.. 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_03_redlich_kwong.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_03_redlich_kwong.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equations_of_state_plot_03_redlich_kwong.py:


Redlich-Kwong isotherms of CO2 against van der Waals and the ideal gas
======================================================================

Redlich and Kwong divided van der Waals's attraction term by
:math:`\sqrt{T}`. This example draws CO2 P-V isotherms well above and
just below the critical temperature from
:class:`~chemistrykit.thermo.systems.equations_of_state.RedlichKwong`,
with :class:`~chemistrykit.thermo.systems.equations_of_state.VanDerWaals`
and :class:`~chemistrykit.thermo.systems.equations_of_state.IdealGas` for
comparison. Both real-gas equations are built from CO2's critical
temperature and pressure alone via
:meth:`~chemistrykit.thermo.systems.equations_of_state.RedlichKwong.from_critical_constants`.
Redlich-Kwong's universal critical compressibility factor is 1/3, closer
to real gases than van der Waals's 3/8.

.. 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 IdealGas, RedlichKwong, VanDerWaals

    Tc, Pc = 304.13, 7.3773e6  # CO2
    ideal = IdealGas()
    vdw = VanDerWaals.from_critical_constants(Tc, Pc)
    rk = RedlichKwong.from_critical_constants(Tc, Pc)

    fig, axes = plt.subplots(1, 2, figsize=(11, 5))
    for ax, T, title in zip(axes, [1.5 * Tc, 0.95 * Tc], ["well above Tc", "just below Tc"]):
        Vm = np.linspace(1.5 * vdw.b, 6.0e-4, 400)
        ax.plot(Vm * 1000.0, rk.pressure(Vm, T) / 1.0e6, color="crimson", linewidth=2, label="Redlich-Kwong")
        ax.plot(Vm * 1000.0, vdw.pressure(Vm, T) / 1.0e6, "--", label="van der Waals")
        ax.plot(Vm * 1000.0, ideal.pressure(Vm, T) / 1.0e6, ":", label="ideal gas")
        ax.axhline(Pc / 1.0e6, color="gray", linestyle=":", linewidth=0.8)
        ax.set_xlabel(r"$V_m$ (L/mol)")
        ax.set_ylabel("P (MPa)")
        ax.set_title(f"T = {T:.1f} K ({title})")
        ax.set_ylim(0, 3.0 * Pc / 1.0e6)
        ax.legend()
    fig.suptitle("CO2 isotherms: Redlich-Kwong vs. van der Waals vs. ideal gas")
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_03_redlich_kwong_001.png
   :alt: CO2 isotherms: Redlich-Kwong vs. van der Waals vs. ideal gas, T = 456.2 K (well above Tc), T = 288.9 K (just below Tc)
   :srcset: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_03_redlich_kwong_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 45-48

The critical-point construction fixes Redlich-Kwong's critical molar
volume at :math:`RT_c/(3P_c)`; the critical isotherm passes through it
at :math:`P = P_c`.

.. GENERATED FROM PYTHON SOURCE LINES 48-54

.. code-block:: Python


    Vc_rk = rk.R * Tc / (3.0 * Pc)
    print(f"Redlich-Kwong: P(Vc, Tc)/Pc = {rk.pressure(Vc_rk, Tc) / Pc:.4f}, Zc = {Pc * Vc_rk / (rk.R * Tc):.4f}")
    print(f"van der Waals: Zc = {Pc * 3.0 * vdw.b / (vdw.R * Tc):.4f}; measured CO2 Zc is about 0.274")

    plt.show()




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

 .. code-block:: none

    Redlich-Kwong: P(Vc, Tc)/Pc = 1.0000, Zc = 0.3333
    van der Waals: Zc = 0.3750; measured CO2 Zc is about 0.274





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

   **Total running time of the script:** (0 minutes 0.077 seconds)


.. _sphx_glr_download_api_gallery_thermo_equations_of_state_plot_03_redlich_kwong.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_redlich_kwong.ipynb <plot_03_redlich_kwong.ipynb>`

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

      :download:`Download Python source code: plot_03_redlich_kwong.py <plot_03_redlich_kwong.py>`

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

      :download:`Download zipped: plot_03_redlich_kwong.zip <plot_03_redlich_kwong.zip>`


.. only:: html

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

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