Interaction cross section in elastic interaction model
======================================================

The Sutherland formula adjusts the formula of the cross section of interacting gas molecules
taking into account their pairwise interactions. See :ref:`Effective cross section <effective_cross_section>`.

**Conditions:**

#. The sizes of the target and field molecules are equal.

#. Applicable to gases under moderate pressure.

**Links:**

#. `Wikipedia <https://ru.wikipedia.org/wiki/%D0%93%D0%B0%D0%B7%D0%BE%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D1%8D%D1%84%D1%84%D0%B5%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D0%B5_%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8B>`__.

..
    TODO: find English link
    NOTE: a more proper law would replace `particle_diameter` with `test_radius + target_radius`

.. py:currentmodule:: symplyphysics.laws.chemistry.interaction_cross_section_in_elastic_interaction_model

.. py:data:: cross_sectional_area_of_interaction

    :attr:`~symplyphysics.symbols.chemistry.cross_section` of interaction of particles.

Symbol:
    :code:`sigma`

Latex:
    :math:`\sigma`

Dimension:
    :code:`area`


.. py:data:: particle_diameter

    :attr:`~symplyphysics.symbols.classical_mechanics.diameter` of a gas particle.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`length`


.. py:data:: sutherland_constant

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

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`temperature`


.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: law

    :code:`sigma = pi * D^2 * (1 + S / T)`


    Latex:
        .. math::
            \sigma = \pi D^{2} \left(1 + \frac{S}{T}\right)