Question

A steel rod 30.0 m long, installed when the temperature was 10°C, is in a bridge that heats up to 40^oC on a hot summer day. Steel's coefficient of linear expansion is 1.2 × 10^-5 K^-1. The bridge is built so the rod has an expansion space of 5 cm. Is this enough space? What is the increase in the length of the rod, in mm?

Answer 1

Expansion in length due to temperature is given by,

dL = L0*alpha*dT

here, L0 = initial length = 30.0 m

alpha = coefficient of linear expansion for steel = 1.2*10^-5 /K

dT = change in temperature = 40 degC - 10.0 degC = 30 degC

So, dL = 30.0*(1.2*10^-5)*30

dL = increase in length of the rod = 0.0108 m = 10.8*10^-3 m

dL = 10.8 mm

During the building of bridge expansion space left is 5 cm, which is greater than increase in length of the steel rod (1.08 cm). So

YES, this is enough space

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