Maxwell construction

In thermodynamics, the Maxwell construction refers to a set of geometrical instructions that modify a given constant temperature curve (isotherm) to produce its experimentally observed vapor-liquid phase transition section. The isotherm is usually generated by an equation of state.

The method was first presented by James Clerk Maxwell in an 1875 lecture to the Chemical Society in London, and subsequently published in Nature. Maxwell used it in connection with the isotherms of the van der Waals equation to describe its phase change, in particular its vapor pressure, the liquid and vapor states that are its extremes, and the temperature dependence of these quantities.

Simply stated, the Maxwell construction produces the horizontal (constant pressure) line between points B and F on the isotherm, shown dashed in Fig. 1 below. This line is the one for which the two areas, I and II, shown in the figure, are equal. Hence, it is also known as the equal area rule.

A few years later, Josiah Willard Gibbs showed that the Maxwell construction was equivalent to the condition of material equilibrium given by the equality of the electrochemical potential of the two phases. As such, Gibbs' formulation is more fundamental than Maxwell's, but due to the ease with which areas could be measured with a planimeter, the equal area rule continued to be widely used for many years. Its use has declined in the present age of digital computers, which can perform complex computations rapidly; however, due to its easily understood physical basis, the Maxwell construction is still discussed whenever phase transitions are studied.