Most probable speed in Maxwell—Boltzmann statistics
===================================================

The *most probable speed* is the speed at which the Maxwell—Boltzmann speed distribution function
is maximum.

**Notation:**

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

**Conditions:**

#. The gas is in thermal equilibrium with the environment.
#. The gas particles are distributed according to Maxwell—Boltzmann statistics.

**Links:**

#. `Wikipedia, first item within the list <https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#Typical_speeds>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.maxwell_boltzmann_statistics.most_probable_speed

.. py:data:: most_probable_speed

    Most probable :attr:`~symplyphysics.symbols.classical_mechanics.speed` of particles.

Symbol:
    :code:`v_prob`

Latex:
    :math:`v_\text{prob}`

Dimension:
    :code:`velocity`


.. py:data:: equilibrium_temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: molecular_mass

    :attr:`~symplyphysics.symbols.basic.mass` of a gas molecule.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: law

    :code:`v_prob = sqrt(2 * k_B * T / m)`


    Latex:
        .. math::
            v_\text{prob} = \sqrt{\frac{2 k_\text{B} T}{m}}