a. The composition of the first solid to form; b. The liquidus temperature, solidus temperature, and freesing range of the alloy; c. The amounts and compositions of each phase at 260°C; d. The amounts and compositions of each phase at 183°C; and e. The amounts and compositions of each phase at 25°C

Elements Of Electromagnetics
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Please answer all of the parts from a to e 

**Problem 11: Analysis of Pb-15% Sn Alloy Solidification**

Consider a Pb-15% Sn alloy. During solidification, determine the following:

a. **The composition of the first solid to form;**
b. **The liquidus temperature, solidus temperature, and freezing range of the alloy;**
c. **The amounts and compositions of each phase at 260°C;**
d. **The amounts and compositions of each phase at 183°C;**
e. **The amounts and compositions of each phase at 25°C**

**Phase Diagram Explanation:**

The provided phase diagram is for a Pb-Sn alloy system. It includes temperature (°C) on the vertical axis and weight percent tin (Sn) on the horizontal axis. Various regions in the diagram are labeled to represent different phases and phase mixtures:

- **L (Liquid):** The region where the alloy is completely liquid.
- **Solidus Line:** Boundary below which the alloy is entirely solid.
- **Liquidus Line:** Boundary above which the alloy is entirely liquid.
- **Solvus Lines:** Boundaries that indicate the limit of solid solubility.

Key Points in the Diagram:
1. **At temperature above 260°C:** The alloy is completely liquid.
2. **Between 260°C and 183°C:** The alloy consists of both liquid (L) and primary α-phase (α + L).
3. **At 183°C:** Eutectic reaction occurs, where liquid transforms into two solid phases (α + β).
4. **Below 183°C:** The alloy consists of both α-phase and β-phase (α + β).

The horizontal line at 183°C represents the eutectic temperature, where liquid transforms into two solid phases, α and β. 

**Answers in Detail:**

a. **The composition of the first solid to form:**
   - The first solid to form from a Pb-15% Sn alloy upon cooling will be a solid solution of tin in lead (α-phase). 

b. **The liquidus temperature, solidus temperature, and freezing range of the alloy:**
   - **Liquidus Temperature:** Approximately 260°C (where the alloy starts to solidify).
   - **Solidus Temperature:** 183°C (where complete solidification occurs).
   - **Freezing Range:** 260°C - 183°C = 77°C.

c. **The amounts and compositions of each phase at
Transcribed Image Text:**Problem 11: Analysis of Pb-15% Sn Alloy Solidification** Consider a Pb-15% Sn alloy. During solidification, determine the following: a. **The composition of the first solid to form;** b. **The liquidus temperature, solidus temperature, and freezing range of the alloy;** c. **The amounts and compositions of each phase at 260°C;** d. **The amounts and compositions of each phase at 183°C;** e. **The amounts and compositions of each phase at 25°C** **Phase Diagram Explanation:** The provided phase diagram is for a Pb-Sn alloy system. It includes temperature (°C) on the vertical axis and weight percent tin (Sn) on the horizontal axis. Various regions in the diagram are labeled to represent different phases and phase mixtures: - **L (Liquid):** The region where the alloy is completely liquid. - **Solidus Line:** Boundary below which the alloy is entirely solid. - **Liquidus Line:** Boundary above which the alloy is entirely liquid. - **Solvus Lines:** Boundaries that indicate the limit of solid solubility. Key Points in the Diagram: 1. **At temperature above 260°C:** The alloy is completely liquid. 2. **Between 260°C and 183°C:** The alloy consists of both liquid (L) and primary α-phase (α + L). 3. **At 183°C:** Eutectic reaction occurs, where liquid transforms into two solid phases (α + β). 4. **Below 183°C:** The alloy consists of both α-phase and β-phase (α + β). The horizontal line at 183°C represents the eutectic temperature, where liquid transforms into two solid phases, α and β. **Answers in Detail:** a. **The composition of the first solid to form:** - The first solid to form from a Pb-15% Sn alloy upon cooling will be a solid solution of tin in lead (α-phase). b. **The liquidus temperature, solidus temperature, and freezing range of the alloy:** - **Liquidus Temperature:** Approximately 260°C (where the alloy starts to solidify). - **Solidus Temperature:** 183°C (where complete solidification occurs). - **Freezing Range:** 260°C - 183°C = 77°C. c. **The amounts and compositions of each phase at
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