Statistical Mechanics Lecture 7 of 29

April 12, 2012 by Antonello Scardicchio

A. Schadicchio, ICTP

This lesson is the first of a series dedicated to phase transitions from the thermodynamic standpoint. A convenient thermodynamic potential to analyze phase transitions is enthalpy. In equilibrium, the variation of enthalpy is zero when small amounts of substance is exchanged between the phases (enthalpy reaches a minimum).

Simple equation counting shows that n - f + 2 variables are needed to describe a state where n substances with f phases coexist. This is the Gibbs' phase rule. For a single substance it implies that just one thermodynamic intensive variable, say temperature, is enough to describe the region of coexistence of two phases. 3 phases can coexist in equilibrium only at isolated points! For most substances, including water, there is one point in which its solid, liquid, and gas phases occur together. This is the triple point.

Finally, the critical point for the vapor - liquid transition was discussed. It is the state where the vapor-liquid transition line in the P - T plane ends. Beyond the critical temperature the liquid and gas phases are indistinguishable. The van der Waals equation of state was examined as an example of e.o.s. having a critical point.

You might not believe that above the critical point, the liquid and vapor phases are indistinguishable. 20 years ago, you'd have to take the word of your teacher for it. Now we have Youtube.

Watch how benzene passes from one to two phases when the temperature is lowered past the critical point. Notice how the meniscus is formed.

Watch how benzene passes from one to two phases when the temperature is lowered past the critical point. Notice how the meniscus is formed.

Weird things happen at the critical point. Watch the phenomenon of critical opalescence in this other video and ignore the colors since the good stuff begins at about 0:40.Weird things happen at the critical point. Watch the phenomenon of critical opalescence in this other video and ignore the colors since the good stuff begins at about 0:40.

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