Question

Find the final height of a concrete column that is 4.950 m tall at 1.6 C when the column is heated to 33.0 C

Answer 1

Given the original length is

`L_0=4.950\text{ m}`

Given the initial temperature is

`T_1=1.6\text{ C}`

The final temperature is

`T_2=33.0\text{ C}`

The linear thermal expansion is given by

`\delta L=L_0*\alpha*(T_2-T_1)`

Here, alpha is the coefficient of linear thermal expansion.

For concrete the value of the coefficient is

`\alpha=1.1*10^(-5)`

The formula is used to calculate the final height of a concrete.

`\begin{gathered} \text{Final height = }\delta L+L_0 \\ \text{Final height = }L_0*\alpha*(T_2-T_1)+L_0 \\ \text{Final height = }L_0\lbrack\alpha*(T_2-T_1)+1\rbrack \end{gathered}`

Substitute the given values.

`\begin{gathered} \text{Final height = 4.950 m}*\lbrack1.1*10^(-5)*(33.0-1.6)+1\rbrack \\ =4.950\text{ m}*\lbrack0.00034+1\rbrack \\ =4.950*1.00034 \\ =4.9516\text{ m} \end{gathered}`

Thus, the value of the final height is 4.9516 m.