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{{Short description|Model for thermodynamic phase transitions}}

{{Short description|Model for thermodynamic phase transitions}}

In [[statistical physics]] and [[thermodynamics]], the '''Maxwell construction''' is a geometrical directive that produces the experimentally observed vapor-liquid [[phase transition]] from a suitable constant temperature curve (isotherm), usually generated by an [[equation of state]]. It was first presented by [[James Clerk Maxwell]] in an 1875 lecture to the Chemical Society in London, and subsequently published in ''Nature''. He used it in connection with the isotherms of the [[van der Waals equation]], an equation of state that had resulted from the 1873 doctoral thesis of [[Johannes Diderik van der Waals]] to produce the vapor pressure at which the phase change occurred.

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 the phase change process, and to produce the vapor pressure at which it occurs.

Simply stated, the Maxwell construction produces the horizontal (constant pressure) line between points B and F, 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.

Simply stated, the Maxwell construction produces the horizontal (constant pressure) line between points B and F, 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.

Subsequently, [[Josiah Willard Gibbs]] showed that the Maxwell construction was identical 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 by 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; however, due to its easily understood physical basis, it is still discussed whenever phase transitions are studied.

Subsequently, [[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 have made high-speed computations effortless; however, due to its easily understood physical basis, the Maxwell construction is still discussed whenever phase transitions are studied.

==Stability criteria==

==Stability criteria==