Entropy is derivative of Gibbs energy
=====================================

Entropy of a system can be found if its Gibbs energy is known as a function of temperature.

**Links:**

#. `Wikipedia, follows from the corresponding fundamental relation <https://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.entropy_is_derivative_of_gibbs_energy

.. py:data:: entropy

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

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/temperature`


.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: pressure

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

Symbol:
    :code:`p`

Latex:
    :math:`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:: gibbs_energy

    :attr:`~symplyphysics.symbols.thermodynamics.gibbs_energy` of the system as a function of :attr:`~temperature`, :attr:`~pressure`,
    and :attr:`~particle_count`.

Symbol:
    :code:`G(T, p, N)`

Latex:
    :math:`G{\left(T,p,N \right)}`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`S = -Derivative(G(T, p, N), T)`


    Latex:
        .. math::
            S = - \frac{\partial}{\partial T} G{\left(T,p,N \right)}