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
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
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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Please answer all of the parts from a to e

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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