He coefficient of linear expansion of steel is 12 × 10-6 k-1 . what is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 k from winter to summer?

ΔL = 12 mm

Explanation:

Given that

Coefficient of linear expansion ,α = 12 x 10⁻⁶ K⁻¹

Length of steel bridge ,Lo= 25 m

Change in the temperature ,ΔT = 40 K (Winter to summer)

It means that change in the temperature is positive.

We know that the change in the length given as

ΔL = Lo α ΔT

Now by putting the values

ΔL = Lo α ΔT

ΔL =25 x  12 x 10⁻⁶  x 40 m

ΔL =12000 x 10⁻⁶  m

ΔL =12 x 10⁻³  m                ( 1 mm =10⁻³  m   )

ΔL = 12 mm

Therefore the change in the length of the bridge

ΔL = 12 mm

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