Question

The Eiffel Tower is built of wrought iron approximately 300 m tall.Estimate how much its height changes between January (averagetemperature of 2o C) and July (average temperature of25o C). Ignore the angles of the iron beams and treatthe tower as a vertical beam.

Answer 1

The concepts required to solve this problem are the thermodynamic expressions of expansion and linear expansion.

In mathematical terms the dilation of a body can be expressed as

$\Delta L = L_0 \alpha \Delta T$

Where,

$L_0 =$ Initial Length

$\alpha =$ Thermal coefficient of linear expansion

$\Delta T =$ Change in Length

Our values are given as

$L_0 = 300m$

$T_f = 25\°C$

$T_i = 2\°C$

$\alpha = 12*10^{-6}C^{-1} (Iron)$

Replacing at the equation we have,

$\Delta L = L_0 \alpha \Delta T$

$\Delta L = (300)(12*10^{{-6})(25-2)$

$\Delta L = 0.0828m$

Therefore the change in the height is 8.28cm