Question

Railway lines are laid with gaps to allow for expansion. If the gap betweeen steel rails 60 m long be 3.60 cm at `10^(@)C`, then at what temperature will the lines just touch? Coefficient of linear expansion of steel `=11//10^(-6) .^(@)C^(-1)`.

Answer 1

We know that the rail expands in both the directions, so the gap between two rails will be filled by the expansion of half length of each rail. For this we take the expansion of one rail in one direction to fill the gap.
Here,`l= 60 m , l = 3.60 cm = 3.6 xx 10^(-2) m`,
`theta_(1) = 10^(@)C , theta_(2) = ? , alpha = 11 xx 10^(-6)` .^@)C^(-1)`
`alpha = (Delta l)/(l(theta_(2)-theta_(1))) or theta_(2) - theta_(1) = ( l)/(l alpha)`
or `theta_(2) = theta_(1) + (Delta l)/(l alpha) = 10 + (3.60 xx 10^(-2))/(60 xx 11 xx 10^(-6))`
`= 10 + 54.54 = 64.54 .^(@)C`