Question

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 30.0°C greater than when they were laid? Their original length is 30.0 m.

Answer 1

Answer:

1.2 cm

Explanation:

Thermal Expansion

It's the tendency that materials have to change its size and/or shape under changes of temperature. It can be in one (linear), two (surface) or three (volume) dimensions.

The formula to compute the expansion of a material under a change of temperature from $T_o$ to $T_f$ is given by.

$\Delta L=L_o.\alpha .(T_f-T_o)$

Where Lo is the initial length and $\alpha$ is the linear temperature expansion coefficient, which value is specific for each material. The data provided in the problem is as follows:

$L_o=30\ m,\ T_f-T_o=30^oC,\ \alpha=13\times 10^{-6}\ ^oC^{-1}$

Computing the expansion we have

$\Delta L=30\times 13\times 10^{-6}(30)=0.0117=1.17\ cm$

The expansion gap should be approximately 1.2 cm