To solve this problem it is necessary to apply the concepts related to the thermodynamic linear expansion of bodies. Said expansion can be mathematically encompassed through the expression
[tex]\Delta L = L_0 \alpha \Delta T[/tex]
Where,
[tex]\Delta L =[/tex] Change in Length
[tex]L_0 =[/tex] Initial Length
[tex]\Delta T =[/tex] Change in Temperature
[tex]\alpha =[/tex] Thermal coefficient of linear expansion
Our values are given as
[tex]L_0 = 17.7 m[/tex]
[tex]T_i = 21.2\°C[/tex]
[tex]T_f = 29.4\°C[/tex]
[tex]\alpha_{steel} = 12*10^{-6} / \°C[/tex]
Replacing the values we have that
[tex]\Delta L = L_0 \alpha \Delta T[/tex]
[tex]\Delta L = (17.7) (12*10^{-6}) (29.4-21.2)[/tex]
[tex]\Delta L = (17.7) (12*10^{-6}) (29.4-21.2)[/tex]
[tex]\Delta L = 1.7416*10^{-3}m =1.74mm[/tex]
Therefore the final length will be
[tex]L_f = 17.7m +1.7416*10^{-3}m[/tex]
[tex]L_f = 17.7017m[/tex]
