Stability

Stability - Stability ChE210A Previously, we saw that the...

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© M. S. Shell 2011 1/12 last modified 11/9/2011 Stability ChE210A Previously, we saw that the stable, equilibrium phase at a given g and G is given by the state that minimizes the Gibbs free energy. Consider the liquid-gas transition, where we examined a Gibbs free energy curve that depends on density. One example, at a particular state point above the boiling point, is: Here, there are two minima, corresponding to the gas and liquid states. The gas is the stable phase at these conditions, since its free energy is lower. That means, if we wait long enough for equilibrium to occur, the system at these conditions will evolve into a gaseous state. However, we could prepare a liquid at the higher density, if we wanted. We could be very careful and heat a liquid above its boiling point without it actually boiling. At this point, the liquid would be superheated . A superheated liquid remains in that state for times long enough to make meaningful investigations of it. When it finally vaporizes, however, the system trans- forms irreversibly to the stable gas phase, and there is a net increase in entropy in the world. How does a superheated liquid exist for finite periods of time? As one can see from the free energy curve above, there is a barrier in free energy in between the liquid and gas states. If the system is at ± ² , it has to temporarily increase its free energy in order to travel over to the gas state at ± ³ . This free energy barrier means that there is a finite rate at which the liquid can turn to gas. If the barrier is high enough, the rate of spontaneously forming a gas will be slow enough that there is time to investigate the properties of the superheated liquid. ´ ± G = G µ g = g µ ± ² ± ³
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© M. S. Shell 2011 2/12 last modified 11/9/2011 The key to forming a superheated liquid is to heat it in a clean container that is not agitated. Any dirt or agitation would kick the system over to the gaseous state by lowering the free energy barrier between the two regions (by way of providing nucleation sites), thus greatly increasing the rate of liquid-to-gas conversion. Superheating is actually quite common: it is relatively easy to superheat liquid water in microwaves, where energy can be added to the liquid without much disturbance. Adding sugar to or suddenly agitating a clean container of water superheated in a microwave is dangerous and can cause explosive boiling. Superheated liquids are part of a more general class of metastable systems: A system that resides at a local, but not a global, free energy minimum is meta- stable . The existence of a free energy barrier between the metastable and glob- ally stable states of the system enables the former to exist for periods of time that permit investigations of it. Ultimately, however, metastable systems will at- tain global equilibrium in the rigorous limit of infinite time. Metastable systems include:
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This note was uploaded on 12/29/2011 for the course CHE 210a taught by Professor Staff during the Fall '08 term at UCSB.

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Stability - Stability ChE210A Previously, we saw that the...

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