Cite the phases that are present and the phase compositions for the following alloys: (a) \(15 \mathrm{wt} \% \mathrm{Sn}-85 \mathrm{wt} \% \mathrm{~Pb}\) at \(100^{\circ} \mathrm{C}\left(212^{\circ} \mathrm{F}\right)\) (b) \(25 \mathrm{wt} \% \mathrm{~Pb}-75 \mathrm{wt} \% \mathrm{Mg}\) at \(425^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right)\) (c) \(85 \mathrm{wt} \% \mathrm{Ag}-15 \mathrm{wt} \% \mathrm{Cu}\) at \(800^{\circ} \mathrm{C}\left(1470^{\circ} \mathrm{F}\right)\) (d) \(55 \mathrm{wt} \% \mathrm{Zn}-45 \mathrm{wt} \% \mathrm{Cu}\) at \(600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)\) (e) \(1.25 \mathrm{~kg} \mathrm{Sn}\) and \(14 \mathrm{~kg} \mathrm{~Pb}\) at \(200^{\circ} \mathrm{C}\left(390^{\circ} \mathrm{F}\right)\) (f) \(7.6 \mathrm{lb}_{\mathrm{m}} \mathrm{Cu}\) and \(144.4 \mathrm{lb}_{\mathrm{m}} \mathrm{Zn}\) at \(600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)\) (g) \(21.7 \mathrm{~mol} \mathrm{Mg}\) and \(35.4 \mathrm{~mol} \mathrm{~Pb}\) at \(350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)\) (h) \(4.2 \mathrm{~mol} \mathrm{Cu}\) and \(1.1 \mathrm{~mol} \mathrm{Ag}\) at \(900^{\circ} \mathrm{C}\left(1650^{\circ} \mathrm{F}\right)\)

Using binary phase diagrams, find the diagrams for each of the systems mentioned in the exercise. To do that, you can consult relevant materials science textbooks or reliable online resources, and it is advised to refer to the problem description for the corresponding percentage of components and temperature so that the phase composition can be correctly determined.

First, locate the point corresponding to the given composition and temperature for each system on the phase diagram. Then, identify the equilibrium phases as well as their compositions for that specific point. Note that the composition axis refers to the weight or molar percentage, while the temperature axis refers to the temperature in Celsius or Fahrenheit.

After identifying the equilibrium phases and composition of each alloy, present the results in the requested format. The solution to all alloys in the given exercise is shown below: (a) \(15 \mathrm{wt} \% \mathrm{Sn}-85 \mathrm{wt} \% \mathrm{~Pb} \text{ at }100^{\circ} \mathrm{C}(212^{\circ} \mathrm{F})\text{ : }\) Single-phase: α-phase; \(89 \text{ wt% Pb}\) and \(11 \text{ wt% Sn}\). (b) \(25 \mathrm{wt} \% \mathrm{~Pb}-75 \mathrm{wt} \% \mathrm{Mg} \text{ at }425^{\circ} C(800^{\circ} F) \text{ : }\) Single-phase: β-phase; \(73 \text{ wt% Mg}\) and \(27\text{ wt% Pb}\). (c) \(85 \mathrm{wt} \% \mathrm{Ag}-15 \mathrm{wt} \% \mathrm{Cu} \text{ at }800^{\circ} \mathrm{C}(1470^{\circ} \mathrm{F})\text{ : }\) Single-phase: γ-phase; \(80\text{ wt% Ag}\) and \(20 \text{ wt% Cu}\). (d) \(55 \mathrm{wt} \% \mathrm{Zn}-45 \mathrm{wt} \% \mathrm{Cu} \text{ at }600^{\circ} \mathrm{C}(1110^{\circ} \mathrm{F})\text{ : }\) Two phases: α-phase (\(78\text{ wt% Cu}\) and \(22\text{ wt% Zn}\)) and β-phase (\(98\text{ wt% Zn}\) and \(2\text{ wt% Cu}\)). (e) \(1.25 \mathrm{~kg} \mathrm{Sn}\) and \(14 \mathrm{~kg} \mathrm{~Pb} \text{ at }200^{\circ} \mathrm{C}(390^{\circ} \mathrm{F})\text{ : }\) Single-phase: α-phase; \(89\text{ wt% Pb}\) and \(11\text{ wt% Sn}\). (f) \(7.6 \mathrm{lb}_{\mathrm{m}} \mathrm{Cu}\) and \(144.4 \mathrm{lb}_{\mathrm{m}} \mathrm{Zn} \text{ at }600^{\circ} C(1110^{\circ} F)\text{ : }\) Two phases: α-phase (\(78\text{ wt% Cu}\) and \(22\text{ wt% Zn}\)) and β-phase (\(98\text{ wt% Zn}\) and \(2\text{ wt% Cu}\)). (g) \(21.7 \mathrm{~mol} \mathrm{Mg}\) and \(35.4 \mathrm{~mol} \mathrm{~Pb} \text{ at }350^{\circ} C(660^{\circ} F)\text{ : }\) Single-phase: β-phase; \(73 \text{ wt% Mg}\) and \(27\text{ wt% Pb}\). (h) \(4.2 \mathrm{~mol} \mathrm{Cu}\) and \(1.1 \mathrm{~mol} \mathrm{Ag} \text{ at }900^{\circ} C(1650^{\circ} F)\text{ : }\) Single-phase: γ-phase; \(80\text{ wt% Ag}\) and \(20 \text{ wt% Cu}\).