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For the equilibrium silver-copper system, if you were at a temperature of 779 °C and a composition of 60 wt% Cu, what fraction of the system would be in the a phase? Your answer should be in the form of a percentage (a value 0-100). °C 1084.$ 1000 961.93 900 a +L B+L 800 780 91.2 80 71.9 700 600 a+B 500 400 Cu 10 20 30 40 50 60 70 80 90 Ag Weight Percent Silver

For the equilibrium silver-copper system, if you were at a temperature of 779 °C and a composition of 60 wt% Cu, what fraction of the system would be in the a phase? Your answer should be in the form of a percentage (a value 0-100). °C 1084.$ 1000 961.93 900 a +L B+L 800 780 91.2 80 71.9 700 600 a+B 500 400 Cu 10 20 30 40 50 60 70 80 90 Ag Weight Percent Silver

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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For the equilibrium silver-copper system, if you were at a temperature of 779°C and a composition of 60 wt% Cu, what fraction of the system would be in the α phase? Your answer should be in the form of a percentage (a value 0-100). ### Diagram Explanation This is a phase diagram for the silver-copper system: - **Axes**: - The x-axis represents the composition in weight percent silver (Ag), ranging from 0 to 100, with the corresponding weight percent copper (Cu) from 0 to 100 on the opposite end. - The y-axis represents temperature in degrees Celsius, ranging from 400°C to 1100°C. - **Phase Regions**: - The diagram shows different phase regions including α (alpha), β (beta), α+L (alpha plus liquid), β+L (beta plus liquid), and α+β (alpha plus beta). - The liquid region (L) is above both the α+L and β+L regions. - **Important Features**: - The line separating the α+L and L regions is horizontal at approximately 779°C. - The eutectic point occurs at the intersection of the α+β, α+L, and β+L phases. ### Calculation of Fraction in α Phase at 779°C and 60 wt% Cu To find the fraction in the α phase at 779°C and 60 wt% Cu: 1. **Locate the Composition and Temperature**: - At 60 wt% Cu (40 wt% Ag), move vertically to intersect the horizontal line at 779°C in the α+L region. 2. **Lever Rule Application**: - Use the lever rule to determine the fraction of phases: - The length of the line from the point to the phase boundary on the left (α phase) is proportional to the amount of β (or liquid phase) present. - The length from the point to the right (liquid) boundary is proportional to the amount of α phase present. 3. **Calculating the Percentage**: - Determine the ratio of the distance from the composition point to the β boundary (on the left) divided by the total length of the tie line in the α+L region. This gives you the fraction in the α phase. - Convert the fraction to a percentage. This process will yield the percentage of
Transcribed Image Text:For the equilibrium silver-copper system, if you were at a temperature of 779°C and a composition of 60 wt% Cu, what fraction of the system would be in the α phase? Your answer should be in the form of a percentage (a value 0-100). ### Diagram Explanation This is a phase diagram for the silver-copper system: - **Axes**: - The x-axis represents the composition in weight percent silver (Ag), ranging from 0 to 100, with the corresponding weight percent copper (Cu) from 0 to 100 on the opposite end. - The y-axis represents temperature in degrees Celsius, ranging from 400°C to 1100°C. - **Phase Regions**: - The diagram shows different phase regions including α (alpha), β (beta), α+L (alpha plus liquid), β+L (beta plus liquid), and α+β (alpha plus beta). - The liquid region (L) is above both the α+L and β+L regions. - **Important Features**: - The line separating the α+L and L regions is horizontal at approximately 779°C. - The eutectic point occurs at the intersection of the α+β, α+L, and β+L phases. ### Calculation of Fraction in α Phase at 779°C and 60 wt% Cu To find the fraction in the α phase at 779°C and 60 wt% Cu: 1. **Locate the Composition and Temperature**: - At 60 wt% Cu (40 wt% Ag), move vertically to intersect the horizontal line at 779°C in the α+L region. 2. **Lever Rule Application**: - Use the lever rule to determine the fraction of phases: - The length of the line from the point to the phase boundary on the left (α phase) is proportional to the amount of β (or liquid phase) present. - The length from the point to the right (liquid) boundary is proportional to the amount of α phase present. 3. **Calculating the Percentage**: - Determine the ratio of the distance from the composition point to the β boundary (on the left) divided by the total length of the tie line in the α+L region. This gives you the fraction in the α phase. - Convert the fraction to a percentage. This process will yield the percentage of
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