Answer
soda lime $ΔT_{f} = 111.11 °C$
borosilicate $ΔT_{f} = 307.42 °C$
aluminum oxide (96% pure) $ΔT_{f} = 114.37 °C$
gallium arsenide $ΔT_{f} = 252.75 °C$
Work Step by Step
Given:
a. soda lime
E = 69 GPa
$σ_{f}$ = 69 MPa
$α_{l}$ = 9.0 x $10^{-6} (°C)^{-1}$
b. borosilicate
E = 69 GPa
$σ_{f}$ = 70 MPa
$α_{l}$ = 3.3 x $10^{-6} (°C)^{-1}$
c. aluminum oxide (96% pure)
E = 358 GPa
$σ_{f}$ = 303 MPa
$α_{l}$ = 7.4 x $10^{-6} (°C)^{-1}$
d. Gallium Arsenide
E = 57 GPa
$σ_{f}$ = 85 MPa
$α_{l}$ = 5.9 x $10^{-6} (°C)^{-1}$
Required:
maximum temperature change for each material
Solution:
Using the given equation and substituting the given values from the Tables cited:
$ΔT_{f} = \frac{σ_{f}}{Eα_{l}}$
a. $ΔT_{f} = \frac{69 MPa}{(69\times 10^{3} MPa)(9.0 \times 10^{-6} (°C)^{-1}} = 111.11 °C$
b. $ΔT_{f} = \frac{70 MPa}{(69\times 10^{3} MPa)(3.3 \times 10^{-6} (°C)^{-1}} = 307.42 °C$
c. $ΔT_{f} = \frac{303 MPa}{(358\times 10^{3} MPa)(7.4 \times 10^{-6} (°C)^{-1}} = 114.37 °C$
d. $ΔT_{f} = \frac{85 MPa}{(57\times 10^{3} MPa)(5.9 \times 10^{-6} (°C)^{-1}} = 252.75 °C$
