Potentially Fascinating

Concrete highways and railway lines. Ever noticed that when a car travels along the former, or a train along the latter, they sound just a little bit similar?

"Bee-dum Bee-dum Bee-dum..."

It is because concrete highways are made of slabs of concrete, and the railway lines, sections of rail.

The reason is simple - seasons! Both are cold in the winter, and warm in the summer.

Heat makes things expand, and if those structures were continuous, the concrete would crack, and the rails buckle.

So the engineers put bitumen between the concrete slabs, and air gaps between the rails, to take the strain, so to speak.

The sound

"Bee-dum Bee-dum Bee-dum..."

Is due to the Doppler effect, which is the same effect you hear as police sirens go past - the pitch sounds lower, but in this case, it is the front wheels versus the back wheels of the vehicle. It is more pronounced for cars as the two pairs are further apart, and the "dum" bit is distinctly behind.

So, when things heat up, they get larger.

They expand.

BUT we don't want to give you that! Since this blog is officially in second gear, there is a need for further thought - the question of WHY this happens.

It is really quite simple.

It is called the "Lennard-Jones 6-12 Potential".

It is an empirical formula (that is, it is based on observation rather than any theory) but it fits the data rather well.

It's proper form is:



Which can be reduced to:



The "r" is the distance between atoms next to each other, and "V" is the amount of energy they have when added together. "A" and "B" are just numbers.

The comparison between this equation and real life can be seen here:



...which is pretty good.

Back to the question: WHY do substances expand when heated?

It is a question of energy. If you heat something up, you give them energy, and if the thing is jiggling, it will jiggle more if it has more energy. There is a related phenomenon called Simple Harmonic Motion, which is illustrated here:



The only difference, for the purposes of this post, between SHM and the Lennard-Jones is that the former is symmetrical, the latter is not. If you twang the ruler further, it will jiggle further from the center, but will always have the same centre. The ruler stays and bounces back and forth across where it normally wants to be. As does the weight, the spring, and the pendulum. Graphically, the energy (or "potential") will look like this:



which is symmetrical, as can be seen by the vertical line. The line is vertical because the ruler, etc still goes back and forth around the same centre point.

Now take another look at the Lennard-Jones graph. It has a similar shape, but if you try to draw a "symmetry" line, it will bend off the vertical to the right. If the central point of the jiggling gets further away from zero, it gets larger, and what we see is that the two atoms actually increase their separation.

The English words for this are "the substance expands".

Told you it was simple.

However, what's the deal with water? If you cool water so that it freezes, what happens? Ice floats and glass bottles shatter BECAUSE - water expands on going from water to ice - the complete opposite!!

Watch this space.