Thermal Expansion is a (property?) of all materials wherein some voodoo magic happens that makes the material expand / contract when subject to heat or cold. I’m an engineer, not a physicist.
In our case, we can figure out the thermal expansion of the Eiffel Tower for a given range of temperature change just by looking up a few things on the interwebs.
First, we need a fancy formula like this:
Then, we need to figure out all the necessary information on the variables. Ultimately, we want to find that “change in length” value so we just need to know a few things:
- Coefficient of Thermal Linear Expansion – Different materials expand and contract differently so we need to determine the construction material. This building is made almost entirely of wrought iron. Wrought Iron is basically steel but without all the sweet sweet benefits a bit of carbon adds to the mixture. For reference, wrought Iron is generally something like 25%-50% weaker than most commonly used “building steel” grades. But anyways – since we know the material, we know that α = 6.5 x 10^(-6)using degrees F (that’s right Fahrenheit – I’m no commie!).
- Original Length – In this case – the height of the structure. According to something that looks official, the height is 984 feet.
- Temperature Change – I’m going to take the liberty of assuming the OP is looking for the height change from hottest recorded temperature ever to the coldest recorded temperature ever – because I can. So, in our case, for Paris, France, that is 105 degrees F and -11 degrees F. Side note – I’m assuming that the paint prevents the iron from getting really extra hot in the sunlight to simplify my research – but it very well could.
So, when we put the numbers together, we get:
δL = 984′ * 0.0000065 * (105 – (-11)) = 0.75′ = 9 inches! …or 23cm for you metric types.
Of course, this is an over-simplification – but generally speaking, the Eiffel Tower should be a handful of inches taller in the summer than it is in the winter.