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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

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Answer:

[tex]l=L\alpha(T_c-T)[/tex]

Explanation:

L = Initial length of segment = 79 m

T = Normal temperature = [tex]20^{\circ}\text{C}[/tex]

l = Width to be left for expansion

[tex]\alpha[/tex] = Coefficient of linear expansion of the material = [tex]12\times 10^{-6}^{\circ}\text{C}^{-1}[/tex]

[tex]T_c[/tex] = Maximum temperature = [tex]39.5^{\circ}\text{C}[/tex]

[tex]\Delta T[/tex] = Change in temperature = [tex]T_c-T[/tex]

The expression of linear expansion is given by

[tex]l=L\alpha\DeltaT\\\Rightarrow l=L\alpha(T_c-T)[/tex]

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

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