A steel railroad track has a length of 23 m when the temperature is 7◦C. What is the increase in the length of the rail on a hot day when the temperature is 30 ◦C? The linear expansion coefficient of steel is 11 × 10−6 ( ◦C)−1 . Answer in units of m.

5.82 mm

Explanation:

length of the track, L = 23 m

Initial temperature, T = 7 °C

final temperature, T' = 30 °C

Coefficient of linear expansion, α = 11 x 10^-6 / °C

Let the increase in length of the track on the hot day is ΔL.

use the formula of the linear expansion

ΔL = L x α x ΔT

ΔL = L x α x (T' - T)

ΔL = 23 x 11 x 10^-6 x (30 - 7)

ΔL = 5.82 x 10^-3 m

ΔL = 5.82 mm

Thus, the increase in the length of the track is 5.82 mm.

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