.. 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_03_antoine_vapor_pressure.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_03_antoine_vapor_pressure.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_phase_equilibria_plot_03_antoine_vapor_pressure.py:


Antoine's equation: vapor pressure beyond Clausius-Clapeyron
============================================================

The integrated Clausius-Clapeyron equation assumes a constant enthalpy of
vaporization, so :math:`\ln P` is exactly linear in :math:`1/T`. Real
vapor-pressure curves bend slightly, because :math:`\Delta H_{vap}`
shrinks as the temperature rises toward the critical point. Antoine's
three-constant equation (:class:`~chemistrykit.thermo.AntoineEquation`),
:math:`\log_{10}P = A - B/(C+T)`, absorbs that curvature in the single
extra constant :math:`C`. Below, both are compared with steam-table
values for water. The Antoine curve uses the NIST constants for
344-373 K.

.. GENERATED FROM PYTHON SOURCE LINES 17-53

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo import AntoineEquation, ClausiusClapeyron

    water = AntoineEquation(A=5.08354, B=1663.125, C=-45.622)  # P in bar, T in K (NIST, 344-373 K)
    cc = ClausiusClapeyron(delta_h_vap=40700.0, T_ref=373.15, P_ref=101325.0)

    # Saturation pressures of water from the IAPWS steam tables, in kPa.
    T_table = np.array([343.15, 348.15, 353.15, 358.15, 363.15, 368.15, 373.15])
    P_table = np.array([31.20, 38.58, 47.41, 57.87, 70.18, 84.61, 101.42])

    T = np.linspace(343.15, 373.15, 200)
    P_antoine = water.pressure(T) * 100.0  # bar -> kPa
    P_cc = cc.pressure(T) / 1000.0

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].plot(T - 273.15, P_antoine, color="darkorange", label="Antoine")
    axes[0].plot(T - 273.15, P_cc, "--", color="steelblue", label="Clausius-Clapeyron")
    axes[0].plot(T_table - 273.15, P_table, "ko", label="steam tables")
    axes[0].set_xlabel("temperature (degC)")
    axes[0].set_ylabel("vapor pressure of water (kPa)")
    axes[0].set_title("Water's vapor-pressure curve")
    axes[0].legend()

    err_antoine = 100 * (water.pressure(T_table) * 100.0 - P_table) / P_table
    err_cc = 100 * (cc.pressure(T_table) / 1000.0 - P_table) / P_table
    axes[1].plot(T_table - 273.15, err_antoine, "o-", color="darkorange", label="Antoine")
    axes[1].plot(T_table - 273.15, err_cc, "s--", color="steelblue", label="Clausius-Clapeyron")
    axes[1].axhline(0.0, color="gray", linewidth=0.8)
    axes[1].set_xlabel("temperature (degC)")
    axes[1].set_ylabel("error vs. steam tables (%)")
    axes[1].set_title("The third constant removes the curvature error")
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/phase_equilibria/images/sphx_glr_plot_03_antoine_vapor_pressure_001.png
   :alt: Water's vapor-pressure curve, The third constant removes the curvature error
   :srcset: /api/gallery/thermo/phase_equilibria/images/sphx_glr_plot_03_antoine_vapor_pressure_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 54-56

The equation inverts in closed form, giving the boiling point at any
pressure -- here, water boiling at reduced pressure:

.. GENERATED FROM PYTHON SOURCE LINES 56-61

.. code-block:: Python


    for P_kPa in (101.325, 70.0, 47.0):
        print(f"P = {P_kPa:7.3f} kPa -> T_boil = {float(water.temperature(P_kPa / 100.0)) - 273.15:5.1f} degC")

    plt.show()




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

 .. code-block:: none

    P = 101.325 kPa -> T_boil = 100.0 degC
    P =  70.000 kPa -> T_boil =  90.0 degC
    P =  47.000 kPa -> T_boil =  79.8 degC





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

   **Total running time of the script:** (0 minutes 0.081 seconds)


.. _sphx_glr_download_api_gallery_thermo_phase_equilibria_plot_03_antoine_vapor_pressure.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_antoine_vapor_pressure.ipynb <plot_03_antoine_vapor_pressure.ipynb>`

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

      :download:`Download Python source code: plot_03_antoine_vapor_pressure.py <plot_03_antoine_vapor_pressure.py>`

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      :download:`Download zipped: plot_03_antoine_vapor_pressure.zip <plot_03_antoine_vapor_pressure.zip>`


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