.. _sphx_glr_api_gallery_statmech_maxwell_boltzmann:

Maxwell-Boltzmann speed distribution
--------------------------------------

The Maxwell-Boltzmann speed distribution and its characteristic speeds,
and a Stern-type molecular-beam sampling check of its shape.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="MaxwellBoltzmannSpeedDistribution at two temperatures, with the most-probable, mean, and rms speeds marked -- their ratios are a fixed, temperature-independent property of the distribution&#x27;s shape.">

.. only:: html

  .. image:: /api/gallery/statmech/maxwell_boltzmann/images/thumb/sphx_glr_plot_01_maxwell_boltzmann_thumb.png
    :alt:

  :doc:`/api/gallery/statmech/maxwell_boltzmann/plot_01_maxwell_boltzmann`

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      <div class="sphx-glr-thumbnail-title">The Maxwell-Boltzmann speed distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Otto Stern&#x27;s 1920 molecular-beam apparatus gave the first direct experimental measurement of a gas&#x27;s actual molecular speeds, rather than only their statistical consequences (pressure, diffusion, viscosity) -- a rotating-drum time-of-flight technique later refined by Zartman and Ko (1930-1934) into a quantitative confirmation of the full Maxwell-Boltzmann functional form, not just its mean. sample draws exactly such a synthetic &quot;beam&quot; of molecular speeds; binning it into a histogram and comparing it to the exact analytic pdf reproduces the kind of check Stern, and later Zartman and Ko, made directly against a real gas.">

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  .. image:: /api/gallery/statmech/maxwell_boltzmann/images/thumb/sphx_glr_plot_02_stern_experiment_thumb.png
    :alt:

  :doc:`/api/gallery/statmech/maxwell_boltzmann/plot_02_stern_experiment`

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      <div class="sphx-glr-thumbnail-title">Verifying the speed distribution: Stern's molecular-beam experiment</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/statmech/maxwell_boltzmann/plot_01_maxwell_boltzmann
   /api/gallery/statmech/maxwell_boltzmann/plot_02_stern_experiment