Page 289 - Fundamentals of Air Pollution

I. Sun, Atmosphere System, and Heat Balance 245

in nature, the properties describable by theory are useful for comparison
with materials found in the real world. The amount of radiation, or radiant
flux over all wavelengths (F), from a unit area of a blackbody is dependent
on the temperature of that body and is given by the Stefan-Boltzmann
law:

1J
where cr is the Stefan-Boltzmann constant and equals 8.17 x 10 cal
2 1 4
cm" muT deg~ and T is the temperature in degrees K. Radiation from
a blackbody ceases at a temperature of absolute zero, 0 K.
In comparing the radiative properties of materials to those of a blackbody,
the terms absorptivity and emissivity are used. Absorptivity is the amount
of radiant energy absorbed as a fraction of the total amount that falls on
the object. Absorptivity depends on both frequency and temperature; for
a blackbody it is 1. Emissivity is the ratio of the energy emitted by an object
to that of a blackbody at the same temperature. It depends on both the
properties of the substance and the frequency. Kirchhoff's law states that
for any substance, its emissivity at a given wavelength and temperature
equals its absorptivity. Note that the absorptivity and emissivity of a given
substance may be quite variable for different frequencies.
As seen in Eq. (17-1), the total radiation from a blackbody is dependent
on the fourth power of its absolute temperature. The frequency of the
maximum intensity of this radiation is also related to temperature through
Wien's displacement law (derived from Planck's law):

l
l
l
where frequency v is in s and the constant is in s K .
The radiant flux can be determined as a function of frequency from
Planck's distribution law for emission:

where

and

The radiation from a blackbody is continuous over the electromagnetic
spectrum. The use of the term black in blackbody, which implies a particular
color, is quite misleading, as a number of nonblack materials approach
blackbodies in behavior. The sun behaves almost like a blackbody; snow
radiates in the infrared nearly as a blackbody. At some wavelengths, water