Q10PE - College Physics (Urone)

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.

Step-by-Step Solution

Answer

Answer

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

Step 1: Introduction

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

Step 2: 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. 

Step 3: 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.