Internal energy change via heat and electric displacement change
================================================================

Internal energy change of the system with a dielectric medium can be
expressed using the infinitesimal heat flowing in or out of the system
and the change in electric displacement.

**Conditions:**

#. The dielectric is isotropic whether or not the electric field is present.
#. The medium is homogeneous.
#. The volume change of the medium is insignificant.

**Links:**

#. Formula 31.2 on p. 122 of "General Course of Physics" (Obschiy kurs fiziki), vol. 3 by Sivukhin D.V. (1979).

.. py:currentmodule:: symplyphysics.laws.thermodynamics.dielectrics.internal_energy_change_via_heat_and_electric_displacement_change

.. py:data:: internal_energy_density_change

    Infinitesimal change in :attr:`~symplyphysics.symbols.thermodynamics.internal_energy` per unit :attr:`~symplyphysics.symbols.classical_mechanics.volume`.

Symbol:
    :code:`dU`

Latex:
    :math:`dU`

Dimension:
    :code:`energy/volume`


.. py:data:: heat_density

    Small amount of :attr:`~symplyphysics.symbols.thermodynamics.heat` added to or taken from the system per unit :attr:`~symplyphysics.symbols.classical_mechanics.volume`.

Symbol:
    :code:`delta(Q)`

Latex:
    :math:`\delta Q`

Dimension:
    :code:`energy/volume`


.. py:data:: electric_field_strength

    :attr:`~symplyphysics.symbols.electrodynamics.electric_field_strength` in the medium.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`voltage/length`


.. py:data:: electric_displacement_change

    Infinitesimal change in :attr:`~symplyphysics.symbols.electrodynamics.electric_displacement`.

Symbol:
    :code:`dD`

Latex:
    :math:`dD`

Dimension:
    :code:`charge/area`


.. py:data:: law

    :code:`dU = delta(Q) + E * dD`


    Latex:
        .. math::
            dU = \delta Q + E dD