# Pressure in the van der Waals equation of state

In textbooks, pressure in the van der Waals equation of state is often explained like this: the effect of attraction of the molecules of the near-wall layer reduces the pressure on the walls of the container because there are no molecules in the walls. I wonder why there is no mention of possible force between these molecules and atoms in the walls (except for impulsive force at the time of collision).

• Trying to explain pressure by focusing on the contribution from walls is doomed to failure. At least in the various textbooks I have lying around my office, this is not the way pressure is explained. Nov 18 '19 at 14:38
• @Jon Custer Thanks for your comments. The point of my question is that textbooks should explain why possible attraction (which should cause the increase in speed of incident molecules) between incident molecules (moving towards the wall) and atoms in the wall (which could display dielectric behavior) is negligible. Nov 18 '19 at 15:35

For a short range interaction (compared to the size of the system) the change in free energy caused by the interaction with the walls will go (to leading order) like the surface area of the system. $$\Delta F \sim A \sim V^{2/3}\;.$$ That is the effect of the interaction will be sub-extensive. It scales more slowly than the volume and so, for a macroscoppically large system, will be a negligable effect.
For comparison, the effect of the particle-particle interactions is proportional to the number of particles and so scales as $$\sim N$$ and so is an extensive quantity, which cannot be neglected as easily.