Average speed in Maxwell—Boltzmann statistics
=============================================

The *average*, or mean, *speed* is the expected value of the speed distribution of gas particles.

**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 <https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#Typical_speeds>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.average_speed_in_maxwell_boltzmann_statistics

.. py:data:: average_speed

    Average molecular :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`avg(v)`

Latex:
    :math:`\langle v \rangle`

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:`avg(v) = sqrt(8 * k_B * T / (pi * m))`


    Latex:
        .. math::
            \langle v \rangle = \sqrt{\frac{8 k_\text{B} T}{\pi m}}