Tag Archives: scale

Fun Science: Vacuum and Pressure

Pressure is caused by collisions between particles. Scientists use the term “vacuum” when there are few particles, and thus few collisions. Air in our atmosphere is dense with particles; atmospheric pressure is very high compared to lab vacuum or the vacuum of space. Scientists use vacuum in many ways. Vacuums were used in lightbulbs and vacuum tubes (such as the old CRT or cathode ray tubes of old TVs and computers). Vacuums are used for depositing materials in clean environments, such as on silicon wafers for microcircuitry. Vacuums are used for separating liquids that have different evaporation points. In scientific labs, we can produce pressures billions of times lower than atmospheric pressure, but the pressure in space is still lower.

Atmospheric pressure: Every cubic centimeter (also called a milliliter) of air contains 2.5 x 1019  air molecules. That’s 25,000,000 trillion molecules, where the US debt is roughly $12 trillion, and a terabyte (TB) hard-drive holds a trillion bytes of information. That is a lot of particles causing a lot of collisions. The average particle travels only 66 nanometers before colliding with another particle. That’s only about 200 times the size of a nitrogen molecule.

On top of Mount Everest: Pressure is roughly 1/3 of the pressure at sea level, and there are 8 x 1018 molecules of air per cubic centimeter. The average particle travels 280 nm before colliding with another particle.

Incandescent light bulb: The pressure inside a lightbulb is 1 to 10 Pascals (pressure at sea level is 100,000 Pascals). There are still about 1014 molecules/cm3, or 100 trillion molecules. The average particle travels a mm to a cm before a collision. This pressure is too low for plants or animals to survive.

Ultra high lab vacuum: The most sophisticated lab vacuum equipment can produce pressures of 10-7 to 10-9 Pascals, yielding about 10,000,000 to 100,000 molecules/cm3, respectively. Particles travel an average distance of 100 to 10,000 km before colliding with another particle. Such extreme vacuums require highly specialized equipment, including specialized pumps and chambers. Only certain materials can be used; paint, many plastics and certain metals can release gases at very low pressures, making them unsuitable.

Space vacuum: The vacuum of space depends on what part of space you mean. The pressure on the moon is 10-9 Pa, or roughly our highest lab vacuum, with 400,000 particles/cm3. The pressure in interplanetary space (within the solar system) is lower yet, with only about 11 particles/cm3. It is estimated that there is only about 1 particle per meter cubed in the space between galaxies. Still, some microorganisms have survived exposures of days to space vacuum by forming a protective glass around themselves.

Going the other way, there are pressures much higher than the pressure of our atmosphere.

At the bottom of the Mariana trench: Pressure is about 1.1 x 108 Pa, or about 1100 atmospheres. A variety of life has been observed in the Mariana trench.

At the center of the sun: Pressure is about 2.5 x 1016 Pa, or 2.5 x 1011 atmospheres, or about 100,000 times the pressure at the core of the earth. This pressure is sufficient to fuel the fusion process of the sun, where hydrogen is combined to form helium.

At the center of a neutron star: Pressure is about 1034 Pa, or 1018 times the pressure at the center of the sun. Here, pressure is so high that normal atoms with electrons around a core of protons and neutrons cannot exists. Nuclei cannot exist in the core of a neutron star.

Read about other science topics on my fun science page.

Fun Science: Astronomical

I first became interested in science when my brother told me there was a black hole under his bed (this was a ploy to prevent me from snooping there– this is how nerd children fight). Once I could read, I wanted to know if this could be possible; one should be skeptical of information provided by siblings. Frustratingly, none of the books I read discussed if an event horizon could be put under a bed. Pretty shoddy science. There was much discussion of micro-blackholes, with some description of their size. But what the heck was a nanometer? Bigger or smaller than a bed?

Even now, the scales of the universe boggle my mind. A human is so small. The diameter of the Earth (a small planet), is roughly 7 million times the height of a typical person. If you lined up every person in the state of Virginia head to toe, you would roughly approximate the Earth’s diameter. The diameter of the Sun is 100 times bigger (two orders of magnitude) than the Earth. If you lined up every person in the United States head to toe, you’d only get to half of the Sun’s diameter. The red giant Betelgeuse (the reddish star that is Orion’s left shoulder) is 700 times bigger than the sun.

The solar system is bigger yet–Neptune is 30 times as far from the Sun as Earth, at about 3200 times the radius of the Sun. It takes light 4 hours to reach Neptune. The Oort cloud, the farthest reach of our solar system and the hypothesized source of most comets, is a light year from the Sun.

From Wikipedia

Our solar system sits on one branch of the Milky Way, which is a galaxy 100,000 light years across (7×1011 times the diameter of the Sun–a meter is roughly 1012 times as big as a hydrogen atom). Our galaxy is 2.5 million light years from the nearest galaxy, Andromeda. Our galaxy is one of more than 50 galaxies in the Local Group. This piece of the universe is about 10 million light years in size. Wikipedia suggests there may be 100 billion galaxies in the universe. We have observed as far as 47 billion light years away, but the universe might be bigger (more intimidating statistics here).

And all of these things are slowly interacting. With all that, how could we not write science fiction?

Fractals in Life: photos

Fractals are a branch of math that better describes nature. Before fractals, there was Euclidean geometry, the geometry of lines, planes, and spaces. Euclidean geometry cannot give the length of a rough coastline; neither can it give the surface area of shaggy tree bark. The answer you arrive at in Euclidean geometry depends upon the scale at which you examine an object– intuitively the distance an ant travels over rough terrain is different from the distance we cover walking. The ant interacts with the terrain at a different length scale than we do. Fractal geometry is designed to handle objects with multiple meaningful length scales.

Fractal objects are sometimes called “scale-free“. This means that the object looks roughly the same even if examined at very different zooms. Many natural objects look similar at multiple zooms. Below, I include a few. The craters on the moon are scale-free. If you keep zooming in, you could not tell the scale of the image.

frac (1)

Terrain is often scale-free in appearance– a few years ago there was a joke photo with a penny for scale. The owners of the photo subsequently revealed that the “penny” was actually 3 feet across. I couldn’t find the photo, but you cannot tell the difference. The reveal was startling. Below is a picture of Mount St Helens. The top of this mountain is five miles (3.2ish km) away. Streams carry silt away from the mountain, as you can see more towards the foreground. They look like tiny streams. These are full-sized rivers. Mount St. Helens lacks much of the vegetation and features we would usually use to determine scale. The result is amazingly disorienting, and demonstrates scale invariance.


Plants are often scale free too. Small branches are very similar in appearance to large branches. Ferns look very fractal. Below is a picture of Huperzia phlegmaria. Each time this plant branches, there are exactly two branches. Along its length, it branches many times. It is a physical realization of a binary tree.


For more about fractals, read my posts about fractal measurement and the mandelbrot set.