Van der Waals Isotherms

The ideal gas law assumes point particles with no volume and no intermolecular forces. The van der Waals equation introduces two parameters to correct for this: one for the excluded volume of the particles, and one for their attractive forces. In reduced units relative to the critical point, the equation becomes universal for all gases.

Experiment: Traversing the mechanical regimes

Use the Van der Waals Isotherms module to observe the physical behavior and mechanical stability of the mean-field model under different conditions.

1. Set the Reduced temperature to 1 and Reduced volume to 1. Note the status "Finite model", pressure of 1.0, and the marginal slope of 0.0 indicating the critical point.
2. Decrease the Reduced temperature to 0.75 and the Reduced volume to 0.75. Notice the pressure dips into negative values (-0.5333) and the slope becomes positive (+2.7022). A positive slope (dp/dv > 0) indicates mechanical instability; an increase in volume would cause an increase in pressure, causing the system to separate into two phases (liquid and gas).
3. Increase the Reduced temperature to 1.25 and Reduced volume to 2. The slope is now negative (-0.45), indicating a stable single phase. The curve here resembles that of an ideal gas at large volumes.
4. Set the Reduced volume to 1/3 (any temperature). Observe that the values become unavailable. This represents the excluded volume limit where the gas is compressed so densely that the particles are packed tightly together, and volume cannot decrease further.