Van der Waals Equation of State

The Van der Waals equation of state was a groundbreaking development in thermodynamics, providing the first realistic description of real gases and their condensation into liquids. It starts with the ideal gas law, [latex]PV = nRT[/latex], and applies two crucial corrections. The first correction addresses the volume. In an ideal gas, particles are treated as points with no volume. The Van der Waals equation subtracts a term ‘nb’ from the container volume [latex]V[/latex], where ‘b’ is the volume excluded by a mole of particles. This term, [latex](V – nb)[/latex], represents the actual free volume available for the molecules to move in.

The second, more significant correction accounts for intermolecular attractive forces. These forces reduce the 压力 exerted by the gas on the container walls because molecules near the wall are pulled inwards by their neighbors. This reduction in pressure is proportional to the square of the particle density ([latex]n/V[/latex]), leading to the correction term [latex]a(n/V)^2[/latex] which is added to the measured pressure [latex]P[/latex]. The parameter ‘a’ is a measure of the average attraction between particles. By incorporating these two parameters, the equation can successfully model the liquid-gas phase transition and predict the existence of a critical point, above which no distinct liquid and gas phases exist. It was for this work that van der Waals received the Nobel Prize in Physics in 1910.