Thermal Expansion

Thermal expansion is an extremely simple concept, however it is so important it has to be taken into account in practically every aspect of engineering and physics. As objects heat up they tend to expand, and as they cool tend to contract. There are of course exceptions, such as water (which is surprisingly most dense at around 4 degrees celsius) - however for simplicity we will discuss solid objects for now. 

My first run in with the concept of thermal expansion came wondering why they put the lines in sidewalk. After asking around it was explained to me that the sidewalk expands when it gets hot, so they put the cracks in so its less likely to crack due to the expansion. So, how is this modeled???

This is the equation that models linear expansion. Lets look at each term piece by piece.

Delta L - is the change in the length of the object

L - The initial length of the object

alpha - the coefficient of expansion that is different for each object

Delta T - is the change in the temperature of the object

Well lets look at a basic example. Concrete is one of the most common ingredient so lets look at that. How much would a strip of sidewalk expand on a hot day? 

Lets start with a 100 meter strip of concrete. The alpha, in this case coefficient of linear expansion, for concrete is about 12 * 10^-6 / Celsius. Now we just need the temperature change. Keep in mind most coefficients are based off the celsius, so the temperature change needs to be in celsius. Lets say it was created at 100 meters long at 20 celsius(68 fahrenheit) and we want to know how long it will be at 38 celsius (100 fahrenheit).

Doing the math we get that it expands about 2.1 centimeters. This may not seem like much, but if there was no room to expand this could cause a lot of problems! Its also good to keep in mind that sidewalks get much hotter due to direct sunlight and heat absorption, which I may cover in the future. 

If you're curious, here is a chart with a few commonly used coefficients. It's also important to keep in mind that this happens in all directions, so while the sidewalk is getting longer its also getting thicker and wider. There is a similar equation used for volumes, with a different set of coefficients referred to as beta, which is actually 3 times alpha. (Should make sense if you think about it). 

You can imagine how important it is to take this into account when designing buildings and bridges, and even very small circuits and coils!

Sorry for such a short and simple one, quite busy with summer school. Hopefully the next one will be much more interesting and unique...