# Question: Foundations of Materials Science and Engineering (5th Edition) – Free Chegg Question Answer

Foundations of Materials Science and Engineering (5th Edition)

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`Answer:`

### Problem

In Fig. 8.12, determine the degree of freedom, F, according to Gibbs rule at the following points:

(a) At the melting point of pure tin.

(b) Inside the α region.

(c) Inside the α + liquid region

(d) Inside the α + β region

(e) At the eutectic point

Figure 8.12 The lead-tin equilibrium phase diagram. This diagram is characterized by the limited solid solubility of each terminal phase (α and β). The eutectic invariant reaction at 61.9% Sn and 183°C is the most important feature of this system. At the eutectic point, α (19.2% Sn), β (97.5% Sn), and liquid (61.9% Sn) can coexist.

### Step-by-step solution

1. Step 1 of 1 The equation for Gibbs phase rule for binary phase diagrams is, …… (1) Here, the number of phases that coexist in the chosen system is , degrees of freedom is F, number of the components in the system is C At the melting point of pure tin: At the melting point of pure tin, number of components , but the number of phases are =2 (solid and liquid). Substitute these values in the equation (1) Therefore, the degree of freedom is . Inside the region: Number of components , but the number of phases is (solid). Substitute these values in the equation (1) Therefore, the degree of freedom is . Inside the + liquid region: Number of components , but the number of phases is (solid and liquid) Substitute these values in the equation (1) Therefore, the degree of freedom is . Inside the + region: Number of components , but the number of phases is (2 numbers solid) Substitute these values in the equation (1) Therefore, the degree of freedom is . At the eutectic point: Number of components , but the number of phases is (1 number of liquid & two numbers of solid) Substitute these values in the equation (1) Therefore, the degree of freedom is 