## Materials Science and Engineering: An Introduction

$α_{l} = 1.5 \times 10^{-5} (°C)^{-1}$
Given: 0.4 m rod of metal with Δl = 0.48 mm (0.019 in.) = 0.48 x $10^{-3}$ m $T_{0} = 20°C (68°F)$T_{f} = 100°C (212 °F) Required: linear coefficient of thermal expansion $(α_{l})$ Solution: Rearranging Equation 19.3b: $α_{l} = \frac{Δl}{l_{0}(T_{f}-T_{0}) } = \frac{0.48 \times 10^{-3} m}{(0.4 m)(100°C - 20°C)} = 1.5 \times 10^{-5} (°C)^{-1}$