Respuesta :
Given the original length is
[tex]L_0=4.950\text{ m}[/tex]Given the initial temperature is
[tex]T_1=1.6\text{ C}[/tex]The final temperature is
[tex]T_2=33.0\text{ C}[/tex]The linear thermal expansion is given by
[tex]\delta L=L_0\times\alpha\times(T_2-T_1)[/tex]Here, alpha is the coefficient of linear thermal expansion.
For concrete the value of the coefficient is
[tex]\alpha=1.1\times10^{-5}[/tex]The formula is used to calculate the final height of a concrete.
[tex]\begin{gathered} \text{Final height = }\delta L+L_0 \\ \text{Final height = }L_0\times\alpha\times(T_2-T_1)+L_0 \\ \text{Final height = }L_0\lbrack\alpha\times(T_2-T_1)+1\rbrack \end{gathered}[/tex]Substitute the given values.
[tex]\begin{gathered} \text{Final height = 4.950 m}\times\lbrack1.1\times10^{-5}\times(33.0-1.6)+1\rbrack \\ =4.950\text{ m}\times\lbrack0.00034+1\rbrack \\ =4.950\times1.00034 \\ =4.9516\text{ m} \end{gathered}[/tex]Thus, the value of the final height is 4.9516 m.
