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0001 <sect1 id="ai-blackbody">
0003 <sect1info>
0005 <author>
0006 <firstname>Jasem</firstname>
0007 <surname>Mutlaq</surname>
0008 <affiliation><address>
0009 </address></affiliation>
0010 </author>
0011 </sect1info>
0013 <title>Blackbody Radiation</title>
0014 <indexterm><primary>Blackbody Radiation</primary>
0015 <seealso>Star Colors and Temperatures</seealso>
0016 </indexterm>
0018 <para>
0019 A <firstterm>blackbody</firstterm> refers to an opaque object that
0020 emits <firstterm>thermal radiation</firstterm>.  A perfect
0021 blackbody is one that absorbs all incoming light and does not
0022 reflect any.  At room temperature, such an object would
0023 appear to be perfectly black (hence the term
0024 <emphasis>blackbody</emphasis>).  However, if heated to a high
0025 temperature, a blackbody will begin to glow with
0026 <firstterm>thermal radiation</firstterm>.
0027 </para>
0029 <para>
0030 In fact, all objects emit thermal radiation (as long as their
0031 temperature is above Absolute Zero, or -273.15 degrees Celsius),
0032 but no object emits thermal radiation perfectly; rather, they are
0033 better at emitting/absorbing some wavelengths of light than others.
0034 These uneven efficiencies make it difficult to study the interaction
0035 of light, heat and matter using normal objects.
0036 </para>
0038 <para>
0039 Fortunately, it is possible to construct a nearly-perfect blackbody.
0040 Construct a box made of a thermally conductive material, such as
0041 metal.  The box should be completely closed on all sides, so that the
0042 inside forms a cavity that does not receive light from the
0043 surroundings.  Then, make a small hole somewhere on the box.
0044 The light coming out of this hole will almost perfectly resemble the
0045 light from an ideal blackbody, for the temperature of the air inside
0046 the box.
0047 </para>
0049 <para>
0050 At the beginning of the 20th century, scientists Lord Rayleigh,
0051 and Max Planck (among others) studied the blackbody
0052 radiation using such a device.  After much work, Planck was able to
0053 empirically describe the intensity of light emitted by a blackbody as a
0054 function of wavelength.  Furthermore, he was able to describe how this
0055 spectrum would change as the temperature changed.  Planck's work on
0056 blackbody radiation is one of the areas of physics that led to the
0057 foundation of the wonderful science of Quantum Mechanics, but that is
0058 unfortunately beyond the scope of this article.
0059 </para>
0061 <para>
0062 What Planck and the others found was that as the temperature of a
0063 blackbody increases, the total amount of light emitted per
0064 second increases, and the wavelength of the spectrum's peak shifts to
0065 bluer colors (see Figure 1).
0066 </para>
0068 <para>
0069 <mediaobject>
0070 <imageobject>
0071 <imagedata fileref="blackbody.png" format="PNG"/>
0072 </imageobject>
0073 <caption><para><phrase>Figure 1</phrase></para></caption>
0074 </mediaobject>
0075 </para>
0077 <para>
0078 For example, an iron bar becomes orange-red when heated to high temperatures and its color
0079 progressively shifts toward blue and white as it is heated further.
0080 </para>
0082 <para>
0083 In 1893, German physicist Wilhelm Wien quantified the relationship between blackbody
0084 temperature and the wavelength of the spectral peak with the
0085 following equation:
0086 </para>
0088 <para>
0089 <mediaobject>
0090 <imageobject>
0091 <imagedata fileref="lambda_max.png" format="PNG"/>
0092 </imageobject>
0093 </mediaobject>
0094 </para>
0096 <para>
0097 where T is the temperature in Kelvin.  Wien's law (also known as
0098 Wien's displacement law) states that the
0099 wavelength of maximum emission from a blackbody is inversely
0100 proportional to its temperature.  This makes sense;
0101 shorter-wavelength (higher-frequency) light corresponds to
0102 higher-energy photons, which you would expect from a
0103 higher-temperature object.
0104 </para>
0106 <para>
0107 For example, the sun has an average temperature of 5800 K, so
0108 its wavelength of maximum emission is given by:
0110 <mediaobject>
0111 <imageobject>
0112 <imagedata fileref="lambda_ex.png" format="PNG"/>
0113 </imageobject>
0114 </mediaobject>
0115 </para>
0117 <para>
0118 This wavelengths falls in the
0119 green region of the visible light spectrum, but the sun's continuum
0120 radiates photons both longer and shorter than lambda(max) and the
0121 human eyes perceives the sun's color as yellow/white.
0122 </para>
0124 <para>
0125 In 1879, Austrian physicist Stephan Josef Stefan showed that
0126 the luminosity, L, of a black body is proportional to the 4th power of its temperature T.
0127 </para>
0129 <para>
0130 <mediaobject>
0131 <imageobject>
0132 <imagedata fileref="luminosity.png" format="PNG"/>
0133 </imageobject>
0134 </mediaobject>
0135 </para>
0137 <para>
0138 where A is the surface area, alpha is a constant of proportionality,
0139 and T is the temperature in Kelvin. That is, if we double the
0140 temperature (e.g. 1000 K to 2000 K) then the total energy radiated
0141 from a blackbody increase by a factor of 2<superscript>4</superscript> or 16.
0142 </para>
0144 <para>
0145 Five years later, Austrian physicist Ludwig Boltzman derived the same
0146 equation and is now known as the Stefan-Boltzman law. If we assume a
0147 spherical star with radius R, then the luminosity of such a star is
0148 </para>
0150 <para>
0151 <mediaobject>
0152 <imageobject>
0153 <imagedata fileref="luminosity_ex.png" format="PNG"/>
0154 </imageobject>
0155 </mediaobject>
0156 </para>
0158 <para>
0159 where R is the star radius in cm, and the alpha is the
0160 Stefan-Boltzman constant, which has the value:
0162 <mediaobject>
0163 <imageobject>
0164 <imagedata fileref="alpha.png" format="PNG"/>
0165 </imageobject>
0166 </mediaobject>
0167 </para>
0169 </sect1>