Van der Waals equation
======================

To more accurately describe the behavior of real gases at low temperatures,
a Van der Waals gas model was created, taking into account the forces of intermolecular interaction.
In this model, internal energy becomes a function not only of temperature, but also of molar volume.

The Van der Waals equation is one of the well-known approximate equations of state describing
the properties of a real gas, having a compact form and taking
into account the main characteristics of a gas with intermolecular interaction.

**Notation:**

#. :math:`R` (:code:`R`) is :attr:`~symplyphysics.quantities.molar_gas_constant`.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.thermodynamics.equations_of_state.van_der_waals.equation

.. py:data:: pressure

    :attr:`~symplyphysics.symbols.classical_mechanics.pressure` in the van der Waals fluid.

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`pressure`


.. py:data:: molar_volume

    :attr:`~symplyphysics.symbols.basic.molar_volume` of the van der Waals fluid.

Symbol:
    :code:`v_m`

Latex:
    :math:`v_\text{m}`

Dimension:
    :code:`volume/amount_of_substance`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the van der Waals fluid.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: attractive_forces_parameter

    :attr:`~symplyphysics.symbols.thermodynamics.attractive_forces_parameter`.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`pressure*volume**2/amount_of_substance**2`


.. py:data:: excluded_volume_parameter

    :attr:`~symplyphysics.symbols.thermodynamics.excluded_volume_parameter`.

Symbol:
    :code:`b`

Latex:
    :math:`b`

Dimension:
    :code:`volume/amount_of_substance`


.. py:data:: law

    :code:`(p + a / v_m^2) * (v_m - b) = R * T`


    Latex:
        .. math::
            \left(p + \frac{a}{v_\text{m}^{2}}\right) \left(v_\text{m} - b\right) = R T