Maxwell construction

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Maxwell construction

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In thermodynamic equilibrium, a necessary condition for stability is that pressure does not increase with volume . This basic consistency requirement—and similar ones for other conjugate pairs of variables—are sometimes violated in analytic models for first order phase transitions. The most famous case is the Van der Waals equation for real gases, see Fig. 1 where a typical isotherm is drawn (black curve). The Maxwell construction is a way of correcting this deficiency. The decreasing right hand part of the curve in Fig. 1 describes a diluted gas, while its left part describes a liquid. The intermediate (rising) part of the curve in Fig. 1 would be correct, if these two parts were to be joined smoothly—meaning in particular that the system would remain also in this region spatially uniform with a well defined density. But this is not what happens. If the volume of a vessel containing a fixed amount of liquid is expanded at constant temperature, there comes a point where some of the liquid boils and the system consists of two well separated phases. While this two-phase coexistence holds as the volume continues to increase, the pressure remains constant. It decreases again, after all liquid is evaporated and the gas expands. Thus the sinusoidal part of the isotherm is replaced by a horizontal line (red line in Fig. 1). According to the Maxwell construction (or "equal area rule"), the height of the horizontal line is such that the two green areas in Fig. 1 are equal. The direct quote from James Clerk Maxwell which became the Maxwell construction:“Now let us suppose the medium to pass from B to F along the hypothetical curve BCDEF in a state always homogeneous, and to return along the straight line path FB in the form of a mixture of liquid and vapour. Since the temperature has been constant throughout, no heat can have been transformed into work. Now the heat transformed into work is represented by the excess of the area FDE over BCD. hence the condition which determine the maximum pressure of the vapour at given temperature is that the line BF cuts off equal areas from the curve above and below.”

Wikipedia Inglés http://en.wikipedia.org/wiki/Maxwell_construction