Question

Two steel bars, 2.0m long each are used to construct a rail line. maximum temperature change is 450C. what would be the safe that must be between the bars

Answer 1

The linear expansion of the steel is given by:

$$\Delta L =\alpha_L L\Delta T$$

where $\alpha_L = 11\cdot 10^{-6}K^{-1}$ is the coefficient of linear thermal expansion (see https://en.wikipedia.org/wiki/Thermal_expansion#Thermal_expansion_coefficients_for_various_materials), $L = 2m$ is the length of the bars and $\Delta T = 45K$ is the temperature change.

Thus, the maximum additional length can be:

$$\Delta L = 11\cdot 10^{-6}\cdot 2\cdot 45 = 0.99mm$$

Answer. The bars should be 0.99 mm appart.