2011 MSE 508 Problem Set 6 Solutions

# 2011 MSE 508 Problem Set 6 Solutions - MSE 508 Solid State...

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MSE 508 Dept. of Materials Science & Engineering Solid State Thermodynamics Spring 2011/Bill Knowlton 1 Problem Set 6 Solutions 1. In class, we found that ln kk R Ta m D= . Using the toolbox 5 tables, derive Toolbox 5- 4 disregarding the first three and last listings in the tables. That is, derive the following: Toolbox 5-4: Relations between the PMPs of component k and its activity , ln ln k k pn a SR a R T T     , ln k k k Tn a VR T P 2 , ln k k k a HR T T 2 ,, ln ln k aa U RT PRT TP  , ln ln k k a FR T aP R T P

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MSE 508 Dept. of Materials Science & Engineering Solid State Thermodynamics Spring 2011/Bill Knowlton 2
MSE 508 Dept. of Materials Science & Engineering Solid State Thermodynamics Spring 2011/Bill Knowlton 3

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MSE 508 Dept. of Materials Science & Engineering Solid State Thermodynamics Spring 2011/Bill Knowlton 4 2. In the system Pandemonium (Pn) – Condominium (Cn), the partial molar heat of mixing of Condominium (Cn) can be fitted by the expression: . 2 where 12,500 Cn Pn Cn J Ha X X a mole     . Calculate and plot the function that describes the variation of the heat of mixing with composition for this system. In plotting the function, do so with a mathematical program that is not Excel. Do comment and provide insight to your plot. units = J/mol
MSE 508 Dept. of Materials Science & Engineering Solid State Thermodynamics Spring 2011/Bill Knowlton 5 0.0 0.2 0.4 0.6 0.8 1.0 0 200 400 600 800 X Cn H mix J mol H 0.0 0.2 0.4 0.6 0.8 1.0 0 200 400 600 800 X Pn H It is evident that from the equation describing the enthalpy of mixing, H mix =a/2(X 2 Cn X Pn ), is not of the form aX Cn X Pn and therefore does not describe a regular solution. Hence, the solution is non-, sub-, or irregular. This is also evident due to the lack of symmetry in the plot above. The solution is skewed toward larger values of X cn (max. ~ 0.7Cn) since the mixture goes by X Cn 2 and only linear in X Pn . Notice that H mix has a positive maximum when the stoichiometry of the alloy is Cn 2 Pn. This means that the reaction for the solution at this stoichiometry is the most endothermic suggesting that this stoichiometry is the least likely to form. This may be due to a repulsive behavior between Cn-Cn. The entropy of the solution is not discussed here and will certainly have an effect on which stoichiometry will form. To determine whether or not the Cn 2 Pn alloy is the least likely to form requires knowledge of G mix .

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MSE 508 Dept. of Materials Science & Engineering Solid State Thermodynamics Spring 2011/Bill Knowlton 6 3. Below is a thoroughly stated problem with a thoroughly provided solution. Create a a
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2011 MSE 508 Problem Set 6 Solutions - MSE 508 Solid State...

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