A copper-zinc alloy of composition \(75 \mathrm{wt} \% \mathrm{Zn}-25\) \(\mathrm{wt} \% \mathrm{Cu}\) is slowly heated from room temperature. (a) At what temperature does the first liquid phase form? (b) What is the composition of this liquid phase? (c) At what temperature does complete melting of the alloy occur? (d) What is the composition of the last solid remaining prior to complete melting?

Understanding the composition of alloys is crucial for predicting their behavior under various conditions. An alloy is a mixture of two or more elements, where at least one is a metal, designed to have specific properties. The alloy composition is usually expressed in weight percent (wt%) or atomic percent. In the case of the copper-zinc alloy in the exercise, the composition is given as 75 wt% Zn and 25 wt% Cu.

Each alloy composition exhibits unique melting and solidification behaviors, which engineers and metallurgists can assess by using a phase diagram. This graphical representation shows temperature versus composition and helps determine what phase or phases are present at a given temperature and alloy composition. For the given alloy, exploring its phase diagram can reveal the temperatures at which phases change, providing insight into material properties and potential applications.

The liquidus and solidus lines are key features in a phase diagram that help understand an alloy's behavior during heating and cooling. The liquidus line is the boundary on the diagram above which the alloy is completely liquid. It indicates the temperature at which a metal or alloy begins to melt and signifies the start of the transition from solid to liquid.

On the other hand, the solidus line marks the upper temperature limit below which the material is entirely solid. Between the liquidus and solidus lines lies the mushy or two-phase region, where the material is a mixture of solid and liquid phases. By examining these lines for the 75 wt% Zn - 25 wt% Cu alloy as outlined in the solution steps, one can determine at which temperatures phase transitions occur. This crucial information can influence manufacturing processes such as casting or forging and guide temperature control during material fabrication.

The phase transformation temperature is the specific temperature at which a substance changes its phase - from solid to liquid, liquid to solid, solid to gas, or vice versa. In the context of alloy analysis, the most relevant transformations are melting, when a solid becomes a liquid, and solidification, when a liquid becomes solid. In phase diagrams, these transformation points for alloys correspond to where the alloy composition line intersects with the liquidus and solidus lines.

For the copper-zinc alloy being examined, the first liquid phase forms at the temperature where the alloy's composition line crosses the liquidus line (as in step 1), and complete melting occurs at the temperature where the same line intersects the solidus line (as in step 3). Knowledge of these transformation temperatures is not only theoretical but also deeply practical, allowing manufacturers to optimize processes such as heat treating, welding, and annealing to enhance the material's desired properties.