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The van der Waals equation, named for its originator, the Dutch physicist Johannes Diderik van der Waals, is an equation of state that extends the ideal gas law to include the non-zero size of gas molecules and the interactions between them (both of which depend on the specific substance).
The Van der Waals equation adjusts for deviations from ideal behavior by incorporating correction factors for molecular size (volume) and intermolecular forces (attraction). It allows for a more precise prediction of gas behavior under conditions where these deviations become significant.
Van der Waals’ equation is \[\left(P+\frac{an^2}{V^2}\right)\left(V-nb\right)=nRT \nonumber \] It fits pressure-volume-temperature data for a real gas better than the ideal gas equation does.
The van der Waals constants for more than 200 gases used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles. The ideal gas law treats the molecules of a gas as point particles with perfectly elastic collisions.
25 Σεπ 2020 · Van der Waals' equation, equation 6.3.1, can be written \[ P = \frac{RT}{V-b} - \frac{a}{V^2}.\] A horizontal inflection point occurs where \( \frac{\partial P}{\partial V}\) and \( \frac{\partial ^2 P}{\partial V^2}\) are both zero.
The van der Waals Equation of State is an equation relating the density of gases and liquids to the pressure, volume, and temperature conditions (i.e., it is a thermodynamic equation of state).
As a specific example of the application of perturbation theory, we consider the Van der Waals equation of state. Let \(U_0\) be given by a pair potential: \[ U_0({{\textbf r}_1,...,{\textbf r}_N}) = {1 \over 2}\sum_{i\neq j} u_0(\vert{\textbf r}_i-{\textbf r}_j\vert) \nonumber \]
