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2005_-_2006_Quiz_Collection

2005_-_2006_Quiz_Collection - MSE 855 Quiz One 1 Write down...

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MSE 855, Quiz One, January 24, 2005 1. Write down the coordinate invariant forms of Fick's First Law, the Continuity equation and Fick's Second Law. Define each symbol and give appropriate physical units for each symbol. (30 points) 2. Use the coordinate invariant forms of Fick's First Law and the Continuity Equation to derive the general form of Fick's Second Law. Show all of your steps and discuss all assumptions. Discuss the conditions under which is it important that D = D(c) and he conditions for which one assumes that D is not a function of c. (20 points) 3. Is the assumption that D is or is not a function of concentration c important for Fick's First Law? Give a short explanation of your answer. (10 points) Quiz Two, MSE 855, Spring 2005 1. Begin with the coordinate-invariant form of Fick's Second Law for D not a function of concentration, c. Demonstrate how the functional form of the equation changes for (i) Steady-state conditions (3 points) and (separately), (ii) Steady-state conditions, one-dimensional Cartesian coordinates. (5 points) 2. (a) Solve the equation you obtained in problem 1 for Fick's Second Law, steady-state conditions, one-dimensional Cartesian coordinates. (Your solution will be an expression for c(x), where x is your spatial coordinate.) In particular, assume a rectilinear slab of thickness L and boundary conditions c(x = 0) = C 0 and c(x = L) = C L . Show your steps and briefly explain the assumptions you make and show explicitly how you make use of the boundary conditions. Your final form for c(x) should include C 0 , C L , L and any other appropriate quantities or variables. NOTE: One point credit for the final answer alone. (26 points) (b) Make a plot of the concentration profile for your solution in part (a). Label the axes and the axes intercepts on your plot. (10 points) (c) Is the problem you solved in 2(a) merely an academic exercise or does the problem represent a physically meaningful problem in solid state diffusion? Does it correspond to a physical situation in which diffusion parameters can be measured? For each question, answer either "yes" or "no" AND give a brief explanation of your answer. (16 points)
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