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Unformatted text preview: Answers for Chapter 6: The Phase Rule and One-Component Systems. 1. A system is some portion of the universe that we want to define/explore. We can define the state of a system by determining all the necessary variables of that system. Such variables include (but are not limited to) the following. After each, indicate whether it is an extensive or an intensive variable with a capital I or E. Mass of each phase extensive Volume of the system extensive Molar Gibbs free energy of each phase intensive Density of the system intensive Molar volume of each phase intensive Entropy of the system extensive The number of moles of the albite component in plagioclase extensive The mole fraction of albite in plagioclase intensive 2. The Phase Rule is an important tool which helps us address and evaluate phase diagrams of all types. When using it, what do we mean by a phase ? A type of physically distinct material in a system that is mechanically separable from the rest. 3. How many phases are represented by the following systems: Ice one Ice water (with the cubes) two Albite one Plagioclase one A tequila sunrise one (unless there are ice cubes) 4. How many components are represented by the following systems: Ice one Ice water (with the cubes) one Albite one Plagioclase two (if the composition is variable) Calcite one (unless heated to the point where it devolatilizes to CaO (lime) + CO 2 ) 5. F is the number of degrees of freedom of the system. It can be defined in either of two different ways. What are they? 1. The minimum number of intensive variables that must be specified in order to completely determine the state of a system at equilibrium. 2. The number of intensive variables that can be independently varied without affecting the number of phases present at equilibrium. 1 There is a discontinuity around 2550 o C when coesite melts and coesite + liquid coexist. 6. The diagram at right is a portion of the SiO 2 phase diagram (Fig. 6.6). a. Determine F at point x in the diagram. Show your work. What are some possible intensive variables that you could determine? F = C – φ + 2 = 1 – 1 + 2 = 2 Temperature, pressure, density or any molar property of coesite. b. Do the same for point y. Compared with point x, are there more or fewer variables that could be determined? Is it necessary to determine more or fewer? Why? F = C – φ + 2 = 1 – 2 + 2 = 1 More intensive variables could be determined (density or any molar property of coesite or of liquid), but fewer need to be determined to define the state. For example, if we define P for coexisting coesite and liquid at equilibrium, T is now fixed to as a point on the equilibrium curve at that P. c. Assuming that pressure is variable, in a single sentence, describe as accurately and completely as you can the meaning of F in this particular circumstance . I’ll get you started: In a one-component system composed of coexisting coesite and liquid, any change in pressure requires a sympathetic change in temperature to maintain equilibrium and a...
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- Fall '09
- Solid solution, Triple point, plagioclase