Bismuth $($melting point $520F)$ and cadmium $($melting point $610F)$ are assumed to be completely soluble in the liquid state and completely insoluble in the solid state. They form a eutectic at $290F$ containing $40$ percent cadmium.

$($a$)$ Draw the equilibrium diagram to scale on a piece of graph paper and label it completely.

$($b$)$ For an alloy containing $70$ percent cadmium $($i$)$ give the temperature of initial solidification; $($ii$)$ give the temperature of final solidification; $($iii$)$ give the chemical composition and relative amounts of the phases present at a temperature of $100F$ below $($i$)$; $($iv$)$ sketch the microstructure at room temperature; $($v$)$ draw the cooling curve of the alloy.