Van der Waals equation

The van der Waals equation is a mathematical formula that describes the behavior of real gases. It is an equation of state that relates the pressure, volume, number of molecules, and temperature in a fluid. The equation modifies the ideal gas law, ${\displaystyle pV=NkT}$ in which ${\displaystyle k}$ is the Boltzmann constant, in two ways: first, it considers particles to have a finite diameter (whereas an ideal gas consists of point particles); second, its particles interact with each other (unlike an ideal gas, whose particles move as though alone in the volume).

The equation is named after Dutch physicist Johannes Diderik van der Waals, who first derived it in 1873 as part of his doctoral thesis. Van der Waals based the equation on the idea that fluids are composed of discrete particles, which few scientists believed existed. However, the equation accurately predicted the behavior of a fluid around its critical point, which had been discovered a few years earlier. Its qualitative and quantitative agreement with experiments ultimately cemented its acceptance in the scientific community. These accomplishments won van der Waals the 1910 Nobel Prize in Physics.^[1] Today the equation is recognized as an important model of phase change processes.^[2]