Older railroad tracks in the U.S. are made of 12-m-long pieces of steel. When the tracks are laid, gaps are left between sections to prevent buckling when the steel termally expands. If a track is laid at 16C, how large should the gaps be if the track is not to buckle when the temperature is as high as 50C?

Thermal expansion of steel is the increase in size of steel as a result of increased temperature. It can be represented by the mathematical expression:

∆L = L(k)∆T .....1

Where;

∆L is the change in length

L is the initial length

∆T is the change in temperature

k is the specific Linear expansion coefficient.

Given;

L = 12m

∆T = 50°C - 16°C = 34°C

k (for steel) = 1.2 × 10^-6 /C

Substituting the values into the equation 1

∆L = 12 × 34 × 12×10^-6

∆L = 4896 × 10^-6 m

∆L = 0.49cm ≈ 0.50cm

Therefore there should be 0.5 cm gap between each piece of steel.

Larus Larus · Answer 2 · 2021-12-09T11:29:57+01:00

There should be a gap of 0.5 cm between each of the piece of steel.

Based on the given information,

• The initial length of the tracks is 12 m.

• The laying of the tracks was done at the temperature of 16 °C (Initial temperature), the final temperature is 50 °C.

• The increase in the size of the steel as an outcome of enhanced temperature is known as the thermal expansion of steel.

The mathematical representation of thermal expansion is,

ΔL = L(k)ΔT

• Here ΔL refers to the change in length, L is the initial length, k is the specific linear expansion, which is 1.2 × 10⁻⁶/C for steel, and ΔT is the change in temperature, which is 50 °C - 16 °C = 34 °C.

Now putting the values we get,

ΔL = 12 × 34 × 12 × 10⁻⁶

ΔL = 4896 × 10⁻⁶ m

ΔL = 0.49 cm or 0.5 cm

Thus, the gap between each piece of steel should be 0.5 cm.

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