# Thermal Expansion

## Key Questions

• Thermal expansion is basically the spreading out of substances when they get heated. The atoms get "excited" as they gain heat energy, and therefore move away from each other, expanding.

Linear thermal expansion is the same concept, but the expansion makes the item longer- if we want to measure linear expansion, we measure the length by which something has expanded (or retracted) due to gaining (or losing) heat.

For example, lets think about a thin metal rod that has gained a certain amount of energy. It will expand linearly, meaning that the rod will become slightly longer. To calculate the change in the length, we use this equation:

$\Delta L = L \alpha \Delta T$
With $\Delta L$ = Change in length.
$L =$ initial length.
$\alpha$=the coefficient of linear expansion (this is normally given, though if given the value of the other variables, can be found!)
$\Delta T$= Change in temperature

Note that this equation gives the change in linear expansion and not the new length. If the object was expanding, then we add the $\Delta L$ to the initial length $L$

Like all materials, an increase in temperature (average non-translational kinetic energy of the particles) will cause them to increase the average distance between particles.

#### Explanation:

Particles have temporary forces between them due to mutual coulombic repulsion of the electron ‘clouds’ that surround them. As temperature rises the oscillation of the mass (effectively the nucleus) in the system becomes more violent hence occupy a larger effective volume.

So far, so normal, but water is unusual as a liquid because of the polarity (and relatively small size) of the molecule. This means the forces between particles can also include hydrogen bonding (still weak, temporary but a bond with both attractive and repulsive effects.) This means that water’s expansivity is unusually variable with temperature and reaches a minimum not at the freezing point, but at ${4}^{\circ}$C where it is most dense.

This provides some more detail on the data, but the anomalous effects in water are better explained here.

It truly is the weirdest fluid - but the one essential ingredient for life as far as we know.