Mean free path of particles in gaseous medium
=============================================

The mean free path of a gas particle, defined as the average distance the particle travels between
consecutive interactions with another particles, depends on the thermodynamical parameters of the
gas as well as the interaction cross section.

**Notation:**

#. :math:`k_\text{B}` (:code:`k_B`) is :attr:`~symplyphysics.quantities.boltzmann_constant`.

**Notes:**

#. Assuming the model of spherical gas molecules, :math:`\sigma = \pi d^2`, where
   :math:`\sigma` is the cross section and :math:`d` is the molecule diameter.

**Conditions:**

#. The gas is in a state of thermodynamic equilibrium.

**Links:**

#. `Wikipedia, the fourth formula <https://en.wikipedia.org/wiki/Mean_free_path#Kinetic_theory_of_gases>`__.
#. `Chemistry LibreTexts, "27.6.4. Mean Free Path" <https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/27%3A_The_Kinetic_Theory_of_Gases/27.06%3A_Mean_Free_Path>`__.

.. py:currentmodule:: symplyphysics.laws.chemistry.mean_free_path_of_particles_in_gaseous_medium

.. py:data:: mean_free_path

    :attr:`~symplyphysics.symbols.thermodynamics.mean_free_path` of particle.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`length`


.. py:data:: pressure

    :attr:`~symplyphysics.symbols.classical_mechanics.pressure` of the gas.

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`pressure`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the gas.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: cross_section

    :attr:`~symplyphysics.symbols.chemistry.cross_section` of the interaction between the particle and the gas.

Symbol:
    :code:`sigma`

Latex:
    :math:`\sigma`

Dimension:
    :code:`area`


.. py:data:: law

    :code:`lambda = k_B * T / (sqrt(2) * p * sigma)`


    Latex:
        .. math::
            \lambda = \frac{k_\text{B} T}{\sqrt{2} p \sigma}