.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/phase_equilibria/plot_02_gibbs_phase_rule.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_phase_equilibria_plot_02_gibbs_phase_rule.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_phase_equilibria_plot_02_gibbs_phase_rule.py:


Gibbs's phase rule on the phase diagram of water
================================================

Gibbs's phase rule, :math:`F = C - P + 2`
(:func:`~chemistrykit.thermo.systems.phase_equilibria.gibbs_phase_rule`),
says how many intensive variables can change while a set of phases
coexists. On a one-component phase diagram, single-phase regions are
areas (:math:`F=2`), two-phase boundaries are curves (:math:`F=1`), and
three phases meet only at a point (:math:`F=0`). The sketch below draws
water's diagram around its triple point (vaporization and sublimation
curves from the Clausius-Clapeyron equation, melting line from the
Clapeyron slope) and labels each feature with its degrees of freedom.

.. GENERATED FROM PYTHON SOURCE LINES 17-50

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.phase_equilibria import ClausiusClapeyron, gibbs_phase_rule

    T_tp, P_tp = 273.16, 611.657  # water triple point
    vaporization = ClausiusClapeyron(delta_h_vap=45050.0, T_ref=T_tp, P_ref=P_tp)
    sublimation = ClausiusClapeyron(delta_h_vap=51060.0, T_ref=T_tp, P_ref=P_tp)
    # Clapeyron slope of the melting line: dP/dT = dH_fus / (T dV_fus), negative for water.
    dH_fus, dV_fus = 6010.0, -1.63e-6
    slope = dH_fus / (T_tp * dV_fus)

    T_vap = np.linspace(T_tp, 300.0, 100)
    T_sub = np.linspace(250.0, T_tp, 100)
    P_melt = np.logspace(np.log10(P_tp), 7, 100)
    T_melt = T_tp + (P_melt - P_tp) / slope

    fig, ax = plt.subplots(figsize=(7, 5))
    ax.plot(T_vap, vaporization.pressure(T_vap), label="liquid-vapor (F = 1)")
    ax.plot(T_sub, sublimation.pressure(T_sub), label="solid-vapor (F = 1)")
    ax.plot(T_melt, P_melt, label="solid-liquid (F = 1)")
    ax.plot([T_tp], [P_tp], "ko", label="triple point (F = 0)")
    ax.set_yscale("log")
    ax.set_xlim(250.0, 300.0)
    ax.set_ylim(50.0, 1e7)
    for x, y, text in [(258.0, 1e5, "ice"), (288.0, 1e5, "liquid"), (288.0, 200.0, "vapor")]:
        ax.text(x, y, f"{text}\nF = {gibbs_phase_rule(1, 1)}", ha="center")
    ax.set_xlabel("T (K)")
    ax.set_ylabel("P (Pa)")
    ax.set_title("Water near its triple point: F = C - P + 2")
    ax.legend(loc="lower right")
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/phase_equilibria/images/sphx_glr_plot_02_gibbs_phase_rule_001.png
   :alt: Water near its triple point: F = C - P + 2
   :srcset: /api/gallery/thermo/phase_equilibria/images/sphx_glr_plot_02_gibbs_phase_rule_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 51-54

The rule for one and two components, and with a reaction constraint
(e.g. :math:`N_2O_4 \rightleftharpoons 2NO_2` in the gas phase, where
the two species count as only one independent component):

.. GENERATED FROM PYTHON SOURCE LINES 54-60

.. code-block:: Python


    for C in (1, 2):
        print(f"C = {C}: " + ", ".join(f"P = {P}: F = {gibbs_phase_rule(C, P)}" for P in range(1, C + 3)))
    print("N2O4/NO2 gas with the reaction at equilibrium: F =", gibbs_phase_rule(n_components=2, n_phases=1, reactions=1))

    plt.show()




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

 .. code-block:: none

    C = 1: P = 1: F = 2, P = 2: F = 1, P = 3: F = 0
    C = 2: P = 1: F = 3, P = 2: F = 2, P = 3: F = 1, P = 4: F = 0
    N2O4/NO2 gas with the reaction at equilibrium: F = 2





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

   **Total running time of the script:** (0 minutes 0.074 seconds)


.. _sphx_glr_download_api_gallery_thermo_phase_equilibria_plot_02_gibbs_phase_rule.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_02_gibbs_phase_rule.ipynb <plot_02_gibbs_phase_rule.ipynb>`

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

      :download:`Download Python source code: plot_02_gibbs_phase_rule.py <plot_02_gibbs_phase_rule.py>`

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

      :download:`Download zipped: plot_02_gibbs_phase_rule.zip <plot_02_gibbs_phase_rule.zip>`


.. only:: html

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

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