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

The internal energy of an ideal gas depends solely on its temperature and the number of gas particles
and is independent of other thermodynamic quantities such as pressure or density.

**Notation:**

#. :math:`d` denotes an exact, path-independent differential.

**Links:**

#. `Wikipedia, equivalent formula <https://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_the_ideal_gas>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.internal_energy_change_of_ideal_gas_via_temperature

.. py:data:: internal_energy_change

    Infinitesimal change in :attr:`~symplyphysics.symbols.thermodynamics.internal_energy` of the system.

Symbol:
    :code:`dU`

Latex:
    :math:`dU`

Dimension:
    :code:`energy`


.. py:data:: isochoric_heat_capacity

    :attr:`~symplyphysics.symbols.thermodynamics.heat_capacity` at constant :attr:`~symplyphysics.symbols.classical_mechanics.volume`.

Symbol:
    :code:`C_V`

Latex:
    :math:`C_{V}`

Dimension:
    :code:`energy/temperature`


.. py:data:: temperature_change

    Infinitesimal change in :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the system.

Symbol:
    :code:`dT`

Latex:
    :math:`dT`

Dimension:
    :code:`temperature`


.. py:data:: law

    :code:`dU = C_V * dT`


    Latex:
        .. math::
            dU = C_{V} dT