**Van der Waals Model** ======================= *Van der Waals equation of state* uses a model which extends the ideal gas law to include the non-zero size of gas molecules and the interactions between them. .. _vdw_critical_parameters_def: **Critical parameters** *Critical parameters* of the van der Waals equation of state are such values of volume, pressure, and temperature at which the isotherm has an inflection point whose tangent at that point is zero, i.e. the first and second derivatives of pressure with respect to volume at constant temperature are zero: .. math:: \left( \frac{\partial p}{\partial V} \right)_T = \left( \frac{\partial^2 p}{\partial V^2} \right)_T = 0 .. _vdw_reduced_units_def: **Reduced units** *Reduced units* are used in the :ref:`dimensionless ` van der Waals equation of state. A reduced quantity :math:`X_r` is defined as the ratio of quantity :math:`X` to the corresponding :ref:`critical parameter ` :math:`X_\text{c}`. .. py:currentmodule:: symplyphysics.thermodynamics.equations_of_state.van_der_waals **Contents:** .. toctree:: :maxdepth: 4 thermodynamics.equations_of_state.van_der_waals.critical_van_der_waals_molar_volume thermodynamics.equations_of_state.van_der_waals.critical_van_der_waals_pressure thermodynamics.equations_of_state.van_der_waals.critical_van_der_waals_temperature thermodynamics.equations_of_state.van_der_waals.dimensionless_van_der_waals_equation thermodynamics.equations_of_state.van_der_waals.reduced_van_der_waals_pressure thermodynamics.equations_of_state.van_der_waals.reduced_van_der_waals_temperature thermodynamics.equations_of_state.van_der_waals.reduced_van_der_waals_volume thermodynamics.equations_of_state.van_der_waals.van_der_vaals_equation thermodynamics.equations_of_state.van_der_waals.van_der_waals_molar_internal_energy thermodynamics.equations_of_state.van_der_waals.van_der_waals_second_virial_coefficient