Question

G Railroad tracks are made from segments L = 79 m long at T = 20° C. When the tracks are laid, the engineers leave gaps of width l between adjacent segments to allow for thermal expansion. The coefficient of linear expansion is α = 12 × 10-6 °C-1 and engineers design the tracks to withstand temperatures of Tc = 39.5 degrees.

(a) Enter an expression, in terms of given variables, for the minimum gap distance l the engineers must leave for a track rated at temperature Tc

Answer 1

`l=L\alpha(T_c-T)`

Step-by-step explanation:

L = Initial length of segment = 79 m

T = Normal temperature =
`20^(\circ)\text{C}`

l = Width to be left for expansion

`\alpha` = Coefficient of linear expansion of the material =
`12* 10^(-6)^(\circ)\text{C}^(-1)`

`T_c` = Maximum temperature =
`39.5^(\circ)\text{C}`

`\Delta T` = Change in temperature =
`T_c-T`

The expression of linear expansion is given by

`l=L\alpha\DeltaT\\\Rightarrow l=L\alpha(T_c-T)`

The expression for the minimum gap distance l the engineers must leave for a track rated at temperature
`T_c` is
`l=L\alpha(T_c-T)`