Respuesta :
Given,
The length of the slab, L=12 m
The initial temperature, T₁=10°C
The final temperature, T₂=30°C
The coefficient of the linear expansion of the concrete is α=12×10⁻⁶ /°C
The change in the length of the slab is given by,
[tex]\Delta L=\alpha L\times\Delta T[/tex]Where ΔT is the change in the temperature.
Therefore,
[tex]\Delta L=\alpha L\times(T_2-T_1)[/tex]On substituting the known values,
[tex]\begin{gathered} \Delta L=12\times10^{-6}\times12\times(30-10) \\ =2.88\times10^{-3}\text{ m} \\ \approx0.003\text{ m} \end{gathered}[/tex]Thus the expansion in the length of the slab in the given temperature range is 0.003 m.
Thus the gap between the slabs should be 0.003 m
