convert
°C to Kelvins), and
σ is the Stefan-Boltzmann constant:
σ = 5.6704 x 10-8 W-m-2-K-4
The Stefan-Boltzmann law was originally derived for perfect "black bodies" that absorb all incident
radiation. Perfect black bodies have an emissivity of 1, by definition. Black bodies
aren't actually "black," because they radiate energy too, sometimes in the visible spectrum.
The sun, for example, behaves like a black body even though it certainly doesn't look
black. Earth is considered to be a perfect black body, too. Its colors
as viewed from space are due to reflected sunlight, as it radiates at wavelengths
far beyond the visible part of the spectrum.
Many objects, including much of Earth's surface, behave very nearly like a black body. An emissivity of 0.95 is often
used as a representative value. For example, non-contact IR thermometers such as shown in the photo
work by detecting radiation from a target object and calculating the corresponding temperature. They typically assume
an emissivity of 0.95.
Wien's law gives a related calculation, the wavelength at which the maximum energy is
emitted for an object at a particular temperature. This is an important value because it
explains why, in studying Earth's radiative balance, the energy flow is separated into
shortwave and longwave components. The shortwave component is due to incoming solar
radiation. The sun has a radiating temperature of about 5800K and a peak emission around 0.5 μm (500 nm), corresponding roughly to the peak
sensitivity
of the
human eye. The Earth radiates to space at a temperature of about 27°C, or about
300K, at a wavelength of around 10 μm (10,000 nm). The total energy emission spectra of
these two objects basically do not overlap -- that is, there is essentially no solar
radiation at the "long" end of the solar emission spectrum that overlaps radiation at the "short"
end of Earth's emission spectrum. You can calculate
these
wavelength values for yourself by selecting the appropriate temperature unit button Kelvin or Celsius,
and inputting the temperature. Note that the sun emits a prodigious amount of energy --
more than 64 MW/m2!
The Stefan-Boltzmann law is based on a quantum theory of electromagnetic radiation, first
expressed in Planck's
law, published in 1901. It successfully describes the relationship between temperature and radiation without the
limitations of earlier theories based on classical physics. Because this equation is so important, both historically and practically,
there is a great deal of information available online.
