.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/equations_of_state/plot_01_ideal_gas_law.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_equations_of_state_plot_01_ideal_gas_law.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equations_of_state_plot_01_ideal_gas_law.py:


Clapeyron's ideal gas law, PV = RT
==================================

Clapeyron's 1834 combined gas law unites Boyle's law (:math:`PV` constant
at fixed :math:`T`), Charles's and Gay-Lussac's law (:math:`V \propto T`
at fixed :math:`P`), and Avogadro's hypothesis into :math:`PV_m = RT`.
This example draws both classic views with
:class:`~chemistrykit.thermo.systems.equations_of_state.IdealGas`:
hyperbolic Boyle isotherms, and straight Charles isobars that all
extrapolate to zero volume at absolute zero.

.. GENERATED FROM PYTHON SOURCE LINES 15-42

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.equations_of_state import IdealGas

    gas = IdealGas()

    fig, axes = plt.subplots(1, 2, figsize=(11, 4.5))

    Vm = np.linspace(0.005, 0.05, 300)  # m^3/mol
    for T in [200.0, 300.0, 400.0, 500.0]:
        axes[0].plot(Vm * 1000.0, gas.pressure(Vm, T) / 1000.0, label=f"T = {T:.0f} K")
    axes[0].set_xlabel(r"$V_m$ (L/mol)")
    axes[0].set_ylabel("P (kPa)")
    axes[0].set_title("Boyle isotherms: P proportional to 1/V")
    axes[0].legend()

    T = np.linspace(0.0, 500.0, 200)
    for P in [50e3, 101325.0, 200e3]:
        axes[1].plot(T - 273.15, gas.molar_volume(P, np.maximum(T, 1e-9)) * 1000.0, label=f"P = {P / 1000:.0f} kPa")
    axes[1].axvline(-273.15, color="gray", linestyle=":")
    axes[1].set_xlabel("t (degC)")
    axes[1].set_ylabel(r"$V_m$ (L/mol)")
    axes[1].set_title("Charles isobars: V extrapolates to 0 at -273.15 degC")
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_01_ideal_gas_law_001.png
   :alt: Boyle isotherms: P proportional to 1/V, Charles isobars: V extrapolates to 0 at -273.15 degC
   :srcset: /api/gallery/thermo/equations_of_state/images/sphx_glr_plot_01_ideal_gas_law_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 43-46

The same law gives the textbook molar volume at 0 degC and 1 atm, and
the product :math:`PV_m` along any isotherm is the constant
:math:`RT`:

.. GENERATED FROM PYTHON SOURCE LINES 46-52

.. code-block:: Python


    print(f"Vm(273.15 K, 101325 Pa) = {gas.molar_volume(101325.0, 273.15) * 1000.0:.3f} L/mol")
    PV = gas.pressure(Vm, 300.0) * Vm
    print(f"PV_m along the 300 K isotherm: min {PV.min():.3f}, max {PV.max():.3f} J/mol (= RT = {gas.R * 300.0:.3f})")

    plt.show()




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

 .. code-block:: none

    Vm(273.15 K, 101325 Pa) = 22.414 L/mol
    PV_m along the 300 K isotherm: min 2494.339, max 2494.339 J/mol (= RT = 2494.339)





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

   **Total running time of the script:** (0 minutes 0.071 seconds)


.. _sphx_glr_download_api_gallery_thermo_equations_of_state_plot_01_ideal_gas_law.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_ideal_gas_law.ipynb <plot_01_ideal_gas_law.ipynb>`

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

      :download:`Download Python source code: plot_01_ideal_gas_law.py <plot_01_ideal_gas_law.py>`

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

      :download:`Download zipped: plot_01_ideal_gas_law.zip <plot_01_ideal_gas_law.zip>`


.. only:: html

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

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