Tuesday, June 18, 2013

Science Clock Series: Part I

For Christmas my parents got me a novelty clock with scientific references for the numbers which I put up in my office. It's a nice clock, although this was the best picture I could get of it:

Now, since there are a lot of different scientific references on this clock I decided to write a mini-series on them, each post focusing on one of the numbers. Although I'm familiar with nearly all of them there are a few that I myself need to look up, so it'll be a learning experience for me as well. I'll be explaining as many of the scientific concepts that come up as I can for those who aren't familiar with them.

Today I'm going to start with number one:

\[\rho\ \text{of}\ \text{H}_2\text{O}\ (\text{g/cm}^3\ \text{at}\ 4^\circ\text{C})\] The Greek lower-case letter \(\rho\) (rho) is traditionally used to represent density in chemistry; H\(_2\)O is water, made up of two hydrogen atoms and one oxygen atom. The g/cm\(^3\) notation means grams per cubic centimeter, so the whole expression means “the density of water in grams per cubic centimeter at four degrees Celsius,” which refers to one.

Why it equals one is rather interesting. Fundamentally it equals one by definition; water is such an important and ubiquitous substance (it makes up 65-70% of the human body, covers 70% of the Earth's surface, etc.) that it was chosen such that the mass of one cubic centimeter of water was equal to one gram (or equivalently one gram of water occupies one cubic centimeter), so that the density of water is exactly one by definition. Thus, you can immediately tell if a substance is more or less dense than water at a glance by seeing whether its density is greater or less than one. If a substance's density is less than water it will float in water; if greater, it will sink. Sodium, for example, has a density of 0.968 g/cm\(^3\), or 96.8% that of water, meaning that sodium will just float on water. (Or at least, it would if it wasn't reacting so incredibly fast with water to produce hydrogen and igniting it in powerful explosions.) Magnesium, with an atomic number merely one higher than sodium, has a density of 1.738 g/cm\(^3\), 70.38% more dense than water, so magnesium would sink in water.

However, there's a wrinkle with this whole scenario that the critically-minded among you may have been wondering about: it turns out that the density of a substance varies with temperature. For most substances, the density decreases as the substance gets hotter, and increases as it gets colder. The reason for this is that greater temperature means greater average energy on the molecular level, which translates into higher average molecular speed, which tends to lead to increased molecular spacing and thus the same amount of mass taking a slightly larger area. Typically the changes in density are fairly small for liquids and solids, larger for gases.

As I mentioned, most substances increase in density as the temperature decreases, and this is mostly true for water; however, it has a slight hiccup as it approaches its freezing point. Rather than decreasing monotonically as the temperature decreases to 0\(^\circ\)C, the density of water reaches a minimum at 4\(^\circ\)C, then begins to increase slightly as it approaches its freezing point.

This behavior is unusual, thought not entirely unique; there are a few other substances that display similar quirks. However, in water's case, this little quirk is quite important for life on Earth. Because of this quirk, ice floats on liquid water, which is highly unusual (most solid substances sink in their liquid forms). Ice is a pretty good insulator, so ice forming on the surface of lakes helps keep the water beneath it from freezing more, leaving liquid regions underneath throughout the winter where fish and other creatures can survive. And when spring comes, the ice floats on the surface of the water where it can be melted by the Sun, rather than sitting out of reach on the bottom of lakes and rivers.

This quirk of density is but one of the many ways water is a very unique substance (one reason it was chosen to define density), but that isn't the focus of this post which is already getting a bit long. Next time we'll take a look at something from nuclear physics! Click here to jump directly to it.

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