Intensive parameters relation
=============================

The *Gibbs—Duhem relation* is a relationship among the intensive parameters of the system.
Subsequently, for a system with :math:`i` components, there are :math:`(i + 1)` independent
parameters, or degrees of freedom.

**Notation:**

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

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Gibbs%E2%80%93Duhem_equation>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.intensive_parameters_relation

.. py:data:: entropy

    :attr:`~symplyphysics.symbols.thermodynamics.entropy` of the system.

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/temperature`


.. py:data:: temperature_change

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

Symbol:
    :code:`dT`

Latex:
    :math:`d T`

Dimension:
    :code:`temperature`


.. py:data:: volume

    :attr:`~symplyphysics.symbols.classical_mechanics.volume` of the system.

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: pressure_change

    Infinitesimal change in :attr:`~symplyphysics.symbols.classical_mechanics.pressure` inside the system.

Symbol:
    :code:`dp`

Latex:
    :math:`d p`

Dimension:
    :code:`pressure`


.. py:data:: particle_count

    :attr:`~symplyphysics.symbols.basic.particle_count` of the system.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: chemical_potential_change

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

Symbol:
    :code:`d(mu)`

Latex:
    :math:`d \mu`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`S * dT - V * dp + N * d(mu) = 0`


    Latex:
        .. math::
            S d T - V d p + N d \mu = 0