Chapter 8.15, Problem 24AAP

If 500 g of a 40 wt% Ag–60 wt% Cu alloy is slowly cooled from 1000°C to just below 780°C (see Fig. P8.23):

1. a. How many grams of liquid and proeutectic alpha are present at 850°C?
2. b. How many grams of liquid and proeutectic alpha are present at 780°C + ΔT?
3. c. How many grams of alpha are present in the eutectic structure at 780°C − ΔT?
4. d. How many grams of beta are present in the eutectic structure at 780°C − ΔT?

To determine

Refer Fig P8.23, if $\text{500}\text{g}$ of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of $\text{1000°C}$ to just below $\text{780°C}$.

Determine the grams of liquid and proeutectic alpha present at $\text{850°C}$.

Answer to Problem 24AAP

The weight of liquid and proeutectic alpha phase is $\text{364}\text{g}\text{and}\text{136}\text{g}$ respectively.

Explanation of Solution

Express wt% of liquid.

$\begin{array}{c}\text{wt\%}\text{liquid}=\frac{40-7.9}{52-7.9}\times 100\%\\ =72.8\%\\ =0.728\end{array}$

Express wt% of proeutectic $\alpha$.

$\begin{array}{c}\text{wt\%}\text{proeutectic}\alpha =\frac{52-40}{52-7.9}\times 100\%\\ =27.2\%\\ =0.272\end{array}$

Express the weight of liquid phase.

$\begin{array}{c}\text{wt}\text{liquid}\text{phase}=\left(\text{500}\text{g}\right)\left(0.728\right)\\ =364\text{g}\end{array}$

Express the weight of proeutectic $\alpha$.

$\begin{array}{c}\text{wt}\text{proeutectic}\alpha =\left(\text{500}\text{g}\right)\left(0.272\right)\\ =136\text{g}\end{array}$

Hence, the weight of liquid and proeutectic alpha phase is $\text{364}\text{g}\text{and}\text{136}\text{g}$ respectively.

To determine

Refer Fig P8.23, if $\text{500}\text{g}$ of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of $\text{1000°C}$ to just below $\text{780°C}$.

Determine the grams of liquid and proeutectic alpha present at $\text{780°C}+\Delta T$.

Answer to Problem 24AAP

The weight of liquid and proeutectic alpha phase is $\text{251}\text{g}\text{and}\text{249}\text{g}$ respectively.

Explanation of Solution

Express wt% of liquid.

$\begin{array}{c}\text{wt\%}\text{liquid}=\frac{40-7.9}{71.9-7.9}\times 100\%\\ =50.2\%\\ =0.502\end{array}$

Express wt% of proeutectic $\alpha$.

$\begin{array}{c}\text{wt\%}\text{proeutectic}\alpha =\frac{71.9-40}{71.9-7.9}\times 100\%\\ =49.8\%\\ =0.498\end{array}$

Express the weight of liquid phase.

$\begin{array}{c}\text{wt}\text{liquid}\text{phase}=500g\left(0.502\right)\\ =251\text{g}\end{array}$

Express the weight of proeutectic $\alpha$.

$\begin{array}{c}\text{wt}\text{proeutectic}\alpha =\left(\text{500}\text{g}\right)\left(0.498\right)\\ =249\text{g}\end{array}$

Hence, the weight of liquid and proeutectic alpha phase is $\text{251}\text{g}\text{and}\text{249}\text{g}$ respectively.

To determine

Refer Fig P8.23, if $\text{500}\text{g}$ of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of $\text{1000°C}$ to just below $\text{780°C}$.

Determine the grams of alpha present in the eutectic structure at $\text{780°C}-\Delta T$.

Answer to Problem 24AAP

The weight of alpha is $\text{307}\text{.5}\text{g}$.

Explanation of Solution

Express wt% of total $\alpha$.

$\begin{array}{c}\text{wt\%}\text{total}\alpha =\frac{91.2-40}{91.2-7.9}\times 100\%\\ =61.5\%\\ =0.615\end{array}$

Express the weight of alpha.

$\begin{array}{c}\text{wt}\text{total}\alpha =\left(500\text{g}\right)\left(0.615\right)\\ =307.5\text{g}\end{array}$

Hence, the weight of alpha is $\text{307}\text{.5}\text{g}$.

To determine

Refer Fig P8.23, if $\text{500}\text{g}$ of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of $\text{1000°C}$ to just below $\text{780°C}$.

Determine the grams of beta present in the eutectic structure at $\text{780°C}-\Delta T$.

Answer to Problem 24AAP

The weight of beta is $\text{192}\text{.5}\text{g}$.

Explanation of Solution

Express wt% of total $\beta$.

$\begin{array}{c}\text{wt\%}\text{total}\beta =\frac{40-7.9}{91.2-7.9}\times 100\%\\ =38.5\%\\ =0.385\end{array}$

Express the weight of beta.

$\begin{array}{c}\text{wt}\text{total}\beta =\left(500\text{g}\right)\left(0.385\right)\\ =192.5\text{g}\end{array}$

Hence, the weight of beta is $\text{192}\text{.5}\text{g}$.