The Assumptions of Van der Waals Equation

The first term is simply the volume of a sphere of radius ro, or eight times the volume of the sphere of diameter ro which represents a molecule. In the second integral, we may expand in power series, since f is relatively 

Here b is four times the volume of No spheres of radius r0/2, or four times the volume of all the molecules in a gram mole. Since the force represented by the potential t is attractive, is negative and the quantity a is positive and measures the strength of the intermolecular attractions. 

It is found experimentally that the formula (5.3) for the second virial coefficient is fairly well obeyed for real gases, showing that the assumptions of Van der Waals are not greatly in error. This formula leads to the equation of state 

Equation (5.4) indicates that for high temperatures (where a/RT is less than b) the pressure should be greater than that calculated for a perfect gas, while at low temperatures (a/RT greater than 6) the pressure should be less than for a perfect gas. The temperature 

We can now take Van der Waals equation (1.3), expand it in the form of Eq. (4.1), and see if the second virial coefficient agrees with the value 

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