vanderWaalsGleichung

The van der Waals equation is a thermodynamic equation of state for real gases, introduced by the Dutch physicist Johannes Diderik van der Waals in 1873. It extends the ideal gas law to account for finite molecular size and intermolecular attractions, providing a more realistic description of gas behavior over a range of temperatures and pressures.

In its common form for n moles of gas, it is written as (P + a n^2 / V^2) (V - n b) = n R T, where P is pressure, V is volume, T is temperature, R is the gas constant, and a and b are empirically determined parameters. For one mole, the molar form is (P + a / v^2) (v - b) = R T, with v as the molar volume. The parameter a accounts for attractive forces between molecules, which reduce the effective pressure, while b represents the finite volume occupied by the molecules, reducing the available space.

When a and b approach zero, the equation reduces to the ideal gas law P V = n R T, highlighting its role as a correction to ideal behavior. The equation is often used to estimate non-ideal P–V–T relationships and to derive critical constants, phase behavior, and thermodynamic properties for many gases.

Limitations include decreasing accuracy at very high pressures or very low temperatures, near the critical point, and for multicomponent or highly complex substances. More advanced equations of state (such as Peng–Robinson or Soave–Redlich–Kwong) are often preferred for engineering applications. The van der Waals equation remains a foundational model in thermodynamics and physical chemistry.