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A 65 wt% Ni-35 wt% Cu alloy is heated to a temperature within the liquid-phase region. If the composition of the phase is 70 wt% Ni, determine: a) The temperature of the alloy b) The composition of the liquid phase c) The mass fractions of both phases

2 Answers

4 votes

Final answer:

To determine the temperature of the alloy, use the lever rule equation. Determine the composition of the liquid phase using the weight fraction equation. The mass fractions of both phases cannot be determined without the density of the phases.

Step-by-step explanation:

To determine the temperature of the alloy, we need to use the lever rule. The lever rule is given by the equation:

weight fraction(x) = (C2 - C)/(C1 - C2)

where:

C is the composition of interest, C1 is the composition on one side of the phase boundary, and C2 is the composition on the other side of the phase boundary.

Using this equation, we can set up the following equation:

0.70 = (0.70 - 0.65)/(1.0 - 0.65)

Simplifying, we find:

0.70 = (0.05/0.35)

0.70 = 1/7

From this, we can determine that the temperature of the alloy is within the liquid phase region when the composition is 70 wt% Ni.

To determine the composition of the liquid phase, we can use the equation:

weight fraction(C2) = (x - C1)/(C2 - C1)

Substituting the given values, we get:

C2 = (70 - 0.65)/(1.0 - 0.65)

C2 = 0.82 wt% Ni

Finally, to determine the mass fractions of both phases, we can use the equation:

mass fraction(phase) = weight fraction(phase) * density(phase)

Substituting the given values, we get:

mass fraction(liquid) = 0.82 * density(liquid)

mass fraction(solid) = [1 - (0.82 * density(liquid))]

Since the density of the liquid phase and solid phase are not provided in the question, we are unable to determine the mass fractions of both phases.

User Rohit Chaudhary
by
8.3k points
3 votes

Final answer:

To find the temperature of the alloy, use the lever rule and the Ni-Cu phase diagram. The composition of the liquid phase is 75% Ni and 25% Cu. The mass fractions of both phases can be calculated using the weight fractions.

Step-by-step explanation:

To determine the temperature of the alloy, we can use the lever rule. The lever rule states that the fraction of each phase present in an alloy is proportional to the difference in composition from the pure phase compositions. Using the lever rule equation, we can find the weight fraction of the liquid phase, which is 0.75. With this information, we can use the Ni-Cu phase diagram to determine the corresponding temperature, which is approximately 1350°C.

The composition of the liquid phase can be calculated using the weight fraction of the liquid phase. Since the weight fraction of the liquid phase is 0.75, the composition of the liquid phase is 75 wt% Ni and 25 wt% Cu.

The mass fractions of both phases can be calculated using the weight fractions of each phase. The mass fraction of the liquid phase is the weight fraction of the liquid phase multiplied by the total mass of the alloy, and the mass fraction of the solid phase is 1 minus the mass fraction of the liquid phase.

User Farhan Ghumra
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8.3k points