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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 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).
Van der waals Equation. Reason for Deviation: - There is no force of attraction between the molecules of gas but it is not true as gaseous particles have force of attraction present between them. So, correction is made in pressure P + a V 2 P + a V 2.
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: \[ U_0({{\textbf r}_1,...,{\textbf r}_N}) = {1 \over 2}\sum_{i\neq j} u_0(\vert{\textbf r}_i-{\textbf r}_j\vert) \nonumber \]
The van der Waals equation, on the other hand, requires us to use values for a and b that are unique to oxygen, and allow us to correct for the size of the oxygen molecule and the interactions that happen between oxygen molecules. When we use the van der Waals equation to solve for the pressure inside this gas tank, we get an adjustment to the ...
By adding corrections for interparticle attractions and particle volumes to the ideal gas law, we can derive a new equation that more accurately describes real gas behavior. This equation, known as the van der Waals equation, can be used to calculate the properties of a gas under non-ideal conditions.
