A 1.5-kg specimen of a 90 wt % Pb-10 wt % Sn alloy is heated to 250^∘ C(480^∘ F); at this tempe

step 1 All right, so using the lever rule, 50 % liquid means the overall composition lies halfway betwe

A 1.5-kg specimen of a 90 wt % Pb-10 wt % Sn alloy is...

A $1.5-\mathrm{kg}$ specimen of a $90 \mathrm{wt} \% \mathrm{~Pb}-10$ wt $\%$ Sn alloy is heated to $250^{\circ} \mathrm{C}\left(480^{\circ} \mathrm{F}\right)$; at this temperature it is entirely an $\alpha$-phase solid solution (Figure 9.8). The alloy is to be melted to the extent that $50 \%$ of the specimen is liquid, the remainder being the $\alpha$ phase. This may be accomplished either by heating the alloy or changing its composition while holding the temperature constant. (a) To what temperature must the specimen be heated? (b) How much tin must be added to the $1.5$-kg specimen at $250^{\circ} \mathrm{C}$ to achieve this state?

A $1.5-\mathrm{kg}$ specimen of a $90 \mathrm{wt} \% \mathrm{~Pb}-10$ wt $\%$ Sn alloy is heated to $250^{\circ} \mathrm{C}\left(480^{\circ} \mathrm{F}\right)$; at this temperature it is entirely an $\alpha$-phase solid solution (Figure 9.8). The alloy is to be melted to the extent that $50 \%$ of the specimen is liquid, the remainder being the $\alpha$ phase. This may be accomplished either by heating the alloy or changing its composition while holding the temperature constant.
(a) To what temperature must the specimen be heated?
(b) How much tin must be added to the $1.5$-kg specimen at $250^{\circ} \mathrm{C}$ to achieve this state?

Key Concepts

Weight Percent Composition

Weight percent composition is a way of expressing the concentration of elements in an alloy or mixture, defined as the mass of a specific component relative to the total mass of the mixture, multiplied by 100. This concept is critical when adjusting compositions in an alloy, as it helps in calculating how much of a component must be added or removed to achieve a desired phase equilibrium state.

Binary Phase Diagram

A binary phase diagram represents the equilibrium relationship between temperature, composition, and phase constitution in a two-component system. It is a crucial tool for understanding how different phases (solid, liquid, or mixtures thereof) coexist at various temperatures and compositions, allowing one to predict melting points, solubility limits, and the overall behavior of alloys or mixtures.

Phase Equilibrium

Phase equilibrium refers to the state where different phases, such as solid and liquid, coexist at constant temperature and composition, with no net change over time. In the context of alloys, understanding phase equilibrium is essential for determining the conditions under which a mixture will have specific ratios of liquid and solid phases, which is critical for processes like melting and solidification.

Lever Rule

The lever rule is a quantitative method used in phase diagrams to determine the relative amounts of different phases in a two-phase region. By treating the phase composition limits as the ends of a lever, the rule allows one to calculate the mass fraction of each phase based on the overall composition and the compositions at the phase boundaries.

Transcript

Please give Ace some feedback