Question

Steel railway tracks are laid at 8°C. What size of expansion gap are needed 10m long rail sections if the ambient temperature varies from -10°C to 50° C? (linear expansivity of the steel = 1.2*10^-6K)​

Answer 1

Given,

Length of track, (L) $\[ = 10m\]$

Temperature varies $\[ = - 10^\circ C\,to\,50^\circ C\]$

Linear expansivity of steel,$\[\left( \propto \right)\]$ $\[ = 1.2 \times {10^{ - 6}}K\]$

Solution,

Calculate the size of expansion gap are needed,

$\[\begin{array}{l}\Delta L = \propto L\left( {\Delta T} \right)\\ \Rightarrow \Delta L = 1.2 \times {10^{ - 6}} \times 10\left( {50 - \left( { - 10} \right)} \right)\\ \Rightarrow \Delta L = 1.2 \times {10^{ - 6}} \times 10 \times 60\\ \Rightarrow \Delta L = 1.2 \times {10^{ - 6}} \times 6\\ \Rightarrow \Delta L = 7.2 \times {10^{ - 6}}m\end{array}\]$

Hence the expansion gap needed is $\[7.2 \times {10^{ - 6}}m\]$.