.. 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_05_lewis_fugacity.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_05_lewis_fugacity.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equations_of_state_plot_05_lewis_fugacity.py:


Lewis fugacity: the effective pressure of a real gas
====================================================

G. N. Lewis replaced pressure by the fugacity :math:`f = \phi P` so that
the ideal-gas form :math:`\mu = \mu^\circ + RT\ln(f/P^\circ)` stays exact
for real fluids. The left panel shows the fugacity coefficient
:math:`\phi` of supercritical CO2 computed by
:func:`~chemistrykit.thermo.systems.fugacity.fugacity_coefficient` from
three equations of state. The right panel shows Lewis's phase-equilibrium
criterion: below :math:`T_c` the liquid and vapor fugacities from
:func:`~chemistrykit.thermo.systems.fugacity.fugacity` cross exactly at
the saturation pressure.

.. GENERATED FROM PYTHON SOURCE LINES 17-38

.. 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 fugacity, fugacity_coefficient, saturation_pressure

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

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    P = np.linspace(0.1e6, 30e6, 120)
    T = 350.0
    for name, eos in models.items():
        axes[0].plot(P / 1e6, [fugacity_coefficient(eos, p, T) for p in P], label=name)
    axes[0].axhline(1.0, color="gray", linestyle=":", label="ideal gas")
    axes[0].set_xlabel("P (MPa)")
    axes[0].set_ylabel(r"fugacity coefficient $\phi = f/P$")
    axes[0].set_title(f"CO2 at {T:.0f} K (supercritical)")
    axes[0].legend()




.. image-sg:: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_05_lewis_fugacity_001.png
   :alt: CO2 at 350 K (supercritical)
   :srcset: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_05_lewis_fugacity_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x11b8ed550>



.. GENERATED FROM PYTHON SOURCE LINES 39-42

Below the critical temperature, the vapor and liquid roots coexist over
a range of pressures; Lewis's criterion picks the one where
:math:`f^L = f^V`.

.. GENERATED FROM PYTHON SOURCE LINES 42-61

.. code-block:: Python


    T_sub = 280.0
    P_sat = saturation_pressure(pr, T_sub)
    P_range = np.linspace(0.75 * P_sat, 1.2 * P_sat, 80)
    f_vap = [fugacity(pr, p, T_sub, "vapor") for p in P_range]
    f_liq = [fugacity(pr, p, T_sub, "liquid") for p in P_range]
    axes[1].plot(P_range / 1e6, np.array(f_vap) / 1e6, label="vapor root")
    axes[1].plot(P_range / 1e6, np.array(f_liq) / 1e6, label="liquid root")
    axes[1].axvline(P_sat / 1e6, color="crimson", linestyle="--", label=f"f(liquid) = f(vapor): {P_sat / 1e6:.2f} MPa")
    axes[1].set_xlabel("P (MPa)")
    axes[1].set_ylabel("fugacity f (MPa)")
    axes[1].set_title(f"Peng-Robinson CO2 at {T_sub:.0f} K")
    axes[1].legend()
    fig.tight_layout()

    print(f"Peng-Robinson saturation pressure of CO2 at {T_sub:.0f} K: {P_sat / 1e6:.3f} MPa (measured: about 4.16 MPa)")
    print(f"phi at saturation: {fugacity_coefficient(pr, P_sat, T_sub):.3f}")

    plt.show()




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

 .. code-block:: none

    Peng-Robinson saturation pressure of CO2 at 280 K: 4.160 MPa (measured: about 4.16 MPa)
    phi at saturation: 0.736





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

   **Total running time of the script:** (0 minutes 0.075 seconds)


.. _sphx_glr_download_api_gallery_thermo_equations_of_state_plot_05_lewis_fugacity.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_05_lewis_fugacity.ipynb <plot_05_lewis_fugacity.ipynb>`

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

      :download:`Download Python source code: plot_05_lewis_fugacity.py <plot_05_lewis_fugacity.py>`

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

      :download:`Download zipped: plot_05_lewis_fugacity.zip <plot_05_lewis_fugacity.zip>`


.. only:: html

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

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