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170 lines
5.0 KiB
170 lines
5.0 KiB
<sect1 id="ai-blackbody">
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<sect1info>
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<author>
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<firstname>Jasem</firstname>
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<surname>Mutlaq</surname>
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<affiliation><address>
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</address></affiliation>
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</author>
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</sect1info>
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<title>Blackbody Radiation</title>
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<indexterm><primary>Blackbody Radiation</primary>
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<seealso>Star Colors and Temperatures</seealso>
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</indexterm>
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<para>
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A <firstterm>blackbody</firstterm> refers to an opaque object that
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emits <firstterm>thermal radiation</firstterm>. A perfect
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blackbody is one that absorbs all incoming light and does not
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reflect any. At room temperature, such an object would
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appear to be perfectly black (hence the term
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<emphasis>blackbody</emphasis>). However, if heated to a high
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temperature, a blackbody will begin to glow with
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<firstterm>thermal radiation</firstterm>.
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</para>
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<para>
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In fact, all objects emit thermal radiation (as long as their
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temperature is above Absolute Zero, or -273.15 degrees Celsius),
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but no object emits thermal radiation perfectly; rather, they are
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better at emitting/absorbing some wavelengths of light than others.
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These uneven efficiencies make it difficult to study the interaction
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of light, heat and matter using normal objects.
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</para>
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<para>
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Fortunately, it is possible to construct a nearly-perfect blackbody.
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Construct a box made of a thermally conductive material, such as
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metal. The box should be completely closed on all sides, so that the
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inside forms a cavity that does not receive light from the
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surroundings. Then, make a small hole somewhere on the box.
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The light coming out of this hole will almost perfectly resemble the
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light from an ideal blackbody, for the temperature of the air inside
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the box.
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</para>
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<para>
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At the beginning of the 20th century, scientists Lord Rayleigh,
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and Max Planck (among others) studied the blackbody
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radiation using such a device. After much work, Planck was able to
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empirically describe the intensity of light emitted by a blackbody as a
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function of wavelength. Furthermore, he was able to describe how this
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spectrum would change as the temperature changed. Planck's work on
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blackbody radiation is one of the areas of physics that led to the
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foundation of the wonderful science of Quantum Mechanics, but that is
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unfortunately beyond the scope of this article.
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</para>
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<para>
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What Planck and the others found was that as the temperature of a
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blackbody increases, the total amount of light emitted per
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second increases, and the wavelength of the spectrum's peak shifts to
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bluer colors (see Figure 1).
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</para>
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<para>
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<mediaobject>
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<imageobject>
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<imagedata fileref="blackbody.png" format="PNG"/>
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</imageobject>
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<caption><para><phrase>Figure 1</phrase></para></caption>
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</mediaobject>
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</para>
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<para>
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For example, an iron bar becomes orange-red when heated to high temperatures and its color
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progressively shifts toward blue and white as it is heated further.
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</para>
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<para>
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In 1893, German physicist Wilhelm Wien quantified the relationship between blackbody
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temperature and the wavelength of the spectral peak with the
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following equation:
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</para>
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<para>
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<mediaobject>
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<imageobject>
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<imagedata fileref="lambda_max.png" format="PNG"/>
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</imageobject>
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</mediaobject>
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</para>
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<para>
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where T is the temperature in Kelvin. Wien's law (also known as
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Wien's displacement law) states that the
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wavelength of maximum emission from a blackbody is inversely
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proportional to its temperature. This makes sense;
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shorter-wavelength (higher-frequency) light corresponds to
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higher-energy photons, which you would expect from a
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higher-temperature object.
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</para>
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<para>
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For example, the sun has an average temperature of 5800 K, so
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its wavelength of maximum emission is given by:
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<mediaobject>
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<imageobject>
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<imagedata fileref="lambda_ex.png" format="PNG"/>
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</imageobject>
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</mediaobject>
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</para>
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<para>
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This wavelengths falls in the
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green region of the visible light spectrum, but the sun's continuum
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radiates photons both longer and shorter than lambda(max) and the
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human eyes perceives the sun's color as yellow/white.
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</para>
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<para>
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In 1879, Austrian physicist Stephan Josef Stefan showed that
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the luminosity, L, of a black body is proportional to the 4th power of its temperature T.
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</para>
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<para>
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<mediaobject>
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<imageobject>
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<imagedata fileref="luminosity.png" format="PNG"/>
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</imageobject>
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</mediaobject>
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</para>
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<para>
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where A is the surface area, alpha is a constant of proportionality,
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and T is the temperature in Kelvin. That is, if we double the
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temperature (e.g. 1000 K to 2000 K) then the total energy radiated
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from a blackbody increase by a factor of 2^4 or 16.
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</para>
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<para>
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Five years later, Austrian physicist Ludwig Boltzman derived the same
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equation and is now known as the Stefan-Boltzman law. If we assume a
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spherical star with radius R, then the luminosity of such a star is
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</para>
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<para>
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<mediaobject>
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<imageobject>
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<imagedata fileref="luminosity_ex.png" format="PNG"/>
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</imageobject>
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</mediaobject>
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</para>
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<para>
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where R is the star radius in cm, and the alpha is the
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Stefan-Boltzman constant, which has the value:
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<mediaobject>
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<imageobject>
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<imagedata fileref="alpha.png" format="PNG"/>
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</imageobject>
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</mediaobject>
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</para>
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</sect1>
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