Question

A steel bridge is 5.5m long. If the linear expansivity of steel is 0.000011/℃, how much will it expand when temperature rise by 10 ℃? Give your answer in cm

Answer 1

The expansion of the steel bridge is 0.0605 cm

Step-by-step explanation:

The given length of the steel bridge, L = 5.5 m

The linear expansivity of the steel bridge,
`\alpha_ L` = 0.000011/°C

The rise (change) in the temperature, ΔT = 10°C

Let, ΔL, represent the expansion of the steel bridge

Given that the linear expansivity,
`\alpha_ L`, of a material is the change in the length of a material per unit length of the material per unit change in the temperature, we have;

`\alpha_ L` = ΔL/(L × ΔT)

∴ ΔL =
`\alpha_ L` × L × ΔT = 0.000011 /°C × 5.5 m × 10 °C = 0.000605 meters

ΔL = 0.000605 meters

The expansion of the steel bridge, ΔL = 0.000605 meters = 0.000605 m × 100 cm/m = 0.0605 cm