Q10PE - College Physics (Urone)

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

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

Step 1: Introduction

We calculate the change in height of the Eiffel Tower by the formula for linear expansion in solids.

Step 2: Given parameters and formula for linear expansion

Coefficient of linear expansion of marble = $1.2\times {10}^{-5}/°\mathrm{C}$

The formula for length expansion of solids is,

$\mathbf{∆}\mathbf{L}\mathbf{=}\mathbf{\alpha L}\mathbf{∆}\mathbf{T}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\left(1\right)$

Here, is the coefficient of linear expansion, L is the original length, and $∆\mathrm{T}$ is the temperature change. 

Step 3: Increase in height

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

$\begin{array}{rcl}\mathbf{∆}\mathbf{L}& \mathbf{=}& \mathbf{\alpha L}\mathbf{∆}\mathbf{T}\\ & \mathbf{=}& \left(1.2\times {10}^{-5}/°C\right)\mathbf{\times }\mathbf{321}\mathbf{m}\mathbf{\times }\left(15°C\right)\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{058}\mathbf{ }\mathbf{m}\end{array}$

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