#### Answer

$E_{0} = 264.54 GPa$

#### Work Step by Step

Given:
The modulus of elasticity for spinel $(MgAl_{2}O_{4})$ having 5 vol% porosity is 240 GPa
($35 \times 10 ^{6} psi$).
Required:
modulus of elasticity for the nonporous material
Solution:
Rearranging Equation 12.9 to solve $E_{0}$ and considering that $P = 0.05$:
$E_{0} =\frac{E}{1 -1.9P + 0.9P^{2}} = \frac{(240 GPa)}{1 -1.9(0.05) + 0.9(0.05)^{2}} = 264.54 GPa$