Entropy is derivative of free energy
====================================

Entropy of a system can be found if its free 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_free_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:: volume

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

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: particle_count

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

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: free_energy

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

Symbol:
    :code:`F(T, V, N)`

Latex:
    :math:`F{\left(T,V,N \right)}`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`S = -Derivative(F(T, V, N), T)`


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