# A steel bridge is built in the summer when its temperature is 37.5 degree C. At the time of...

## Question:

A steel bridge is built in the summer when its temperature is 37.5 {eq}^{\circ} {/eq}C. At the time of construction, its length is 78.25 m. What is the length of the bridge on a cold winter day when its temperature is -13.5 {eq}^{\circ} {/eq}C?

## Length of bridge

The temperature of the bridge is decreased, so there will be a contraction in the length of the bridge. The length on the cold winter day will be less than the original length of the bridge at the time of construction.

## Answer and Explanation:

The initial length of the bridge is {eq}\rm L_0 = 78.25 \ m {/eq}

Initial temperature of the bridge = {eq}\rm T_i = 37.5 \ ^{\circ} C {/eq}

Final temperature of the bridge = {eq}\rm T_f= -13.5 \ ^{\circ} C {/eq}

Coefficient of thermal expansion of steel is {eq}\rm \alpha = 7.2 \times 10^{-6} / ^{\circ} C {/eq}

The length of the bridge is given as:

{eq}\rm L = L_0( 1 + \alpha(T_f - T_i)) {/eq}

{eq}\rm L = 78.25( 1 + 7.2 \times 10^{-6} \times (-13.5 - 37.5)) {/eq}

{eq}\rm L = 78.25( 1 - 7.2 \times 10^{-6} \times 51) {/eq}

{eq}\rm L = 78.22 \ m {/eq}

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Chapter 16 / Lesson 3