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II) The Cu-Ag phase diagram is reproduced on the following page, and the following two equations model the molar Gibbs free energy of the solid (SS) and liquid (LS) solutions reasonably well. Gss = (24,600 J/mol)XX + RT (X^ In X +Xc„ In Xcu) SS Cu Ag Ag Cu 1)(1- |Xcμ + (12,787 J/mol)XgXCu + RT (X^g ln X^g +Xcm In Xcu) T = LS GS (11,300 J/mol) 1- 1235K Ag XA + (13,300 J/mol)| 1– T 1358K Си Ag Ag R is the molar gas constant, and has a value of 8.314 J/mol/K a) Make the substitution X = 1-X CM in each of the above equations to produce equations in Ag Cu terms of temperature T and the single compositional variable Xcu. Си b) Produce three graphs of GSS and GLS vs. XC (from 0 to 1) at temperatures of 600°C, Cu 780°C, and 900°C. Each graph should contain both curves, and if you produce curves by calculating individual points, they should be done in intervals no greater than 0.01. Note also that the quantity (1-X) In(1-XC)+X In X is undefined at XC = 0 and Си Си Cu Cu Си XC₁ = 1; however its limit as ✗Cu →0* and XC₁ →1¯ is zero and you may treat that as the value for the purposes of evaluating the entire expression at the ends of the compositional domain. Preview c) For each of your graphs in (b), describe how consistent the model is with the experimentally determined phase diagram shown below. In other words, compare the compositions of the phase field boundaries predicted from the free energy model with those on the actual phase diagram at each temperature. Temperature °C 10 20 1200 1000 961.93°C 800 (Ag) 600 400 Weight Percent Copper 30 L 200 0 10 20 30 40 50 18- 40 50 60 70 80 90 100 60 1084.87°C 780°C (Cu) 70 80 90 100

II) The Cu-Ag phase diagram is reproduced on the following page, and the following two equations model the molar Gibbs free energy of the solid (SS) and liquid (LS) solutions reasonably well. Gss = (24,600 J/mol)XX + RT (X^ In X +Xc„ In Xcu) SS Cu Ag Ag Cu 1)(1- |Xcμ + (12,787 J/mol)XgXCu + RT (X^g ln X^g +Xcm In Xcu) T = LS GS (11,300 J/mol) 1- 1235K Ag XA + (13,300 J/mol)| 1– T 1358K Си Ag Ag R is the molar gas constant, and has a value of 8.314 J/mol/K a) Make the substitution X = 1-X CM in each of the above equations to produce equations in Ag Cu terms of temperature T and the single compositional variable Xcu. Си b) Produce three graphs of GSS and GLS vs. XC (from 0 to 1) at temperatures of 600°C, Cu 780°C, and 900°C. Each graph should contain both curves, and if you produce curves by calculating individual points, they should be done in intervals no greater than 0.01. Note also that the quantity (1-X) In(1-XC)+X In X is undefined at XC = 0 and Си Си Cu Cu Си XC₁ = 1; however its limit as ✗Cu →0* and XC₁ →1¯ is zero and you may treat that as the value for the purposes of evaluating the entire expression at the ends of the compositional domain. Preview c) For each of your graphs in (b), describe how consistent the model is with the experimentally determined phase diagram shown below. In other words, compare the compositions of the phase field boundaries predicted from the free energy model with those on the actual phase diagram at each temperature. Temperature °C 10 20 1200 1000 961.93°C 800 (Ag) 600 400 Weight Percent Copper 30 L 200 0 10 20 30 40 50 18- 40 50 60 70 80 90 100 60 1084.87°C 780°C (Cu) 70 80 90 100

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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II) The Cu-Ag phase diagram is reproduced on the following page, and the following two equations model the molar Gibbs free energy of the solid (SS) and liquid (LS) solutions reasonably well. Gss = (24,600 J/mol)XX + RT (X^ In X +Xc„ In Xcu) SS Cu Ag Ag Cu 1)(1- |Xcμ + (12,787 J/mol)XgXCu + RT (X^g ln X^g +Xcm In Xcu) T = LS GS (11,300 J/mol) 1- 1235K Ag XA + (13,300 J/mol)| 1– T 1358K Си Ag Ag R is the molar gas constant, and has a value of 8.314 J/mol/K a) Make the substitution X = 1-X CM in each of the above equations to produce equations in Ag Cu terms of temperature T and the single compositional variable Xcu. Си b) Produce three graphs of GSS and GLS vs. XC (from 0 to 1) at temperatures of 600°C, Cu 780°C, and 900°C. Each graph should contain both curves, and if you produce curves by calculating individual points, they should be done in intervals no greater than 0.01. Note also that the quantity (1-X) In(1-XC)+X In X is undefined at XC = 0 and Си Си Cu Cu Си XC₁ = 1; however its limit as ✗Cu →0* and XC₁ →1¯ is zero and you may treat that as the value for the purposes of evaluating the entire expression at the ends of the compositional domain. Preview c) For each of your graphs in (b), describe how consistent the model is with the experimentally determined phase diagram shown below. In other words, compare the compositions of the phase field boundaries predicted from the free energy model with those on the actual phase diagram at each temperature. Temperature °C 10 20 1200 1000 961.93°C 800 (Ag) 600 400 Weight Percent Copper 30 L 200 0 10 20 30 40 50 18- 40 50 60 70 80 90 100 60 1084.87°C 780°C (Cu) 70 80 90 100
Transcribed Image Text:II) The Cu-Ag phase diagram is reproduced on the following page, and the following two equations model the molar Gibbs free energy of the solid (SS) and liquid (LS) solutions reasonably well. Gss = (24,600 J/mol)XX + RT (X^ In X +Xc„ In Xcu) SS Cu Ag Ag Cu 1)(1- |Xcμ + (12,787 J/mol)XgXCu + RT (X^g ln X^g +Xcm In Xcu) T = LS GS (11,300 J/mol) 1- 1235K Ag XA + (13,300 J/mol)| 1– T 1358K Си Ag Ag R is the molar gas constant, and has a value of 8.314 J/mol/K a) Make the substitution X = 1-X CM in each of the above equations to produce equations in Ag Cu terms of temperature T and the single compositional variable Xcu. Си b) Produce three graphs of GSS and GLS vs. XC (from 0 to 1) at temperatures of 600°C, Cu 780°C, and 900°C. Each graph should contain both curves, and if you produce curves by calculating individual points, they should be done in intervals no greater than 0.01. Note also that the quantity (1-X) In(1-XC)+X In X is undefined at XC = 0 and Си Си Cu Cu Си XC₁ = 1; however its limit as ✗Cu →0* and XC₁ →1¯ is zero and you may treat that as the value for the purposes of evaluating the entire expression at the ends of the compositional domain. Preview c) For each of your graphs in (b), describe how consistent the model is with the experimentally determined phase diagram shown below. In other words, compare the compositions of the phase field boundaries predicted from the free energy model with those on the actual phase diagram at each temperature. Temperature °C 10 20 1200 1000 961.93°C 800 (Ag) 600 400 Weight Percent Copper 30 L 200 0 10 20 30 40 50 18- 40 50 60 70 80 90 100 60 1084.87°C 780°C (Cu) 70 80 90 100
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