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

Answer:

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

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 = $12\times 10^{-6}^{\circ}\text{C}^{-1}$

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