Question

The eiffel tower in paris is 300 meters tall on a cold day (t= -5 degrees celsius). What is its height o a ot day when the temperature is 35 degrees? ( it is made of iron which has a coefficient of linear epansion of 0.000012 per degree Celsius).

Answer 1

Well, let's take a look at the formula for linear expansion of a metal structure.

\[dl=L _{0}\alpha(T _{1}-T _{0})\]
\[dl =\Delta length \\L _{0} = initial\ length\\ \alpha=coefficient \ of \ linear \ expansion\\T _{0} = initial \ temperature \\ T _{1} = final \ temperature\]

Let's plug your information in.

\[dl = (\frac{ 300m }{ 1 })(\frac{ 0.000012m }{ m°C })(35°C-(-5°C))\\dl=(\frac{ 300 }{ 1 })(\frac{ 0.000012m }{ 1 })(40)\\dl=0.144\]
So, the height of the eiffel tower would be 300m +0.144m tall on a 35°C day or 300.144m.

Answer 2

By the way, °C and meters canceled if you were wondering, leaving us with a single unit of meters.