Chemical potential is particle count derivative of free energy
==============================================================

The chemical potential of the system is the amount of energy the system absorbs or releases
due to the introduction of a particle into the system, i.e. when the particle count increases
by one.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Chemical_potential#Thermodynamic_definition>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.chemical_potential_is_particle_count_derivative_of_free_energy

.. py:data:: chemical_potential

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

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`energy`


.. 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

    Helmholtz free energy of the system as a function of its natural variables.

    ..
        TODO add link to definition file

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

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

Dimension:
    :code:`energy`


.. py:data:: law

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


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