.. 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_01_clausius_clapeyron.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_01_clausius_clapeyron.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_phase_equilibria_plot_01_clausius_clapeyron.py:


The Clausius-Clapeyron vapor-pressure curve of water
====================================================

Water's liquid-vapor phase boundary from the integrated
Clausius-Clapeyron equation
(:class:`~chemistrykit.thermo.systems.phase_equilibria.ClausiusClapeyron`),
anchored at the normal boiling point. Plotting :math:`\ln P` against
:math:`1/T` gives a straight line of slope :math:`-\Delta H_{vap}/R`;
:meth:`~chemistrykit.thermo.systems.phase_equilibria.ClausiusClapeyron.from_two_points`
recovers :math:`\Delta H_{vap}` from two measured points, and
:meth:`~chemistrykit.thermo.systems.phase_equilibria.ClausiusClapeyron.boiling_point`
inverts the curve to find the boiling point at altitude.

.. GENERATED FROM PYTHON SOURCE LINES 17-41

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.phase_equilibria import ClausiusClapeyron

    water = ClausiusClapeyron(delta_h_vap=40700.0, T_ref=373.15, P_ref=101325.0)

    T = np.linspace(280.0, 373.15, 200)
    P = water.pressure(T)

    fig, axes = plt.subplots(1, 2, figsize=(11, 4.5))
    axes[0].plot(T, P / 1000.0, color="steelblue")
    axes[0].scatter([373.15], [101.325], color="crimson", zorder=3, label="normal boiling point")
    axes[0].set_xlabel("T (K)")
    axes[0].set_ylabel("vapor pressure (kPa)")
    axes[0].set_title("Water's liquid-vapor phase boundary")
    axes[0].legend()

    axes[1].plot(1000.0 / T, np.log(P), color="steelblue")
    axes[1].set_xlabel("1000 / T (1/K)")
    axes[1].set_ylabel("ln(P / Pa)")
    axes[1].set_title(r"Straight line of slope $-\Delta H_{vap}/R$")
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/phase_equilibria/images/sphx_glr_plot_01_clausius_clapeyron_001.png
   :alt: Water's liquid-vapor phase boundary, Straight line of slope $-\Delta H_{vap}/R$
   :srcset: /api/gallery/thermo/phase_equilibria/images/sphx_glr_plot_01_clausius_clapeyron_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 42-45

Two points on the curve fix :math:`\Delta H_{vap}`, and inverting the
model gives the boiling point at a mountain-altitude pressure of about
70 kPa:

.. GENERATED FROM PYTHON SOURCE LINES 45-52

.. code-block:: Python


    fit = ClausiusClapeyron.from_two_points(353.15, float(water.pressure(353.15)), 373.15, 101325.0)
    print(f"Enthalpy of vaporization from two points: {fit.delta_h_vap / 1000.0:.2f} kJ/mol")
    T_boil = water.boiling_point(70_000.0)
    print(f"At 70 kPa, water boils at {T_boil:.2f} K ({T_boil - 273.15:.2f} degC)")

    plt.show()




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

 .. code-block:: none

    Enthalpy of vaporization from two points: 40.70 kJ/mol
    At 70 kPa, water boils at 362.92 K (89.77 degC)





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

   **Total running time of the script:** (0 minutes 0.057 seconds)


.. _sphx_glr_download_api_gallery_thermo_phase_equilibria_plot_01_clausius_clapeyron.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_clausius_clapeyron.ipynb <plot_01_clausius_clapeyron.ipynb>`

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

      :download:`Download Python source code: plot_01_clausius_clapeyron.py <plot_01_clausius_clapeyron.py>`

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

      :download:`Download zipped: plot_01_clausius_clapeyron.zip <plot_01_clausius_clapeyron.zip>`


.. only:: html

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

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