.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/equations_of_state/plot_04_peng_robinson.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_thermo_equations_of_state_plot_04_peng_robinson.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equations_of_state_plot_04_peng_robinson.py:


Peng-Robinson: vapor pressures from the acentric factor
=======================================================

Peng and Robinson tuned the temperature dependence of their attraction
term, :math:`\alpha(T)`, to Pitzer's acentric factor :math:`\omega` so
that the equation reproduces pure-fluid vapor pressures. This example
computes the CO2 vapor-pressure curve predicted by
:class:`~chemistrykit.thermo.systems.equations_of_state.PengRobinson`
(:math:`\omega = 0.224`) with
:func:`~chemistrykit.thermo.systems.fugacity.saturation_pressure`, and
compares it with van der Waals and Redlich-Kwong built from the same
critical constants. Only Peng-Robinson passes through Pitzer's defining
point, :math:`\log_{10}(P_{sat}/P_c) = -1 - \omega` at
:math:`T/T_c = 0.7`.

.. GENERATED FROM PYTHON SOURCE LINES 19-44

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.equations_of_state import PengRobinson, RedlichKwong, VanDerWaals
    from chemistrykit.thermo.systems.fugacity import saturation_pressure

    Tc, Pc, omega = 304.13, 7.3773e6, 0.224  # CO2
    models = {
        "Peng-Robinson": PengRobinson(Tc, Pc, omega),
        "Redlich-Kwong": RedlichKwong.from_critical_constants(Tc, Pc),
        "van der Waals": VanDerWaals.from_critical_constants(Tc, Pc),
    }

    Tr = np.linspace(0.6, 0.98, 25)
    fig, ax = plt.subplots(figsize=(7, 5))
    for name, eos in models.items():
        Pr = [saturation_pressure(eos, t * Tc) / Pc for t in Tr]
        ax.plot(1.0 / Tr, np.log10(Pr), label=name)
    ax.plot([1.0 / 0.7], [-1.0 - omega], "k*", markersize=12, label=r"acentric-factor point ($\omega$ = 0.224)")
    ax.set_xlabel(r"$T_c / T$")
    ax.set_ylabel(r"$\log_{10}(P_{sat}/P_c)$")
    ax.set_title("CO2 vapor-pressure curve from three cubic equations of state")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_04_peng_robinson_001.png
   :alt: CO2 vapor-pressure curve from three cubic equations of state
   :srcset: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_04_peng_robinson_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 45-46

The acentric factor implied by each equation at :math:`T/T_c = 0.7`:

.. GENERATED FROM PYTHON SOURCE LINES 46-53

.. code-block:: Python


    for name, eos in models.items():
        implied = -1.0 - np.log10(saturation_pressure(eos, 0.7 * Tc) / Pc)
        print(f"{name:14s}: implied omega = {implied:+.3f}")
    print(f"Peng-Robinson Zc = 0.3074 (critical isotherm check: P(Vc)/Pc = {models['Peng-Robinson'].pressure(0.30740 * 8.314462618 * Tc / Pc, Tc) / Pc:.4f})")

    plt.show()




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

 .. code-block:: none

    Peng-Robinson : implied omega = +0.226
    Redlich-Kwong : implied omega = +0.058
    van der Waals : implied omega = -0.302
    Peng-Robinson Zc = 0.3074 (critical isotherm check: P(Vc)/Pc = 1.0001)





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

   **Total running time of the script:** (0 minutes 0.092 seconds)


.. _sphx_glr_download_api_gallery_thermo_equations_of_state_plot_04_peng_robinson.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_04_peng_robinson.ipynb <plot_04_peng_robinson.ipynb>`

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

      :download:`Download Python source code: plot_04_peng_robinson.py <plot_04_peng_robinson.py>`

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

      :download:`Download zipped: plot_04_peng_robinson.zip <plot_04_peng_robinson.zip>`


.. only:: html

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

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