Average kinetic energy of ideal gas from temperature
====================================================

The kinetic theory of ideal gases allows us to determine the *average kinetic energy* for an ideal gas.
It states that the average kinetic energy for all ideal gases is directly proportional to the absolute
temperature of the gas and only depends on the temperature.

**Notation:**

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

**Conditions:**

#. The gas is ideal.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Temperature_and_kinetic_energy>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.average_kinetic_energy_of_ideal_gas_from_temperature

.. py:data:: average_kinetic_energy

    Average :attr:`~symplyphysics.symbols.classical_mechanics.kinetic_energy` of the ideal gas.

Symbol:
    :code:`avg(K)`

Latex:
    :math:`\langle K \rangle`

Dimension:
    :code:`energy`


.. py:data:: equilibrium_temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: law

    :code:`avg(K) = 3 * k_B / 2 * T`


    Latex:
        .. math::
            \langle K \rangle = \frac{3 k_\text{B}}{2} T