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Why does pressure due to van der Waals' forces increase as the square of density?

  1. Aug 14, 2011 #1
    In van der Waals' equation for real gases, the adaptation to account for intermolecular attractions in real gas is [itex]a\frac{n^2}{V^2}[/itex]. This implies that the pressure due to the VDW forces on the container is proportional to the square of the density, [itex]\rho^2 = \frac{n^2}{V^2}[/itex].

    When I do calculations following from [itex]P_{VDW}=\frac{\pi \rho^2 \lambda}{H^3}[/itex], I end up with a cubic dependence.

    Is there a qualitative way to imagine why the pressure is proportional to the square of the molecular density, [itex]\rho[/itex]?
  2. jcsd
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