Lecture_6a_4e

Lecture_6a_4e - CHAPTER 6 LECTURE NOTES Degrees of Freedom...

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CHAPTER 6 LECTURE NOTES Degrees of Freedom: The number of degrees of freedom (number of variables we can change without affecting the &nature± of the system) is determined by the equation known as the phase rule : f = c ² p + 2, (6.2) where f is the no. of degrees of freedom, p is the number of phases present and the &2± represents the two variables temperature and pressure. Applying this rule to a one-component phase diagram such as that of water, we see that in the interior of the solid, liquid or vapor regions, where only one phase is present, we get two degrees of freedom, since f = 1 ² 1 + 2 = 2. This means that we can change two variables, in this case temperature and pressure, and still have a system consisting only of one phase. When we have two phases in equilibrium, the number of degrees of freedom decreases to 1: f = 1 ² 2 + 2 = 1. This means that if we wish to change the conditions and still retain the equilibrium between the two phases, we can only change one of the variables independently. The other variable is then determined by the equilibrium condition. When three phases are in equilibrium, as at the triple point, the number of degrees of freedom drops to zero. Therefore, the triple point is a unique point for the system. In some cases, as in the case of sulfur, multiple triple points are present (see Fig. 6.1). Each of these are unique points with zero degree of freedom. Components: Determining the number of components in a system is not a trivial task. We may make up a formula for this as follows: c = n ² e ² o , where c is the number of components, n is the number of chemical species present, e is the number of equilibria between them, and o represents any other relationships that may determine the relative amount of one species with respect to another. See Section 6.1 to see applications of these ideas.
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Lecture_6a_4e - CHAPTER 6 LECTURE NOTES Degrees of Freedom...

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