The Magic of Density
Before we get started, we need to agree on a couple bits of background information gleaned from the realm of physics (sorry, but it’s gotta be done).
First, all matter is composed of tiny little particles called atoms, which are in turn composed of even smaller “sub-atomic particles” called protons, neutrons, and electrons. The protons and neutrons are linked together into the “nucleus” of the atom, and are surrounded by a cloud of electrons. When I was in school, they told me that atomic structure resembled a solar system, with the nucleus being the sun and the electrons representing the planets in orbit around it. The relationship between the nucleus and electrons has been found to be more complicated than this, but the solar system model still resonates in my simple brain. (I promise more details on atomic structure in a later post.)
Secondly, there is no such thing as “cold” — there is only heat or the lack thereof. The amount of heat (commonly measured in degrees Fahrenheit or Celsius, or Kelvin for science geeks) is controlled by a thing called “molecular motion,” which is nothing more than a measure of how fast the atom’s electrons are moving.
If the electrons are racing around the nucleus, friction (not to make it any more difficult than it has to be), causes the material to “heat up.” Slow the electrons down, and the atom loses heat. Too simple? Probably, but you can study thermodynamics and quantum mechanics on your own time — this simple explanation is usually good enough for me.
Take water as a familiar example. Add heat — we should actually use the term “energy” here, but heat is what most of us think of when we talk about changing the phase of water — and the electrons start zipping around to the point that the atoms can actually break apart and jump into the atmosphere (we call this new gaseous form of water “vapor,” or “steam”). Take away energy and the molecules lose heat, and can slow to the point that they actually link up in rigid rank and file and turn into a solid (with water, we call the result of this freezing process “ice”). All natural substances work exactly like this. (I also promise more details on phase changes and water in a future post, but this should get us through the next thousand words.)
Simple, huh? On to density…
It’s really quite simple: heavy stuff sinks and light stuff floats. We see this all the time and don’t even think about how fundamental it is, or how such an obvious thing can so directly impact our lives. This familiar ordering is based on a property of matter called density.
We like density for all kinds of good reasons: it’s why the rocks are safely tucked away at the bottom of the river, and why a dollop of whipped cream will float on steaming hot chocolate while you’re curled up on a brisk winter’s evening, all cozy and warm in your favorite chair next to the fire. (Density is also why your feet are still cold, so there’s apparently a downside too.)
Density is easy. Some things seem to weigh more: like iron, or gold in a prospector’s pan. Even a small nugget feels “heavier” than a much larger piece of gravel, and the gold will sink through the overburden and get stuck at the bottom, allowing us to sluice off the “lighter” stuff and find it. The way different elements are put together at the atomic level is the culprit: an equal-sized chunk of gold has more particles packed into it—there’s more stuff and less empty space, so it “weighs” more.
Other forms of matter seem to weigh less, and again it’s a packing thing. They have a looser atomic structure and more open space. This lighter stuff tends to float, like oil on water, water on rock, or a hot air balloon in the atmosphere.
It’s a very specific, mathematically defined relationship: density equals the amount of stuff divided by how big it is. More mass in the same volume increases the density. Less mass and the density will be reduced.
The concept works for all kinds of things: the density of humanity clogging Tokyo is much greater than in the Badlands of the Dakotas, and we all appreciate what this means.
Density equals mass (in grams) divided by volume (in cubic centimeters)
D = m / V
Finally! A formula we can all understand.
Let’s do a short lab exercise: Back in the day, I used to do a great demo in class. I’d place two identical one-quart flasks on the front table: one filled with water (with a density of 1 gr/cm3), and the other (VERY well sealed) filled with exactly the same volume of mercury (at a density of 13.6 gr/cm3).
After giving each student a pair of latex gloves, they’d troop past the table. First, they’d pick up the water (no surprise here — they all could guess how heavy it would feel), and then they’d pick up the mercury. Oh my! The facial expressions when this flask weighed over 13 times more than the water was priceless (at least from this instructor’s point of view). To say they all understood the reality of density by the end of the demo would be an understatement. (Sadly, we stopped doing this demonstration many, many years ago.)
Anyway, gold and gravel are different materials, as are oil and water and rock; variations in density seem inevitable. So far, so good. But what about the hot air balloon? Hot air and cold air are both air—just at a different temperature. Why the difference in density?
Well, the earth usually gets it right, and one of its more clever and useful touches is that it’s possible to change the density of matter by adding or taking away energy. In many cases, this energy is in the form of heat.
Again, it’s pretty simple. Adding energy to the air molecules inside the balloon gets them excited, so they vibrate faster and need extra space. They jostle about and crash into each other like tiny little bumper cars and literally shove excess air molecules out of the balloon to make more room for themselves. It may sound rude, but this is the way nature does it.
But rude or not, the end result is fewer air molecules inside the balloon than in the atmosphere outside the balloon, giving it a lower density.
The balloon goes up…
This relationship between energy and density (hot equals low density, cold equals high) also explains why your feet were chilly, why cold water lives at the bottom of the lake… and why hot magma will rise through relatively cooler surrounding rock to ultimately erupt at the surface in volcanic fury.
Let’s circle back to water one more time. I have little doubt that you have spotted the contradictory relationship here: if losing energy slows the molecules and increases the density, ice should sink. But as we all know (and the Titanic learned the hard way), ice floats. The reason is again locked into water’s atomic structure: just before it freezes, the electrons start to move apart so the resulting solid is actually less dense than the cold water around it. So, like the balloon, it goes up. Water is the only natural substance I know of that does it this way, and it’s probably a good thing — imagine how weird the earth would be if ice sunk, like every other substance.
We’ll build on all of this in some later posts about volcanic activity, igneous rocks, and the internal structure of the earth (don’t be scared — I promise to keep it pretty basic and well within the grasp of even the most ardent science-phobe).
