.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrochem/fuel_cell/plot_01_grove_gas_battery.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_electrochem_fuel_cell_plot_01_grove_gas_battery.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_electrochem_fuel_cell_plot_01_grove_gas_battery.py:


Grove's gas battery: the hydrogen-oxygen fuel cell
====================================================

In 1839-1842 William Grove ran electrolysis backwards: hydrogen and
oxygen over platinum electrodes in dilute acid recombined to produce a
current. This example computes the reversible voltage of that cell two
ways -- from the standard potentials of the O2/H2O and H+/H2 couples and
from :math:`\Delta G^\circ` via
:func:`~chemistrykit.electrochem.systems.fuel_cell.reversible_cell_voltage` --
its temperature dependence
(:func:`~chemistrykit.electrochem.systems.fuel_cell.reversible_cell_voltage_at_temperature`),
and its thermodynamic efficiency limit :math:`\Delta G/\Delta H`
(:func:`~chemistrykit.electrochem.systems.fuel_cell.fuel_cell_efficiency_limit`)
compared with the Carnot limit of a heat engine.

.. GENERATED FROM PYTHON SOURCE LINES 19-32

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.electrochem.systems.fuel_cell import (
        fuel_cell_efficiency_limit,
        reversible_cell_voltage,
        reversible_cell_voltage_at_temperature,
    )
    from chemistrykit.electrochem.systems.standard_potentials import standard_cell_potential

    # H2 + 1/2 O2 -> H2O(l) at 298.15 K (standard thermochemical data).
    dG, dH, dS, n = -237.13e3, -285.83e3, -163.3, 2








.. GENERATED FROM PYTHON SOURCE LINES 33-38

.. code-block:: Python

    E_table = standard_cell_potential("O2/H2O", "H+/H2")
    E_gibbs = reversible_cell_voltage(dG, n)
    print(f"From standard potentials: {E_table:.3f} V; from Delta G: {E_gibbs:.3f} V")
    print(f"Maximum efficiency Delta G / Delta H = {fuel_cell_efficiency_limit(dG, dH):.1%}")





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

 .. code-block:: none

    From standard potentials: 1.230 V; from Delta G: 1.229 V
    Maximum efficiency Delta G / Delta H = 83.0%




.. GENERATED FROM PYTHON SOURCE LINES 39-41

Reversible voltage and efficiency limit vs. temperature, compared with
a Carnot engine rejecting heat at 298 K.

.. GENERATED FROM PYTHON SOURCE LINES 41-59

.. code-block:: Python

    T = np.linspace(300.0, 1000.0, 100)
    E_T = reversible_cell_voltage_at_temperature(dH, dS, n, T)
    eff_fc = fuel_cell_efficiency_limit(dH - T * dS, dH)
    eff_carnot = 1.0 - 298.15 / T

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
    ax1.plot(T, E_T)
    ax1.set_xlabel("T (K)")
    ax1.set_ylabel("Reversible voltage (V)")
    ax1.set_title(r"$E(T) = -(\Delta H - T\Delta S)/nF$")
    ax2.plot(T, eff_fc * 100, label=r"fuel cell, $\Delta G/\Delta H$")
    ax2.plot(T, eff_carnot * 100, label="Carnot engine (cold side 298 K)")
    ax2.set_xlabel("T (K)")
    ax2.set_ylabel("Efficiency limit (%)")
    ax2.legend()
    fig.suptitle("Grove's hydrogen-oxygen cell")
    fig.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/electrochem/fuel_cell/images/sphx_glr_plot_01_grove_gas_battery_001.png
   :alt: Grove's hydrogen-oxygen cell, $E(T) = -(\Delta H - T\Delta S)/nF$
   :srcset: /api/gallery/electrochem/fuel_cell/images/sphx_glr_plot_01_grove_gas_battery_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.059 seconds)


.. _sphx_glr_download_api_gallery_electrochem_fuel_cell_plot_01_grove_gas_battery.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_grove_gas_battery.ipynb <plot_01_grove_gas_battery.ipynb>`

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

      :download:`Download Python source code: plot_01_grove_gas_battery.py <plot_01_grove_gas_battery.py>`

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

      :download:`Download zipped: plot_01_grove_gas_battery.zip <plot_01_grove_gas_battery.zip>`


.. only:: html

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

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