# 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.

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} 