Question

Compute the volume percent of graphite, VGr, in a 3.1 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

The volume percent of graphite is 9.9%

Step-by-step explanation:

Given;

weight percent of graphite, C = 3.1wt%

density of ferrite,
`\rho _f` = 7.9 g/cm³

density of graphite,
`\rho _g` = 2.3 g/cm³

Determine the mass fraction;

`W_f = (C_g - C_0)/(C_g -C_f) \\\\W_f =(100 - 3.1)/(100-0)\\\\W_f = 0.969\\\\\\W_g = (C_0 - C_a)/(C_g -C_f) \\\\W_g =(3.1-0)/(100-0)\\\\W_g = 0.031`

Determine the volume fraction;

`V = (W_g/ \rho_g)/(W_f / \rho_f \ + \ W_g / \rho_g) *100 \%\\\\V = (0.031/ 2.3)/(0.969 / 7.9 \ + 0.031 / 2.3)*100\%\\\\V = 9.9\%`

Therefore, the volume percent of graphite is 9.9%