.. _sphx_glr_api_gallery_thermo_phase_equilibria:

Phase equilibria
----------------

The Clausius-Clapeyron liquid-vapor phase boundary, and the Gibbs phase
rule.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Water&#x27;s liquid-vapor phase boundary from the integrated Clausius-Clapeyron equation (~chemistrykit.thermo.systems.phase_equilibria.ClausiusClapeyron), anchored at the normal boiling point. Plotting \ln P against 1/T gives a straight line of slope -\Delta H_{vap}/R; from_two_points recovers \Delta H_{vap} from two measured points, and boiling_point inverts the curve to find the boiling point at altitude.">

.. only:: html

  .. image:: /api/gallery/thermo/phase_equilibria/images/thumb/sphx_glr_plot_01_clausius_clapeyron_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/phase_equilibria/plot_01_clausius_clapeyron`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Clausius-Clapeyron vapor-pressure curve of water</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gibbs&#x27;s phase rule, F = C - P + 2 (~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 (F=2), two-phase boundaries are curves (F=1), and three phases meet only at a point (F=0). The sketch below draws water&#x27;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.">

.. only:: html

  .. image:: /api/gallery/thermo/phase_equilibria/images/thumb/sphx_glr_plot_02_gibbs_phase_rule_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/phase_equilibria/plot_02_gibbs_phase_rule`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gibbs's phase rule on the phase diagram of water</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/thermo/phase_equilibria/plot_01_clausius_clapeyron
   /api/gallery/thermo/phase_equilibria/plot_02_gibbs_phase_rule