HW4 DiffusionI Solutions

# HW4 DiffusionI Solutions - HW4 Diffusion I 1 The following...

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HW4 Diffusion I 1. The following figure shows the self-diffusion coefficient as a function of reciprocal temperature for two hypothetical metals, A and B. a) Which metal has a larger activation energy for diffusion? metal A or metal B. Prove your assertion using an equation. Metal B has a larger activation energy for diffusion, because it has a steeper slope. Look at the relation in y- mx + b form, with “x” being 1/T (reciprocal temperature.) The slope, m, is equal to –Q/R. The slope is negative, so Q is positive (as it should be. A negative activation energy barrier makes no sense.) b) Calculate the activation energy for self-diffusion for metal B, using values from the graph. Be sure that you interpolate numbers properly on the logarithmic scale. To find the activation energy, we need the slope. You can calculate the slope by selecting two points on the line of interest. I have circled the points I selected with green and purple circles. = T R Q D D o 1 ln ln mR Q R Q m = =

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HW4 Diffusion I Let the green point be point 1, and the purple point be point 2. Point 1: To find the x-coordinate of point 1, use a ruler: From 0.80 to the x-coordinate is 0.67 cm. From 0.80 to 0.90 is 3.16 cm. Therefore, the point’s x-coordinate is: The y-coordinate was conveniently chosen to be -13.00 Point 2: The x-coordinate is 0.44 cm to the left of 1.10 on the x-axis. This corresponds to an x-coordinate of: The y-coordinate was chosen to be something easy to read: -15.5 point 1 x1 = 0.82 y1 = -13.00 point 2 x2 = 1.09 y2 =-15.50 Our equation requires a natural log on the y-axis. We have a base 10 log. You can do the conversion with different methods. Since it is hard to remember all the logarithm rules, I’ll just convert to a regular number
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HW4 DiffusionI Solutions - HW4 Diffusion I 1 The following...

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