Internal energy of ideal gas via temperature
============================================

Internal energy of an ideal gas is the sum of the kinetic energy of all of its molecules.

**Notation:**

#. :math:`R` (:code:`R`) is :attr:`~symplyphysics.quantities.molar_gas_constant`.

**Conditions:**

#. The gas is ideal.

**Links:**

#. `Physics LibreTexts <https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/03%3A_The_First_Law_of_Thermodynamics/3.03%3A_Work_Heat_and_Internal_Energy>`__.

#. `Wikipedia, see text <https://en.wikipedia.org/wiki/Ideal_gas#Internal_energy>`__.

..
    TODO replace `mass/molar_mass` with `amount_of_substance`
    TODO add to conditions that the gas is monatomic

.. py:currentmodule:: symplyphysics.laws.thermodynamics.internal_energy_of_ideal_gas_via_temperature

.. py:data:: internal_energy

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

Symbol:
    :code:`U`

Latex:
    :math:`U`

Dimension:
    :code:`energy`


.. py:data:: mass

    :attr:`~symplyphysics.symbols.basic.mass` of the gas.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: molar_mass

    :attr:`~symplyphysics.symbols.basic.molar_mass` of the gas.

Symbol:
    :code:`M`

Latex:
    :math:`M`

Dimension:
    :code:`mass/amount_of_substance`


.. py:data:: law

    :code:`U = 3 * m * R * T / (2 * M)`


    Latex:
        .. math::
            U = \frac{3 m R T}{2 M}