# The Eiffel Tower in Paris stands 300.0 m tall on a day of average temperature, 22.0°C. How much taller is the steel tower on a hot summer day (T = 40°C) in centimeters? (αsteel = 11 x 10-6 °C-1)

May 28, 2014

Let's use the GRASS method to solve this problem.

Given:
Original length $\left({L}_{o}\right)$ = 300.0 m
Coefficient of Linear expansion of steel $\left(\alpha\right) = 11 x {10}^{6} ^ o {C}^{-} 1$
Temperature change $\left(\Delta T\right) = 40 - 22 = {18.0}^{o} C$

Required to find: Change in length $\left(\Delta L\right)$

Analysis: The formula for figuring out this question is

$\Delta L = \alpha {L}_{o} \Delta T$

The unknown value is already isolated, so we do not need to manipulate the formula.

Solve and Significant Figures:

$\Delta L = \left(11 x {10}^{6} ^ o {C}^{-} 1\right) \left(300.0 m\right) \left({18}^{o} C\right)$
$\Delta L = 0.0594 m$

Convert to centimeters by multiplying by 100:
$\Delta L = 5.94 c m$

This means the Eiffel Tower is 5.94 cm taller on a hot day of 40 degrees than it is at 22 degrees.