Deriving vdW-equation from kinetic theory

• Philip Koeck
In summary, the van der Waals equation is an important equation of state for describing the behavior of real gases, taking into account intermolecular forces and the finite volume of gas molecules. It can be derived from kinetic theory by considering the interactions between molecules and the volume they occupy. The main assumptions made in this derivation are that gas molecules have no volume and intermolecular forces are proportional to the square of the distance between molecules. The vdW-equation differs from the ideal gas law by accounting for the volume of gas molecules and attractive forces between them. However, it has limitations in that it is only applicable to low pressures and temperatures and does not accurately describe phase transitions. Other equations, such as the Redlich-Kwong equation,
Philip Koeck
Does anybody know of a derivation of the van der Waals equation from the molecular kinetic theory of gases, but without using the tools of statistical physics (such as partition functions)?

The vdW EoS can be understood as a virial expansion. You find a nice derivation in Landau&Lifshitz vol. V (which is anyway one of the best books on thermodynamics and statistics).

Philip Koeck and Dale

1. How is the van der Waals equation derived from kinetic theory?

The van der Waals equation is derived from kinetic theory by considering the behavior of gas particles at the microscopic level. It takes into account the volume of the gas particles and the attractive and repulsive forces between them, which are not accounted for in the ideal gas law.

2. What assumptions are made in the derivation of the van der Waals equation?

The derivation of the van der Waals equation assumes that gas particles are point masses with no volume, and that they only interact through elastic collisions. It also assumes that the attractive and repulsive forces between particles are constant and do not change with temperature or pressure.

3. How does the van der Waals equation improve upon the ideal gas law?

The van der Waals equation improves upon the ideal gas law by accounting for the volume of gas particles and the intermolecular forces between them. This allows for a more accurate prediction of gas behavior at high pressures and low temperatures, where the ideal gas law breaks down.

4. Can the van der Waals equation be applied to all gases?

No, the van der Waals equation is most accurate for gases that have small molecules and weak intermolecular forces, such as noble gases. It is less accurate for gases with larger molecules and stronger intermolecular forces, such as water vapor or ammonia.

5. How is the van der Waals equation used in practical applications?

The van der Waals equation is used in various practical applications, such as predicting the behavior of real gases in industrial processes, designing gas storage tanks, and understanding the properties of gases at high pressures and low temperatures. It is also used in the study of phase transitions, such as the liquid-vapor transition.

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