Answer
The length of the bridge might change by $1.28~m$ during the year.
Work Step by Step
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.
