Question

A steel railroad track has a length of 24 m when the temperature is 3◦C. What is the increase in the length of the rail on a hot day when the temperature is 32 ◦C? The linear expansion coefficient of steel is 11×10−6 (◦C)−1. Answer in units of m.

Answer 1

The linear thermal expansion of a steel railroad track is described by equation

$$L'=L(1+\alpha \Delta T)$$

So

$$L'=24(1+11\times 10^{-6}\times 29)=24.008\:\rm m.$$ $$\Delta L=L'-L=0.008\:\rm m.$$