Linear Expansion Help

Question

A steel bridge frame is 70.0 meters in length at a temperature of 25.0°C.

- If the bridge contracts evenly in both directions, how much shorter (in cm) is either end of the bridge at a temperature of -20.0°C?

Answer 1

First let's calculate the total length of the frame at 20C using the formula for linear expansion:

L = L₀ x (1 + α x Δt) where L_o is the original length, α the coefficient of linear expansion for steel, Δt the temperature change (f_final - t_initial).

Subtract the old length from the new length then divide the result by 2 to get the shrinkage at each end. Remember to change the result from meters to centimeters.

You could also get the length change at each end using ΔL = α x Δt / 2