## Materials Science and Engineering: An Introduction

soda lime $ΔT_{f} = 111.11 °C$ borosilicate $ΔT_{f} = 307.42 °C$ aluminum oxide (96% pure) $ΔT_{f} = 114.37 °C$ gallium arsenide $ΔT_{f} = 252.75 °C$
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. $ΔT_{f} = \frac{85 MPa}{(57\times 10^{3} MPa)(5.9 \times 10^{-6} (°C)^{-1}} = 252.75 °C$