Chemical potential of ideal gas
===============================

The chemical potential of an ideal gas can be calculated from its temperature, concentration,
and thermal wavelength.

**Notation:**

#. :math:`k_\text{B}` (:code:`k_B`) is :attr:`~symplyphysics.quantities.boltzmann_constant`.

**Conditions:**

#. The gas is ideal.

**Links:**

#. Formula on p. 394 of "Statistical Mechanics" by Terrent L. Hill (1987)

.. py:currentmodule:: symplyphysics.laws.thermodynamics.chemical_potential_of_ideal_gas

.. py:data:: chemical_potential

    :attr:`~symplyphysics.symbols.thermodynamics.chemical_potential` of ideal gas.

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`energy`


.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: concentration

    Concentration of the gas, or :attr:`~symplyphysics.symbols.basic.number_density`.

Symbol:
    :code:`n`

Latex:
    :math:`n`

Dimension:
    :code:`1/volume`


.. py:data:: thermal_wavelength

    :attr:`~symplyphysics.symbols.thermodynamics.thermal_wavelength` of the gas. Also see :doc:`Thermal de Broglie wavelength
    <definitions.thermal_de_broglie_wavelength>`.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`mu = k_B * T * log(n * lambda^3)`


    Latex:
        .. math::
            \mu = k_\text{B} T \log \left( n \lambda^{3} \right)