Dimensionless equation
======================

The *dimensionless form* of the van der Waals equation of state features :ref:`reduced quantities
<vdw_reduced_units_def>`. One notable property of the dimensionless equation of state is that it
contains no substance-specific quantities, i.e. all van der Waals fluids will plot on the same
reduced pressure-volume curve at the same reduced temperature.

**Links:**

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

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

.. py:data:: reduced_pressure

    See :doc:`laws.thermodynamics.equations_of_state.van_der_waals.reduced_pressure`.

Symbol:
    :code:`p_r`

Latex:
    :math:`p_{r}`

Dimension:
    :code:`dimensionless`


.. py:data:: reduced_volume

    See :doc:`laws.thermodynamics.equations_of_state.van_der_waals.reduced_volume`.

Symbol:
    :code:`V_r`

Latex:
    :math:`V_{r}`

Dimension:
    :code:`dimensionless`


.. py:data:: reduced_temperature

    See :doc:`laws.thermodynamics.equations_of_state.van_der_waals.reduced_temperature`.

Symbol:
    :code:`T_r`

Latex:
    :math:`T_{r}`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`(p_r + 3 / V_r^2) * (V_r - 1/3) = 8 * T_r / 3`


    Latex:
        .. math::
            \left(p_{r} + \frac{3}{V_{r}^{2}}\right) \left(V_{r} - \frac{1}{3}\right) = \frac{8 T_{r}}{3}