Free energy differential
========================

The fundamental thermodynamic relations are fundamental equations which demonstate how important
thermodynamic quantities depend on variables that are measurable experimentally.

**Notation:**

#. :math:`d` denotes an exact, path-independent differential.

**Notes:**

#. Temperature, volume, and particle count are so called natural variables of free energy as a
   thermodynamic potential.
#. For a system with more than one type of particles, the last term can be represented as a sum over all
   types of particles, i.e. :math:`\sum_i \mu_i \, d N_i`.

**Conditions:**

#. The system is in thermal equilibrium with its surroundings.
#. The system is composed of only one type of particles, i.e. the system is a pure substance.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.thermodynamics.free_energy_differential

.. py:data:: free_energy_change

    Infinitesimal change in :attr:`~symplyphysics.symbols.thermodynamics.helmholtz_free_energy` of the system.

Symbol:
    :code:`dF`

Latex:
    :math:`dF`

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:: temperature_change

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

Symbol:
    :code:`dT`

Latex:
    :math:`dT`

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:: volume_change

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

Symbol:
    :code:`dV`

Latex:
    :math:`dV`

Dimension:
    :code:`volume`


.. py:data:: chemical_potential

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

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`energy`


.. py:data:: particle_count_change

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

Symbol:
    :code:`dN`

Latex:
    :math:`dN`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`dF = -S * dT - p * dV + mu * dN`


    Latex:
        .. math::
            dF = - S dT - p dV + \mu dN