Probability of finding ideal gas molecules in volume
====================================================

For ideal gas molecules, we can calculate the probability of N molecules occupying a certain region
in space, say, a container with gas particles.

**Conditions:**

#. The gas is ideal.
#. :math:`V \le V_0`
#. There are no external fields acting on the particles.

**Links:**

#. Formula 80.1 on p. 292 of "General Course of Physics" (Obschiy kurs fiziki), vol. 1 by Sivukhin D.V. (1979).

..
    TODO find English link

.. py:currentmodule:: symplyphysics.laws.thermodynamics.probability_of_finding_ideal_gas_molecules_in_volume

.. py:data:: probability

    :attr:`~symplyphysics.symbols.basic.probability` of finding :attr:`~particle_count` gas particles in :attr:`~partial_volume`.

Symbol:
    :code:`P`

Latex:
    :math:`P`

Dimension:
    :code:`dimensionless`


.. py:data:: total_volume

    Total :attr:`~symplyphysics.symbols.classical_mechanics.volume` of the region.

Symbol:
    :code:`V_0`

Latex:
    :math:`V_{0}`

Dimension:
    :code:`volume`


.. py:data:: partial_volume

    :attr:`~symplyphysics.symbols.classical_mechanics.volume` of part of the container where we are looking for the particles.

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: particle_count

    :attr:`~symplyphysics.symbols.basic.particle_count` in :attr:`~partial_volume`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`P = (V / V_0)^N`


    Latex:
        .. math::
            P = \left(\frac{V}{V_{0}}\right)^{N}