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<h1>Calculate Planck curves as a function of wavelength and temperature</h1>
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<h1>Calculate Planck curves as a function of wavelength and temperature<a class="headerlink" href="#calculate-planck-curves-as-a-function-of-wavelength-and-temperature" title="Permalink to this headline">#</a></h1>
<p><i>© Von P. Walden, Washington State University</i></p>
<div class="cell docutils container">
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">pylab</span> inline
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>%pylab is deprecated, use %matplotlib inline and import the required libraries.
Populating the interactive namespace from numpy and matplotlib
</pre></div>
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<section id="dessler-figure-3-2a">
<h2>Dessler, Figure 3.2a<a class="headerlink" href="#dessler-figure-3-2a" title="Permalink to this headline">#</a></h2>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">c</span> <span class="o">=</span> <span class="mf">2.998e8</span> <span class="c1"># m s-1</span>
<span class="n">h</span> <span class="o">=</span> <span class="mf">6.626e-34</span> <span class="c1"># m2 kg s-1</span>
<span class="n">kB</span> <span class="o">=</span> <span class="mf">1.381e-23</span> <span class="c1"># m2 kg s-2 K-1</span>
<span class="n">l</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="mf">0.25</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># meters</span>
<span class="n">T</span> <span class="o">=</span> <span class="mf">300.</span> <span class="c1"># K</span>
<span class="n">B</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span><span class="o">**</span><span class="mi">5</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span> <span class="o">*</span><span class="n">kB</span> <span class="o">*</span> <span class="n">T</span><span class="p">))</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># W m-2 um-1</span>
<span class="n">spectralFlux</span> <span class="o">=</span> <span class="n">pi</span> <span class="o">*</span> <span class="n">B</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plot</span><span class="p">(</span><span class="n">l</span><span class="o">/</span><span class="mf">1e-6</span><span class="p">,</span><span class="n">spectralFlux</span><span class="p">)</span>
<span class="n">xlabel</span><span class="p">(</span><span class="s1">'Wavelength, microns'</span><span class="p">);</span>
<span class="n">ylabel</span><span class="p">(</span><span class="s1">'Spectral Flux, W m-2 um-1'</span><span class="p">);</span>
<span class="n">text</span><span class="p">(</span><span class="mf">17.5</span><span class="p">,</span><span class="mi">30</span><span class="p">,</span><span class="s1">'300 K'</span><span class="p">);</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<img alt="../_images/PlancksLaw_5_0.png" src="../_images/PlancksLaw_5_0.png" />
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">l_max</span> <span class="o">=</span> <span class="n">l</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">spectralFlux</span><span class="o">==</span><span class="n">spectralFlux</span><span class="o">.</span><span class="n">max</span><span class="p">())]</span>
<span class="nb">print</span><span class="p">(</span><span class="n">l_max</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[9.75e-06]
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Wiens Law gives wavelength of maximum flux at: </span><span class="si">{</span><span class="p">(</span><span class="mi">2989</span><span class="o">/</span><span class="n">T</span><span class="p">)</span><span class="si">:</span><span class="s2">3.1f</span><span class="si">}</span><span class="s2"> um."</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Wiens Law gives wavelength of maximum flux at: 10.0 um.
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"The Stefan-Boltzmann Law gives the total flux for this object as: </span><span class="si">{</span><span class="p">(</span><span class="mf">5.67e-8</span><span class="o">*</span><span class="n">T</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span><span class="si">:</span><span class="s2">4.0f</span><span class="si">}</span><span class="s2"> W m-2."</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The Stefan-Boltzmann Law gives the total flux for this object as: 459 W m-2.
</pre></div>
</div>
</div>
</div>
</section>
<section id="dessler-figure-3-2b">
<h2>Dessler, Figure 3.2b<a class="headerlink" href="#dessler-figure-3-2b" title="Permalink to this headline">#</a></h2>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">l</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span><span class="mi">12</span><span class="p">,</span><span class="mf">0.05</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># meters</span>
<span class="n">T</span> <span class="o">=</span> <span class="mf">1600.</span> <span class="c1"># K</span>
<span class="n">B</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span><span class="o">**</span><span class="mi">5</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span> <span class="o">*</span><span class="n">kB</span> <span class="o">*</span> <span class="n">T</span><span class="p">))</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># W m-2 um-1</span>
<span class="n">spectralFlux</span> <span class="o">=</span> <span class="n">pi</span> <span class="o">*</span> <span class="n">B</span> <span class="c1"># W m-2 um-1</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plot</span><span class="p">(</span><span class="n">l</span><span class="o">/</span><span class="mf">1e-6</span><span class="p">,</span><span class="n">spectralFlux</span><span class="p">)</span>
<span class="n">xlabel</span><span class="p">(</span><span class="s1">'Wavelength, microns'</span><span class="p">);</span>
<span class="n">ylabel</span><span class="p">(</span><span class="s1">'Spectral Flux, W m-2 um-1'</span><span class="p">);</span>
<span class="n">text</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">120000</span><span class="p">,</span><span class="s1">'1600 K'</span><span class="p">);</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<img alt="../_images/PlancksLaw_11_0.png" src="../_images/PlancksLaw_11_0.png" />
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Wiens law gives wavelength of maximum flux at: </span><span class="si">{</span><span class="p">(</span><span class="mi">2989</span><span class="o">/</span><span class="n">T</span><span class="p">)</span><span class="si">:</span><span class="s2">3.1f</span><span class="si">}</span><span class="s2"> um."</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Wiens law gives wavelength of maximum flux at: 1.9 um.
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"The Stefan-Boltzmann Law gives the total flux for this object as: </span><span class="si">{</span><span class="p">(</span><span class="mf">5.67e-8</span><span class="o">*</span><span class="n">T</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span><span class="si">:</span><span class="s2">4.0f</span><span class="si">}</span><span class="s2"> W m-2."</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The Stefan-Boltzmann Law gives the total flux for this object as: 371589 W m-2.
</pre></div>
</div>
</div>
</div>
</section>
<section id="dessler-figure-3-2c">
<h2>Dessler, Figure 3.2c<a class="headerlink" href="#dessler-figure-3-2c" title="Permalink to this headline">#</a></h2>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">l</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.01</span><span class="p">,</span><span class="mf">3.5</span><span class="p">,</span><span class="mf">0.01</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># meters</span>
<span class="n">T</span> <span class="o">=</span> <span class="mf">6000.</span> <span class="c1"># K</span>
<span class="n">B</span> <span class="o">=</span> <span class="n">pi</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span><span class="o">**</span><span class="mi">5</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span> <span class="o">*</span><span class="n">kB</span> <span class="o">*</span> <span class="n">T</span><span class="p">))</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># W m-2 um-1</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plot</span><span class="p">(</span><span class="n">l</span><span class="o">/</span><span class="mf">1e-6</span><span class="p">,</span><span class="n">B</span><span class="p">)</span>
<span class="n">xlabel</span><span class="p">(</span><span class="s1">'Wavelength, microns'</span><span class="p">);</span>
<span class="n">ylabel</span><span class="p">(</span><span class="s1">'Flux, W m-2 um-1'</span><span class="p">);</span>
<span class="n">text</span><span class="p">(</span><span class="mf">2.8</span><span class="p">,</span><span class="mf">90e6</span><span class="p">,</span><span class="s1">'6000 K'</span><span class="p">);</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<img alt="../_images/PlancksLaw_16_0.png" src="../_images/PlancksLaw_16_0.png" />
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Wiens law gives wavelength of maximum flux at: </span><span class="si">{</span><span class="p">(</span><span class="mi">2989</span><span class="o">/</span><span class="n">T</span><span class="p">)</span><span class="si">:</span><span class="s2">3.1f</span><span class="si">}</span><span class="s2"> um."</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Wiens law gives wavelength of maximum flux at: 0.5 um.
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"The Stefan-Boltzmann Law gives the total flux for this object as: </span><span class="si">{</span><span class="p">(</span><span class="mf">5.67e-8</span><span class="o">*</span><span class="n">T</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span><span class="si">:</span><span class="s2">4.0f</span><span class="si">}</span><span class="s2"> W m-2."</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The Stefan-Boltzmann Law gives the total flux for this object as: 73483200 W m-2.
</pre></div>
</div>
</div>
</div>
</section>
</section>
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