To solve this problem we apply the thermodynamic equations of linear expansion in bodies.
Mathematically the change in the length of a body is subject to the mathematical expression
[tex]\Delta L = L_0 \alpha \Delta T[/tex]
Where,
[tex]L_0 =[/tex] Initial Length
[tex]\alpha =[/tex] Thermal expansion coefficient
[tex]\Delta T =[/tex] Change in temperature
Since we have values in different units we proceed to transform the temperature to degrees Celsius so
[tex]0\°F \Rightarrow (0-32)*\frac{5}{9} = -17.77\°C[/tex]
[tex]103\°F \Rightarrow (103-32)*(\frac{5}{9})= 39.44\°C[/tex]
The coefficient of thermal expansion given is
[tex]\alpha = 1.1*10^{-5}/\°C[/tex]
The initial length would be,
[tex]L_0 = 565m[/tex]
Replacing we have to,
[tex]\Delta L = L_0 \alpha \Delta T[/tex]
[tex]\Delta L = (565)(1.1*10^{-5})(39.44-(-17.77))[/tex]
[tex]\Delta L = (565)(1.1*10^{-5})(39.44-(-17.77))[/tex]
[tex]\Delta L = 0.355m[/tex]
This means that the building will be 35.5cm taller
