Differences From the Basic Postulates
Van der Waals modified the basic postulates of kinetic energy in two significant ways.
Volume: In our previous examination of the basic postulates, we ignored the volume of the molecules themselves, focusing on the total volume of the container. This allowed us to assume that all of the molecules were point masses, and that they were evenly distributed throughout the container. Van der Waals decided that the space or volume occupied by individual gas molecules should be taken into account. Thus the assumption of the uniform distribution of the molecules throughout the entire container no longer holds true.
Intermolecular Forces: These were neglected, as we considered them to be too small compared with the kinetic energy generated by molecular collisions. Only direct contact between the molecules was allowed into our calculations. Van der Waals assumed that these forces are actually quite large, being greater than the size of the molecules themselves, and hence must be taken into consideration. Therefore, there is indeed an action at a distance, albeit quite small and weak.
These two changes transformed the basic postulates into something more fitting for real gases, and allowed the derivation of van der Waals' formula. As before, assume the molecules are spherical with a radius of r, and that they collide with each other but bounce back. These collisions will occur when the distance between their centers become small, as shown in figure 2.
In the next article, we will use the ideal gas law and van der Waals' postulates to derive the equation of state for a real gas.
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