Question

11.4 Compute the volume percent of graphite VGr in a 3.5 wt% C cast iron, assuming that all the carbon exists as the graphite phase. Assume densities of 7.9 and 2.3 g/cm3 for ferrite and graphite, respectively.

Answer 1

Answer:

The volume percent of graphite in a 3.5 wt% C cast iron is 11%.

Explanation:

Consider 100 grams 3.5% C cast iron.

Mass of  carbon in 100 grams of cast iron = $m_1=100 g\times \frac{3.5 }{100}=3.5 g$

Mass of iron in cast iron =$m_2$ = 100 g - 3.5 g = 96.5 g

Density of graphite = $d_1=2.3g/cm^3$

Volume of the graphite = $v_1$

$v_1=\frac{m_1}{d_1}=\frac{3.5 g}{2.3g/cm^3}=1.52 cm^3$

Density of iron= $d_2=7.9 g/cm^3$

Volume of the iron = $v_2$

$v_2=\frac{m_2}{d_2}=\frac{96.5 g}{7.9 g/cm^3}=12.22 cm^3$

Total volume of the cast iron ,V=$v_1+v_2=1.52 cm^3+12.22 cm^3=13.74 cm^3$

Volume percent of the graphite :

$=\frac{v_1}{V}\times 100$

$=\frac{1.52 cm^3}{13.74 cm^3}\times 100=11.06\%\approx 11\%$

The volume percent of graphite in a 3.5 wt% C cast iron is 11%.