Question

Question: How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15ºC? Its original height is 321 m and you can assume it is made of steel.

Short answer

Answer

The Eiffel Tower gets taller by a length of 0.058m by the end of the day.

Step-by-step solution

Introduction

We calculate the change in height of the monument and hence, by subtracting it from the original height we find the new height.

Given parameters and formula for linear expansion

Coefficient of linear expansion of marble =$1.2\mathbf{\times }{{\mathbf{10}}^{-5}}^{\mathbf{0}}\mathit{C}$

The formula for length expansion of solids is,

$∆L=\alpha L∆T$……………..(1)

Here, is the coefficient of linear expansion, L is the original length, and is the temperature change.

Increase in height

Substitute the given values in equation (1), and we get,

$$\begin{gathered} ∆L=\alpha L∆T \\ =(\text{1.2}\mathbf{\times }{\text{10}}^{-5}{\text{/}}^O\text{C})\times 321m\times \left({15}^{0}C\right) \\ =0.058m \end{gathered}$$

Therefore, the Eiffel Tower gets taller by a length of 0.058m by the end of the day.