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A 60 wt% Ni-40 wt% Cu alloy is heated to a temperature of 1300 °C, within the liquid-solid 
phase region. The total mass of the alloy is 100g. Determine the masses of the alloy that 
are in the liquid and solid phases at a given temperature (plot on the figure below)

To determine the masses of the alloy that are in the liquid and solid phases, we can apply the **lever rule** using the phase diagram. The steps involve:

1. **Locate the alloy composition and temperature on the phase diagram**:
   - The alloy has a composition of 60 wt% Ni (40 wt% Cu).
   - The temperature is 1300 °C.
   - On the phase diagram, 60 wt% Ni at 1300 °C lies in the "Liquid + Solid" phase region between the liquidus and solidus lines.

2. **Determine the compositions at the liquidus and solidus lines**:
   - From the phase diagram at 1300 °C:
     - The composition at the liquidus line is approximately **47 wt% Ni**.
     - The composition at the solidus line is approximately **72 wt% Ni**.

3. **Use the Lever Rule to calculate the mass fractions of each phase**:
   The lever rule states:
   \[
   \frac{W_s}{W_l} = \frac{C_L - C_0}{C_0 - C_S}
   \]
   Where:
   - \( W_s \) and \( W_l \) are the mass fractions of the solid and liquid phases.
   - \( C_L \) is the composition of Nickel at the liquidus line (47 wt% Ni).
   - \( C_0 \) is the overall composition of the alloy (60 wt% Ni).
   - \( C_S \) is the composition of Nickel at the solidus line (72 wt% Ni).

   Using this, the mass fractions of solid and liquid phases can be determined.

Let me calculate this step for you.Using the lever rule, the masses of the liquid and solid phases at 1300 °C for the 60 wt% Ni - 40 wt% Cu alloy are:

- **Mass of liquid phase**: 48 grams
- **Mass of solid phase**: 52 grams

Would you like further clarification on any step, or do you have any other questions?

Here are 5 related questions to expand on this:

1. How would the phase composition change if the temperature is reduced below 1300°C?
2. What happens to the mass fractions when the alloy composition changes to 70 wt% Ni?
3. Can we predict the phases for an alloy at 80 wt% Ni at the same temperature?
4. How does the lever rule apply when the alloy is in the fully solid or fully liquid phase region?
5. How is the liquidus line different from the solidus line in this phase diagram?

**Tip**: In binary phase diagrams, the lever rule helps quantify phase amounts at equilibrium, but it's only applicable within the two-phase regions.

A 60 wt% Ni-40 wt% Cu alloy is heated to a temperature of 1300 °C, within the liquid-solid phase region. The total mass of the alloy is 100g. Determine the masses of the alloy that are in the liquid and solid phases at a given temperature (plot on the figure below).

This solution details how to calculate the masses of liquid and solid phases in a 60 wt% Ni-40 wt% Cu alloy at 1300°C using the Lever Rule. Understand phase diagrams and use the key formulas to determine the amounts of each phase. Ideal for undergraduate students in materials science.

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