# Consider a steel bridge, 200m long, in a locality when temperature varies from 243K to 313K. Find...

## Question:

Consider a steel bridge, 200m long, in a locality when temperature varies from 243K to 313K. Find the change in length of the bridge for above seasonal variations in the temperature. Coefficient of linear expansion of steel=11*10/1000000/K.

## Coefficient of Linear Expansion:

The thermal property of an object that represents how the length of the object varies by its temperature is known as the coefficient of linear expansion. Its measurable unit is the inverse Kelvin.

Given Data:

• The length of steel bridge is: {eq}{L_i} = 200\;{\rm{m}} {/eq}
• The initial temperature is: {eq}{T_i} = 243\;{\rm{K}} {/eq}
• The final temperature is: {eq}{T_f} = 313\;{\rm{K}} {/eq}
• The coefficient of linear expansion of steel is: {eq}{\alpha _s} = 11 \times 10/1000000/{\rm{K}} = {\rm{11}} \times {\rm{1}}{{\rm{0}}^{ - 5}}\;{{\rm{K}}^{ - 1}} {/eq}

The expression for the change in length of the steel bridge by thermal expansion is

{eq}\Delta {L_o} = {L_i}{\alpha _s}\left( {{T_f} - {T_i}} \right) {/eq}

Substitute the known values and solve the above expression

{eq}\begin{align*} \Delta {L_o} &= 200 \times 11 \times {10^{ - 5}}\left( {313 - 243} \right)\\ &= 1.54\;{\rm{m}} \end{align*} {/eq}

Thus the change in length of steel bridge by thermal expansion is {eq}1.54\;{\rm{m}} {/eq}.