A lead-tin (Pb-Sn) alloy of composition 50 wt % Sn and 50 wt % Pb is slowly heated from a temperature of 100 °C. Refer to the phase diagram provided in **Figure 1** and answer the following:(i) At what temperature does the first liquid phase form?(ii) What is the composition of this liquid phase?(iii) At what temperature does complete melting of the alloy occur?(iv) What is the composition of the last solid remaining prior to complete melting?![Lead (Pb) and Tin (Sn) Phase diagram](Lead-Tin%20Phase%20Diagram.png)**Figure 1.** Lead (Pb) and Tin (Sn) Phase diagram---### Explanation of the Phase Diagram (Figure 1):**Axes:**- The x-axis represents the composition of the alloy in terms of weight percentage of tin (Sn), ranging from 0% to 100%, with the corresponding weight percentage of lead (Pb) from 100% to 0%.- The left y-axis indicates temperature in degrees Celsius (°C), ranging from 0°C to 400°C.- The right y-axis shows temperature in degrees Fahrenheit (°F), this can be converted from °C using the formula \( F = \frac{9}{5}C + 32 \).**Regions:**- The diagram is divided into several regions, representing different phases: - **Solid Phase (α)**: Exists at lower temperatures for compositions with a higher percentage of lead. - **Solid Phase (β)**: Exists at lower temperatures for compositions with a higher percentage of tin. - **Liquid Phase**: Exists at higher temperatures where the alloy is completely molten. - **Mixed Phase (α + L)**: A mixture of solid α and liquid. - **Mixed Phase (β + L)**: A mixture of solid β and liquid. - **Mixed Phase (α + β)**: A mixture of solid α and solid β.**Key Points in the Diagram:**- **Eutectic Point (183°C)**: At this point, the composition is 61.9 wt % Sn (and 38.1 wt % Pb). The entire alloy melts or solidifies at a single temperature.### Answers to the Questions:(i) **At what temperature does the first liquid phase form?**- The first liquid phase forms at the eutectic temperature of

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A lead-tin (Pb-Sn) alloy of composition 50 wt % Sn and 50 wt % Pb is slowly heated from a temperature of 100 °C. Refer to the phase diagram provided in Figure 1 and answer the following. (i) At what temperature does the first liquid phase form? (ii) What is the composition of this liquid phase? (iii) At what temperature does complete melting of the alloy occur? (iv) What is the composition of the last solid remaining prior to complete melting? Composition (at% Sn) 20 40 60 80 100 327°C 600 300 Liquid 500 232°C a +L 200 B+L 400 183°C 18.3 61.9 97.8 300 100 a + B 200 H100 20 40 60 80 100 (Pb) Composition (wt% Sn) (Sn) Figure 1. Lead (Pb) and Tin (Sn) Phase diagram Temperature (°C) Temperature (°F)

A lead-tin (Pb-Sn) alloy of composition 50 wt % Sn and 50 wt % Pb is slowly heated from a temperature of 100 °C. Refer to the phase diagram provided in Figure 1 and answer the following. (i) At what temperature does the first liquid phase form? (ii) What is the composition of this liquid phase? (iii) At what temperature does complete melting of the alloy occur? (iv) What is the composition of the last solid remaining prior to complete melting? Composition (at% Sn) 20 40 60 80 100 327°C 600 300 Liquid 500 232°C a +L 200 B+L 400 183°C 18.3 61.9 97.8 300 100 a + B 200 H100 20 40 60 80 100 (Pb) Composition (wt% Sn) (Sn) Figure 1. Lead (Pb) and Tin (Sn) Phase diagram Temperature (°C) Temperature (°F)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Problem 1.1MA

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Concept explainers

Binary Phase Diagram

The Hume-Rothery conditions are restricted to solid solutions that form either substitutional or interstitial solutions.

Question

A lead-tin (Pb-Sn) alloy of composition 50 wt % Sn and 50 wt % Pb is slowly heated from a temperature of 100 °C. Refer to the phase diagram provided in **Figure 1** and answer the following:

(i) At what temperature does the first liquid phase form?

(ii) What is the composition of this liquid phase?

(iii) At what temperature does complete melting of the alloy occur?

(iv) What is the composition of the last solid remaining prior to complete melting?

![Lead (Pb) and Tin (Sn) Phase diagram](Lead-Tin%20Phase%20Diagram.png)

**Figure 1.** Lead (Pb) and Tin (Sn) Phase diagram

---

### Explanation of the Phase Diagram (Figure 1):

**Axes:**
- The x-axis represents the composition of the alloy in terms of weight percentage of tin (Sn), ranging from 0% to 100%, with the corresponding weight percentage of lead (Pb) from 100% to 0%.
- The left y-axis indicates temperature in degrees Celsius (°C), ranging from 0°C to 400°C.
- The right y-axis shows temperature in degrees Fahrenheit (°F), this can be converted from °C using the formula \( F = \frac{9}{5}C + 32 \).

**Regions:**
- The diagram is divided into several regions, representing different phases:
- **Solid Phase (α)**: Exists at lower temperatures for compositions with a higher percentage of lead.
- **Solid Phase (β)**: Exists at lower temperatures for compositions with a higher percentage of tin.
- **Liquid Phase**: Exists at higher temperatures where the alloy is completely molten.
- **Mixed Phase (α + L)**: A mixture of solid α and liquid.
- **Mixed Phase (β + L)**: A mixture of solid β and liquid.
- **Mixed Phase (α + β)**: A mixture of solid α and solid β.

**Key Points in the Diagram:**
- **Eutectic Point (183°C)**: At this point, the composition is 61.9 wt % Sn (and 38.1 wt % Pb). The entire alloy melts or solidifies at a single temperature.

### Answers to the Questions:

(i) **At what temperature does the first liquid phase form?**
- The first liquid phase forms at the eutectic temperature of

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