Page 1 1 MATSCI 204 Thermodynamics and Phase Equilibria Winter ...
MATSCI 204 Thermodynamics and Phase Equilibria Winter 2013 Problem Set #5 Due: Week of Feb. 25th Problem 1 (20 points) Tin obeys Henry’s Law in dilute Sn-Cd liquid solutions and the Henrian activity coefficient of Sn γSn varies with temperature as: 750 ln (! Sn ) = ! +1.58 T Calculate the change in temperature when 1 mole of liquid Sn and 99 moles of liquid Cd are mixed in an adiabatic enclosure. The molar constant pressure heat capacity of the alloy formed is 29.5 J/K Problem 2 (40 points) XS Liquid Fe-Mn alloys at 1863K form a regular solution. The "gmix of the solution was measured as a function of composition:
xMn XS "gmix (J/mol)
!
A B C D
0.1 395
0.2 703
0.3 925
0.4 1054
0.5 0.6 ! 1100 1054
0.7 925
0.8 703
0.9 395
(20 points) Does the solution deviate positively or negatively from ideality? XS XS Calculate "µMn,mix and "µFe,mix at xMn=0.6 XS (10 points) Plot "gmix as a function of xMn. Draw the tangent to the curve at xMn=0.6. Where does it intersect the xMn=0 and xMn=1 axes? (10 points) Calculate Δgmix at xMn=0.4 ! ! (20 points) Plot the activity of Mn and Fe as a function of xMn. On the same plot, ! lines representing an ideal solution. Estimate Henry’s coefficients for show the Mn and Fe from the figure. How does it compare to the theoretical value?
Problem 3 (20 points) Here is the phase diagram of the Si/Ge binary system
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1- Label everything in this phase diagram (indicate species at the composition ends, label one-phase fields and two-phase fields. 2- A uniform liquid with a composition of 50 at.% Ge is cooled. At what temperature does the first solid appear? What is its composition? 3- A uniform solid with a composition of 50 at% Si is heated. At what temperature does the first liquid appear? What is its composition? 4- Sketch a reasonable g vs. x curve corresponding to a situation where the temperature is in between those found in questions 2 and 3. It should look like Fig. 5.3 in the notes. Make sure you label everything in the sketch and clarify your choice of reference states.
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xMn XS "gmix (J/mol)
!
A B C D
0.1 395
0.2 703
0.3 925
0.4 1054
0.5 0.6 ! 1100 1054
0.7 925
0.8 703
0.9 395
(20 points) Does the solution deviate positively or negatively from ideality? XS XS Calculate "µMn,mix and "µFe,mix at xMn=0.6 XS (10 points) Plot "gmix as a function of xMn. Draw the tangent to the curve at xMn=0.6. Where does it intersect the xMn=0 and xMn=1 axes? (10 points) Calculate Δgmix at xMn=0.4 ! ! (20 points) Plot the activity of Mn and Fe as a function of xMn. On the same plot, ! lines representing an ideal solution. Estimate Henry’s coefficients for show the Mn and Fe from the figure. How does it compare to the theoretical value?
Problem 3 (20 points) Here is the phase diagram of the Si/Ge binary system
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1- Label everything in this phase diagram (indicate species at the composition ends, label one-phase fields and two-phase fields. 2- A uniform liquid with a composition of 50 at.% Ge is cooled. At what temperature does the first solid appear? What is its composition? 3- A uniform solid with a composition of 50 at% Si is heated. At what temperature does the first liquid appear? What is its composition? 4- Sketch a reasonable g vs. x curve corresponding to a situation where the temperature is in between those found in questions 2 and 3. It should look like Fig. 5.3 in the notes. Make sure you label everything in the sketch and clarify your choice of reference states.
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