## College Physics (4th Edition)

The length of the bridge might change by $1.28~m$ during the year.
We can convert the two temperatures to $^{\circ}C$: $C_1 = \frac{5}{9}(F-32)$ $C_1 = \frac{5}{9}(-15-32)$ $C_1 = -26.1^{\circ}C$ $C_2 = \frac{5}{9}(F-32)$ $C_2 = \frac{5}{9}(105-32)$ $C_2 = 40.6^{\circ}C$ The change in temperature is $66.7^{\circ}C$ We can find the increase in length of the steel bridge when it is heated from $-26.1^{\circ}C$ to $40.6^{\circ}C$: $\Delta L = \alpha~\Delta T~L$ $\Delta L = (12\times 10^{-6}~K^{-1})(66.7~K)~(1600~m)$ $\Delta L = 1.28~m$ The length of the bridge might change by $1.28~m$ during the year.