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Calculate the degrees of freedom for Points 1-4

Calculate the degrees of freedom for Points 1-4

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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Calculate the degrees of freedom for Points 1-4 in the copper-nickel binary phase diagram
This image is a phase diagram for a copper-nickel alloy system. The diagram maps out the temperature (in degrees Celsius) on the vertical axis ranging from 500°C to 1500°C against the weight percentage of nickel on the horizontal axis ranging from 0% to 100%. Additionally, the atomic percentage of nickel is displayed on the top horizontal axis. ### Phases and Regions: - **L (Liquid Phase):** The topmost region, shaded lightly, represents the liquid phase of the alloy. - **$\alpha + L$ (Alpha and Liquid Phase):** The middle region, indicated between the upper and lower curves, shows the coexistence of the solid alpha phase and liquid phase. - **$\alpha$ (Alpha Phase):** The bottom region, shaded darkly, shows the solid alpha phase. ### Key Temperatures and Points: 1. **Point 1:** Located near the top portion of the $\alpha + L$ region, this signifies a higher concentration of nickel, close to the liquid boundary. 2. **Point 2:** An intermediate position in the $\alpha + L$ region, where both phases coexist. 3. **Point 3:** Positioned on the boundary between liquid and $\alpha + L$ regions at approximately 1,084.87°C. 4. **Point 4:** Near the boundary between the liquid and $\alpha + L$ regions, at a temperature close to 1,455°C. ### Miscellaneous: - There are numerical indicators along the diagram referring to specific points critical to understanding phase transitions. - The phases transition smoothly from solid to liquid with increasing temperature and nickel content. - Observations like these guide metallurgists in understanding the melting points and temperature boundaries for industrial applications of copper-nickel alloys.
Transcribed Image Text:This image is a phase diagram for a copper-nickel alloy system. The diagram maps out the temperature (in degrees Celsius) on the vertical axis ranging from 500°C to 1500°C against the weight percentage of nickel on the horizontal axis ranging from 0% to 100%. Additionally, the atomic percentage of nickel is displayed on the top horizontal axis. ### Phases and Regions: - **L (Liquid Phase):** The topmost region, shaded lightly, represents the liquid phase of the alloy. - **$\alpha + L$ (Alpha and Liquid Phase):** The middle region, indicated between the upper and lower curves, shows the coexistence of the solid alpha phase and liquid phase. - **$\alpha$ (Alpha Phase):** The bottom region, shaded darkly, shows the solid alpha phase. ### Key Temperatures and Points: 1. **Point 1:** Located near the top portion of the $\alpha + L$ region, this signifies a higher concentration of nickel, close to the liquid boundary. 2. **Point 2:** An intermediate position in the $\alpha + L$ region, where both phases coexist. 3. **Point 3:** Positioned on the boundary between liquid and $\alpha + L$ regions at approximately 1,084.87°C. 4. **Point 4:** Near the boundary between the liquid and $\alpha + L$ regions, at a temperature close to 1,455°C. ### Miscellaneous: - There are numerical indicators along the diagram referring to specific points critical to understanding phase transitions. - The phases transition smoothly from solid to liquid with increasing temperature and nickel content. - Observations like these guide metallurgists in understanding the melting points and temperature boundaries for industrial applications of copper-nickel alloys.
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