.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/statmech/maxwell_boltzmann/plot_01_maxwell_boltzmann.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_statmech_maxwell_boltzmann_plot_01_maxwell_boltzmann.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_statmech_maxwell_boltzmann_plot_01_maxwell_boltzmann.py:


The Maxwell-Boltzmann speed distribution
===========================================

:class:`~chemistrykit.statmech.MaxwellBoltzmannSpeedDistribution` at two
temperatures, with the most-probable, mean, and rms speeds marked --
their ratios are a fixed, temperature-independent property of the
distribution's shape.

.. GENERATED FROM PYTHON SOURCE LINES 12-32

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.statmech import MaxwellBoltzmannSpeedDistribution

    mass = 6.63e-26  # argon-like, kg

    fig, ax = plt.subplots(figsize=(7, 5))
    for T, color in [(200.0, "steelblue"), (800.0, "crimson")]:
        dist = MaxwellBoltzmannSpeedDistribution(mass=mass, temperature=T)
        v = np.linspace(0.0, 2500.0, 400)
        ax.plot(v, dist.pdf(v), color=color, label=f"T = {T:.0f} K")
        ax.axvline(dist.most_probable_speed(), color=color, linestyle=":", linewidth=0.8)

    ax.set_xlabel("speed (m/s)")
    ax.set_ylabel("probability density")
    ax.set_title("Maxwell-Boltzmann speed distribution at two temperatures")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/statmech/maxwell_boltzmann/images/sphx_glr_plot_01_maxwell_boltzmann_001.png
   :alt: Maxwell-Boltzmann speed distribution at two temperatures
   :srcset: /api/gallery/statmech/maxwell_boltzmann/images/sphx_glr_plot_01_maxwell_boltzmann_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 33-36

The three characteristic speeds stand in a fixed ratio, independent of
temperature or mass -- a purely geometric property of the
distribution's shape:

.. GENERATED FROM PYTHON SOURCE LINES 36-43

.. code-block:: Python


    dist = MaxwellBoltzmannSpeedDistribution(mass=mass, temperature=298.15)
    vp, vbar, vrms = dist.most_probable_speed(), dist.mean_speed(), dist.rms_speed()
    print(f"v_p : v_bar : v_rms = 1 : {vbar / vp:.4f} : {vrms / vp:.4f}")
    print(f"expected             = 1 : {np.sqrt(8.0 / np.pi) / np.sqrt(2.0):.4f} : {np.sqrt(3.0) / np.sqrt(2.0):.4f}")

    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    v_p : v_bar : v_rms = 1 : 1.1284 : 1.2247
    expected             = 1 : 1.1284 : 1.2247





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.040 seconds)


.. _sphx_glr_download_api_gallery_statmech_maxwell_boltzmann_plot_01_maxwell_boltzmann.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_maxwell_boltzmann.ipynb <plot_01_maxwell_boltzmann.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_maxwell_boltzmann.py <plot_01_maxwell_boltzmann.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_maxwell_boltzmann.zip <plot_01_maxwell_boltzmann.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_