<sect1 id="ai-blackbody">
<sect1info>

<author>
<firstname>Jasem</firstname>
<surname>Mutlaq</surname>
<affiliation><address>
<email>mutlaqja@ku.edu</email>
</address></affiliation>
</author>
</sect1info>

<title>Blackbody Radiation</title>

<para>
A <firstterm>blackbody</firstterm> refers to an idealized concept of
an object that emits <firstterm>thermal radiation</firstterm>
perfectly.  Since emission of light and absorption of light are
inverse processes, a perfect emitter of light would also need to be a
perfect absorber of light.  Therefore, at room temperature, such an
object would appear to be perfectly black.  Hence the term
<emphasis>blackbody</emphasis>.
</para>

<para>
All objects emit thermal radiation (as long as their temperature is
above Absolute Zero, or -273.15 degrees Celsius), but no object is
really a perfect emitter; rather, they are better at
emitting/absorbing some wavelengths of light than others.  These
uneven efficiencies make it difficult to study the interaction of
light, heat and matter using normal objects.
</para>

<para>
Fortunately, it is possible to construct a nearly-perfect blackbody.  
Construct a box made of a thermally conductive material, such as
metal.  The box should be completely closed on all sides, so that the
inside forms a cavity that does not receive light from the
surroundings.  Then, make a very small hole somewhere on the box.
The light coming out of this hole will almost perfectly resemble the
light from an ideal blackbody, for the temperature of the air inside
the box.
</para>

<para>
At the beginning of the 20th century, scientists Lord Rayleigh,
Wilhelm Wein, and Max Planck (among others) studied the blackbody
radiation using such a device.  After much work, Planck was able to
perfectly describe the intenisty of light emitted by a blackbody as a
function of wavelength.  Furthermore, he was able to describe how this
spectrum would change as the temperature changed.  Planck's work on
blackbody radiation is one of the areas of physics that led to the
foundation of the wonderful science of Quantum Mechanics, but that is
unfortunately beyond the scope of this article.
</para>

<para>
What Planck and the others found was that as the temperature of a 
blackbody increases, the total amount of light emitted per 
second increases, and the wavelength of the spectrum's peak shifts to
bluer colors (see Figure 1).
</para>

<mediaobject>
<imageobject>
<imagedata fileref="graph1.png" format="PNG"/>
</imageobject>
<textobject><phrase>Figure 1</phrase></textobject>
<caption><para>The spectrum of three blackbodies at different temperatures.</para></caption>
</mediaobject>

<para>
Wilhelm Wein quantified the relationship between blackbody
temperature and the wavelength of the spectral peak with the 
following equation:
</para>

<para>
lamdba(max} * T = 0.29 cm K
</para>

<para>
where T is the temperature in Kelvin.  Wein's law (also known as
Wein's displacement law) can be stated in words as "the
wavelength of maximum emission from a blackbody is inversely
proportional to its temperature".  This makes sense;
shorter-wavelength (higher-frequency) light corresponds to
higher-energy photons, which you would expect from a
higher-temperature object.
</para>

<para>
For example, the sun has an average temperature of 5800 K with a
wavelength of maximum emission equal to 
lambda(max) = 0.29 cm / 5800 = 500 nm. This wavelengths falls in the
green region of the visible light spectrum, but the sun's continuum
radiates photons both longer and shorter than lambda(max) and the
human eyes perceives the sun's color as white.
</para>

<para>
In 1879, Austrian physicist Stephan Josef Stefan showed that
the <firstterm>luminosity</firstterm>, L, of
a black body is proportional to the 4th power of its temperature T.
</para>

<para>
L = A * alpha * T^4
</para>

<para>
where A is the surface area, alpha is a constant of proportionality,
and T is the temperature in Kelvin. That is, if we double the
temperature (e.g. 1000 K to 2000 K) then the total energy radiated
from a blackbody increase by a
factor of 2^4 or 16.
</para>

<para>
Five years later, Austrian physicist Ludwig Boltzman derived the same
equation and is now known as he Stephan-Boltzman law. If we assume a
spherical star with radius R, then the luminosity of such a star is
</para>

<para>
L = 4*PI*R^2 * Alpha * T^4
</para>

<para>
where R is the star radius in cm, and the alpha is the
Stephan-Boltzman constant, which has the value: Alpha = 5.670 * 10^-5
erg/s/cm^2/K^-4.
</para>
</sect1>