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

The chemical potential of a 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_internal_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:: entropy

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

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/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:: internal_energy

    :attr:`~symplyphysics.symbols.thermodynamics.internal_energy` of the system as a function of its natural variables.

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

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

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`mu = Derivative(U(S, V, N), N)`


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