.. _sphx_glr_api_gallery_thermo_equations_of_state:

Equations of state
-------------------

The ideal gas law, van der Waals, Redlich-Kwong, and Peng-Robinson
equations of state, and Lewis fugacities computed from them.


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


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

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    <div class="sphx-glr-thumbcontainer" tooltip="Clapeyron&#x27;s 1834 combined gas law unites Boyle&#x27;s law (PV constant at fixed T), Charles&#x27;s and Gay-Lussac&#x27;s law (V \propto T at fixed P), and Avogadro&#x27;s hypothesis into PV_m = RT. This example draws both classic views with IdealGas: hyperbolic Boyle isotherms, and straight Charles isobars that all extrapolate to zero volume at absolute zero.">

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  .. image:: /api/gallery/thermo/equations_of_state/images/thumb/sphx_glr_plot_01_ideal_gas_law_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/equations_of_state/plot_01_ideal_gas_law`

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      <div class="sphx-glr-thumbnail-title">Clapeyron's ideal gas law, PV = RT</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Andrews&#x27;s CO2 isotherms showed a flat liquid-vapor plateau below a critical temperature and none above it. The van der Waals equation (~chemistrykit.thermo.systems.equations_of_state.VanDerWaals), built from CO2&#x27;s critical constants with from_critical_constants, reproduces the whole family: loops with three volume roots below T_c, an inflection at T_c, and single-valued isotherms above it, so gas can be turned into liquid continuously by going around the critical point.">

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  .. image:: /api/gallery/thermo/equations_of_state/images/thumb/sphx_glr_plot_02_van_der_waals_continuity_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/equations_of_state/plot_02_van_der_waals_continuity`

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      <div class="sphx-glr-thumbnail-title">Andrews and van der Waals: continuity of the liquid and gas states</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Redlich and Kwong divided van der Waals&#x27;s attraction term by \sqrt{T}. This example draws CO2 P-V isotherms well above and just below the critical temperature from RedlichKwong, with VanDerWaals and IdealGas for comparison. Both real-gas equations are built from CO2&#x27;s critical temperature and pressure alone via from_critical_constants. Redlich-Kwong&#x27;s universal critical compressibility factor is 1/3, closer to real gases than van der Waals&#x27;s 3/8.">

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  .. image:: /api/gallery/thermo/equations_of_state/images/thumb/sphx_glr_plot_03_redlich_kwong_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/equations_of_state/plot_03_redlich_kwong`

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      <div class="sphx-glr-thumbnail-title">Redlich-Kwong isotherms of CO2 against van der Waals and the ideal gas</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Peng and Robinson tuned the temperature dependence of their attraction term, \alpha(T), to Pitzer&#x27;s acentric factor \omega so that the equation reproduces pure-fluid vapor pressures. This example computes the CO2 vapor-pressure curve predicted by PengRobinson (\omega = 0.224) with saturation_pressure, and compares it with van der Waals and Redlich-Kwong built from the same critical constants. Only Peng-Robinson passes through Pitzer&#x27;s defining point, \log_{10}(P_{sat}/P_c) = -1 - \omega at T/T_c = 0.7.">

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  .. image:: /api/gallery/thermo/equations_of_state/images/thumb/sphx_glr_plot_04_peng_robinson_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/equations_of_state/plot_04_peng_robinson`

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      <div class="sphx-glr-thumbnail-title">Peng-Robinson: vapor pressures from the acentric factor</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="G. N. Lewis replaced pressure by the fugacity f = \phi P so that the ideal-gas form \mu = \mu^\circ + RT\ln(f/P^\circ) stays exact for real fluids. The left panel shows the fugacity coefficient \phi of supercritical CO2 computed by fugacity_coefficient from three equations of state. The right panel shows Lewis&#x27;s phase-equilibrium criterion: below T_c the liquid and vapor fugacities from fugacity cross exactly at the saturation pressure.">

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  .. image:: /api/gallery/thermo/equations_of_state/images/thumb/sphx_glr_plot_05_lewis_fugacity_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/equations_of_state/plot_05_lewis_fugacity`

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      <div class="sphx-glr-thumbnail-title">Lewis fugacity: the effective pressure of a real gas</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/thermo/equations_of_state/plot_01_ideal_gas_law
   /api/gallery/thermo/equations_of_state/plot_02_van_der_waals_continuity
   /api/gallery/thermo/equations_of_state/plot_03_redlich_kwong
   /api/gallery/thermo/equations_of_state/plot_04_peng_robinson
   /api/gallery/thermo/equations_of_state/plot_05_lewis_fugacity