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:

\(R\) (R) is molar_gas_constant.

Links:

Wikipedia.

pressure¶: pressure in the van der Waals fluid.

Symbol:: p
Latex:: \(p\)
Dimension:: pressure

molar_volume¶: molar_volume of the van der Waals fluid.

Symbol:: v_m
Latex:: \(v_\text{m}\)
Dimension:: volume/amount_of_substance

temperature¶: temperature of the van der Waals fluid.

Symbol:: T
Latex:: \(T\)
Dimension:: temperature

attractive_forces_parameter¶: attractive_forces_parameter.

Symbol:: a
Latex:: \(a\)
Dimension:: pressure*volume**2/amount_of_substance**2

excluded_volume_parameter¶: excluded_volume_parameter.

Symbol:: b
Latex:: \(b\)
Dimension:: volume/amount_of_substance

law¶

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

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