Internal energy is first order homogeneous function
===================================================

Internal energy is a first-order homogeneous function of its internal variables (entropy, volume,
and particle count).

**Links:**

#. `Wikipedia, first equation <https://en.wikipedia.org/wiki/Thermodynamic_potential#Euler_relations>`__.

.. py:currentmodule:: symplyphysics.conditions.thermodynamics.internal_energy_is_first_order_homogeneous_function

.. py:data:: entropy

    :attr:`~symplyphysics.symbols.thermodynamics.entropy`.

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/temperature`


.. py:data:: volume

    :attr:`~symplyphysics.symbols.classical_mechanics.volume`

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: particle_count

    :attr:`~symplyphysics.symbols.basic.particle_count`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: internal_energy

    :attr:`~symplyphysics.symbols.thermodynamics.internal_energy` as a function of :attr:`~entropy`, :attr:`~volume`, and
    :attr:`~particle_count`.

Symbol:
    :code:`U(S, V, N)`

Latex:
    :math:`U{\left(S,V,N \right)}`

Dimension:
    :code:`energy`


.. py:data:: factor

    Dimensionless real-valued factor.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`dimensionless`


.. py:data:: homogeneity_condition

    :code:`U(k * S, k * V, k * N) = k * U(S, V, N)`


    Latex:
        .. math::
            U{\left(k S,k V,k N \right)} = k U{\left(S,V,N \right)}