Answer
By ranking from greatest to least based on TSR:
Silicon, fused silica, and soda lime.
Work Step by Step
Given:
a. soda lime
E = 69 GPa
k = 1.7 W/m.K
$σ_{f}$ = 69 MPa
$α_{l}$ = 9.0 x $10^{-6} (°C)^{-1}$
b. fused silica
E = 73 GPa
k = 1.4 W/m.K
$σ_{f}$ = 104 MPa
$α_{l}$ = 0.4 x $10^{-6} (°C)^{-1}$
c. silicon
E = 129 GPa
k = 141 W/m.K
$C$ = 130 MPa
$α_{l}$ = 2.5 x $10^{-6} (°C)^{-1}$
Required:
ranking based on thermal shock resistance
Solution:
Using Equation 19.9 and substituting the given values from the Tables cited:
$TSR = \frac{σ_{f}k}{Eα_{l}}$
a. $TSR = \frac{(69 MPa) (1.7 W/m.K}{(69 \times 10^{3} MPa)(9.0 x 10^{-6} (°C)^{-1})} = 188.89 W/m$
b. $TSR = \frac{(104 MPa) (1.4 W/m.K}{(73 \times 10^{3} MPa)(0.4 x 10^{-6} (°C)^{-1})} = 4986.30 W/m$
c. $TSR = \frac{(130 MPa) (141 W/m.K}{(129 \times 10^{3} MPa)(2.5 x 10^{-6} (°C)^{-1})} = 56,837.21 W/m$
