Enthalpy formula
================

The enthalpy differential can be integrated using the Euler's theorem on homogeneous functions for
internal energy.

**Notes:**

#. This formula works for a single-component system. For a multi-component system replace the
   product of chemical potential and particle count with a sum over each type of components.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.thermodynamics.euler_relations.enthalpy_formula

.. py:data:: enthalpy

    :attr:`~symplyphysics.symbols.thermodynamics.enthalpy` of the system. Also see :doc:`laws.thermodynamics.enthalpy_is_internal_energy_plus_pressure_energy`.

Symbol:
    :code:`H`

Latex:
    :math:`H`

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:: entropy

    :attr:`~symplyphysics.symbols.thermodynamics.entropy` of the system. Also see :doc:`laws.thermodynamics.entropy_change_in_reversible_process`.

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/temperature`


.. py:data:: chemical_potential

    :attr:`~symplyphysics.symbols.thermodynamics.chemical_potential` of the system. Also see
    :doc:`laws.thermodynamics.chemical_potential_is_particle_count_derivative_of_internal_energy`.

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`energy`


.. py:data:: particle_count

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

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`H = T * S + mu * N`


    Latex:
        .. math::
            H = T S + \mu N