The van der Waals Gas Model

Real gases are more complex than ideal gases. The ideal gas model predicts that the pressure depends only on the temperature and the gas density (p = N/V = p/kT). The pressure of an ideal gas does not depend on the types or atomic structures of the gas molecules. But ideal behavior applies only at low densities where molecules don t interact much with each other. For denser gases, intermolecular interactions affect the pressures, and gases differ from 

The van der Waals gas law can be derived in various ways from an underlying model of intermolecular interactions. The next two sections give a simple derivation. 

We will find the pressure as a sum of energy and entropy components (combining Equations (8.12) and (8.29)), 

The lattice model in Example 7.1 gives the second term, the entropic component, as T dS/dV)r,N = NkT/(V - Nb). The next section shows that inter-molccular attractions lead to -(dU/dV)T,N = -aN - /V, the energetic component. 

To describe the energetic component of the pressure, you need a model for the energy as a function of volume, U(V). The total interaction energy- U of the gas is the sum of all the intcrparticle interactions. You can treat only the interactions between the particles and ignore the contributions from the internal partition functions of the particles because they don t change with V, and won t contribute to the pressure (dU/dV)T,N- (The translational partition function does depend on V, but this contribution is treated in the entropy component.) 

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