Question

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 40.0°C greater than when they were laid? Their original length is 41.0 m.

Answer 1

Answer:

19.68 × 10⁻³ m

Explanation:

Given;

Original Length, L₁ = 41.0 m

Temperature Change, ΔT = 40.0°C

Thermal Linear expansion of steel is given to be, ∝$_{steel}$ = 12 × 10⁻⁶ /°C

   Generally, Linear expansivity is expressed as;

                               ∝ = ΔL / L₁ΔT

Where

∝ is the Linear expansivity

ΔL is the change in length, L₂ - L₁

L₂ is the final length

L₁ is the original length

ΔT is the change in temperature θ₂ - θ₁ (Final Temperature - Initial Temperature)              

From equation of linear expansivity

                         ΔL = ∝$_{steel}$L₁ΔT

                         ΔL = 12 × 10⁻⁶ /°C × 41.0 m × 40.0 °C

                         ΔL = 19.68 × 10⁻³ m

                         ΔL = 19.68 mm