$9\mathrm{.}8).$ The alloy is to be melted to the extent that $50\%$ of the specimen is liquid, the remainder being the $$ 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 $1\mathrm{.}5-kg$ specimen at $250C$ to achieve this state?

$\mathrm{.}18$ A magnesium$-$lead alloy of mass $5\mathrm{.}5$ kg consists of a solid $$ phase that has a composition that is just slightly below the solubility limit at $200C(390F).$

$($a$)$ What mass of lead is in the alloy?

$($b$)$ If the alloy is heated to $350C(660F),$ how much more lead may be dissolved in the $$ phase without exceeding the solubility limit of this phase?

composition $50wt\%Ag-50wt\%Cu,$ which, at equilibrium, consists of $$ and $$ phases having mass fractions $W_{}=0\mathrm{.}60$ and $W_{}=0\mathrm{.}40?$ If so$,$ what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

$9\mathrm{.}24$ For $11\mathrm{.}20$ kg of a magnesium$-$lead alloy of composition $30wt\%Pb-70wt\%Mg,$ is it possible, at equilibrium, to have $$ and $M{g}_{2}Pb$ phases having respective masses of $7\mathrm{.}39$ kg and $3\mathrm{.}81$ kg $?$ If so$,$ what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

$9\mathrm{.}25$ Derive Equations $9\mathrm{.}6$a and $9\mathrm{.}7$a$,$ which may be used to convert mass fraction to volume fraction, and vice versa.

$9\mathrm{.}26$ Determine the relative amounts $($in terms of volume fractions$)$ of the phases for the alloys and temperatures given in Problem $9\mathrm{.}10$a$,$ b$,$ and c$.$ Below are given the approximate densities of t

he various metals at the alloy temperatures:

Do $9\mathrm{.}24$ please the one that is highlighted blue. Thank you