Question

A bridge is made from 20 m long iron rods. At temperature 18^∘C, the distance between two rods in 0.4 cm. Up to what temperature will the bridge be in good shape?

Answer 1

Length of the iron rod = 20 m = 2000 cm at 18^∘C

Distance between the length of two rods, = 0.4 cm

Temperature coefficient of linear expansion of iron = 11.5 × 10^-6 °C^-1

The bridge will be in good shape till both the rods expand by 0.2 cm as the temperature is increased. Let at temperature T, both the rods expand by 0.2 cm i.e. the total expansion is 0.4 cm.
Using formula for linear expansion of solids, we have 

`(triangle l )/l = alpha_l triangle T`

`=> 0.4/2000 = 11.5 xx 10^(-6) xx ("T" - 18)`

`"T" =18 + 0.4/(2000 xx 11.5 xx 10^(-6)) = 35.4° "C"`