Friday, March 30, 2007

Hot Air Rises

In order to continue explaining air masses I must first explain density and pressure. Density is a measurement of how close together the air molecules are, or, put another way, a measure of what weight of air exists in any given volume. More weight per volume is the same thing as higher density.

If you pack socks into a box there are two ways to maximize the sock density. One is to use thin, non-fluffy socks and the other is to cram your socks in as hard as you can, stomping on them to get them to fit before you seal the box. (You know I just moved house, right?) These two factors are the same as the ones that affect air density.

'Fluffiness' of the air corresponds of temperature. The higher the temperature, the greater the volume the air wants to occupy. It's actually because the speed of the air molecules is greater at high temperature, but you can think of the volume they thus occupy as them being all fluffed up hot out of the tumble drier. All else being equal, warm air occupies more volume than the same weight of cold air. Therefore, all else being equal, an equivalent volume of cold air weighs more than warm air.

Stomping on the pile of socks corresponds to pressure. Is pressure, really. Pressure is defined as force per unit area, and in the atmosphere it is a result of all the air stacked up on top of the bit of air you're considering. Imagine you're looking at a cubic litre of air(*). Its pressure is equivalent to the weight of all the ten by ten by ten cubes of air that are stacked on top of it, all the way up to the top of the atmosphere. Sure, one little cube of air doesn't weigh much, but stack enough up and it adds up. So air down near the bottom of the atmosphere is at a higher pressure than air further up in the atmosphere, where it has fewer boxes stacked on top of it. Kind of like the box of drinking glasses underneath four boxes of aviation textbooks is under more pressure than the one that is ony one box into a pile.

You can see pressure and temperature kind of work against one another with respect to density. If the pressure increases and the temperture stays the same, the density will increase. If the temperature increases and the pressure stays the same, the density will decrease. Cold air at a high altitude is less dense than warm air at a low altitude, because the effect of the low pressure at high altitude more than balances the effect of the temperature difference. There's even a formula:
  P x V = T x constant
P = pressure, T = temperature, V = volume.

So, we have a bunch of air hanging about. Air in the same vicinity within the same air mass is pretty much interchangeable. It's all mostly nitrogen, and contains some amount of moisture, and at the same pressure because its under the same pile of air. And its at the same temperature. If some of it were to be heated up to be warmer than the surrounding air, look at what would happen. Firstly, it doesn't warm the air around it. If air were good at sharing its heat with the molecules around it, down-filled parkas wouldn't be such treasured possessions in the north. (The puffy feathers create little air pockets and heat doesn't travel well through air, so that keeps me warm.) If a little bit of air is warmer than the air around it then it is also less dense than the air around it. And that means that the gravitational force holding it down isn't as great as the pressure differential between the air above it and the air below it, so it is pushed up, and rises.

And yes, I did just spend six paragraphs explaining that hot air rises. Just think of it as a demonstration of hot air. The reason I did it that way is that warm air doesn't always rise. If that were true it would be warmer at the tops of mountains than at the bottom. Air rises if it is less dense than the air around it. If the pressure is the same, then temperature determines density. So it rises if it is warmer than the air around it, sinks if it is colder than the air around it, and stays in the same place if it is the same temperature as the air around it.

There's one further trick to the rising air, as it rises, the pressure around it decreases, so according to the formula, if the temperature stays the same, the volume has to increase. And it does. The rising air expands. It actually also cools as it expands, so the result is that the same air occupies a greater volume at a lower pressure and temperature.

What it does next is for next time this multi-threaded blog returns to weather theory.

(*)If you didn't go to elementary school in Canada after metrification you missed out on carefully measuring ten centimetres by ten centimetres by ten centimetres and building a little cardboard box. That's about four inches cubed, for the aggressively non-metric. Once you'd built and folded your cardboard cube, and mended any measuring or folding errors with vast quantities of cellophane tape, you had a concrete way to visualize a ten centimetre length, one thousand cubic centimetres, one litre capacity, and, if you imagined what your cube would feel like if it were filled with water, one kilogram. I'm not making this up. They used to hand these things out at fairgrounds, in modern 1970s colours like pink, yellow and lime green. Someone back me up here. I'll trade you a working flashlight for a genuine 1970s MetriCube.


Astroprof said...

Excellent post!
I love it when you talk physics.

Aluwings said...

I don't have one to trade, but apparently we can still order a Metricube here...

ward said...

That's not the right Metricube... the ones we got in grade 6 (uh, let's see, that's about 1975, aaaahhhh I'm old!) were a lot more colourful. I remember lots of red, and a funny slanted M symbol (or maybe I'm getting that mixed up w/ something).

Garrett said...

Its pretty funny that here in the aggressively non-metric US someone decided a tiny subset of the SI system should be taught to us as well in Grade 6, but such a clever little cube was never seen.

As a guy in engineering school where several chip on the shoulder profs DEMAND the most obscure dimensional analyses to be carried out in ridiculous FPS units, I really, really, really wish I could never have to see a slug outside of its proper slimy context again.

nec Timide said...

"the ones we got in grade 6 (uh, let's see, that's about 1975, aaaahhhh I'm old!)"

Hmmm, I must be ready for the old folks home then. No wonder I don't remember the metric cube, grade 6 was already a fading memory in 1975.

Ed said...

Being even pickier than normal: the liter/litre is not technically an SI unit. The litre is a "unit outside the SI which is accepted for use with the SI" as the US government points out:

Units outside the SI

The SI unit of volume is the cubic metre.

And yes, I too wish the US would switch to SI and also that the UK would finish off the job instead of sitting in this horrible in-between state which seems to be the worst of all possible solutions.

Aviatrix said...

Thank you Ward, for confirming the existence of the brightly coloured 1970s MetriCube.

For those of you with no memory of the 1970s, think of the clour schemes you see on C172s that still have original paint. And then imagine that colour without thirty years of exposure to the sun.

Flyboy Chris said...

Great post and great analogy, but there was one term used incorrectly. Now I get to have my (small) physics lesson for the group:

Weight vs Mass.

Aviatrix used the term "weight" incorrectly in this lesson. The proper term is "mass". Here is the difference between them (and my own analogy from 6th Grade [Thanks Mr. Gwynn!]).

I found a nice site that briefly explains the difference and I'm quoting their content verbatim:

To understand the differences we need to compare a few points:

1) Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the pull of gravity on an object.

2) Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter. Weight is measured on a scale.

3) The Mass of an object doesn't change when an object's location changes. Weight, on the otherhand does change with location.

Back to my own writing now...
What they're saying is the doctor measures your mass when they have the scale that they slide the weights around on. On the moon, your weight is 1/6th what it is on the earth, but your mass is constant.

Keep up the very educational and entertaining blogging!

Aviatrix said...

Aviatrix of course learned the difference between mass and weight from her childhood metricube, but uses "weight" the same way your doctor does to colloquially represent mass. There is no change in the value of g in any of the systems I discuss, and to use the word mass in close proximity to the term "air mass" could be confusing. I know that geeks can translate colloquialism-to-geek more readily than non-geeks can do the reverse, and the geeks get to have a nice burst of self-righteousness to boot. Everyone wins.