Question

An aluminum flagpole 33 m ishigh. By how much does its length increase as the temperature increases by $\mathbf{15}{\mathit{C}}^{\mathbf{\circ }}$?

Short answer

The increase in length due to its temperature increase is 0.001m.

Step-by-step solution

The given data

• i)Height of flagpole is, L= 33m
• ii)The temperature increase,$△T=15°C$$△T={15}^{\circ }C$

Determine the formulas for the thermal expansion

The linear expansion of length is given by:

$△L=L{\alpha }_b△T$ ...........(i)

Here, $\alpha$is the coefficient of linear expansion of body.

Calculate the increase in length

Change in the height of the flagpole is a linear expansion.

From this, write the increase in the length of flagpole as
$△L=L{\alpha }_{Al}△T$$△L=L{\alpha }_{Al}△T$

Here, the linear coefficient of expansion for aluminum is${\alpha }_{Al}=23\times {10}^{-6}\frac{1}{°C}$

Hence, the increase in length is given as:

$$\begin{gathered} △L=33\times 23\times {10}^{-6}\times 15 \\ =0.011m \end{gathered}$$

Hence, the value of increase in length is 0.011m