AIRport

Here's a completely pointless insight into where my head was a few days ago. I was standing at the airport waiting in the very slow line to check in my bags, and this old guy spent about ten minutes at one of the four counters, moving cloths and items of luggage from one bag to another, trying to get the weights right. I thought to myself; if you've got too much weight old-timer, it doesn't matter where you put it, you're still going to be over-weight and have to pay the excess baggage fee. Then I thought; maybe he's trying to reduce the amount of 'air' in his bag in a misguided attempt to avoid paying for the extra weight that air provided, (so futile did his efforts look to me). Immediately my mind went off on one of its tangents of strange thoughts, which I will try to recreate in this blog:

When I was younger I saw a TV show which proved that air has mass by by the following 'demonstration':

They created a makeshift set of scales and at each end they placed a balloon. They then balanced the scales. Then they inflated one of the balloons, and sure enough, the one with air in it was heavier and tipped the scales.

I suppose then, that to demonstrate that air has mass the test is okay. BUT; does that mean that if you had two empty luggage bags on scales and they were exactly the same except one was full of air, and the other was crushed down with minimal air, the one with air would be heavier?

The answer is no, they would weight the same, the experiment was a better demonstration of elasticity, pressure, buoyancy and weight than it was a demonstration of mass.

The balloon, being elastic, pushes in on the air contained within it. This inward push caused by the elasticity means that the air within the balloon is at a higher pressure than that of the atmosphere around it. The high pressure air inside the balloon wants to push outwards on the interior surface of the balloon until the pressure is the same as the atmosphere, however the elasticity of the balloon (pushing inwards) balances with the pressure inside it (pushing outwards) and prevents this from happening. Balloons burst when the material reaches its elastic limit and the balloon can no longer expand elastically, so the pressure inside it then causes the material to fail, the balloon ruptures and the air rapidly reverts to atmospheric pressure, causing a 'pop' or explosion.

Assuming the air inside the balloon is the same temperature as the atmosphere around it (I will come back to this later), the pressure inside the balloon will be directly proportional to the number of air 'particles' inside the balloon, which move about randomly, colliding with the walls of the balloon, pushing outwards on it, so higher pressure means that there are more air particles inside the balloon than there are in the same volume of air outside, i.e. the air is more dense.

Now we get onto the issue of buoyancy; the basic rule is that every object with volume has a buoyancy force acting on it equal to the weight of the matter (be it air or water) displaced, (that is why you are more buoyant in water, because water is heavier than air, you are displacing more weight and as such are more buoyant. Now, because the balloon has denser air contained within it, it contains more mass, and as such has more weight than the atmospheric air it is displacing. Therefore, the weight force pulling the balloon downwards is now greater than the buoyancy force trying to lift the balloon. This along with the weight of the balloon itself is why balloons inflated with normal air fall to the ground, however they fall quite slowly (because even though it has more weight than buoyancy, the difference is quite small compared to a rock or a person).

In the case in which there are two balloons on scales, one inflated and one deflated, the mass of the balloons cancel out, it is the pressure exerted by the inflated balloon which makes the air within it denser and causes it to tip the scale. So yes, it does demonstrate that air has mass. However, if you were to conduct the same test using plastic shopping bags instead of balloons, with one bag filled with air at atmospheric pressure, and the other crushed down so it contains no air, the scales would still balance because the buoyancy of the air in the inflated bag would be equal to its weight. So the only element that would affect the scales would be the bag itself, which cancels with the crushed bag on the other end of the scales.

So, air has mass, that's true. But at atmospheric pressure, while surrounded with air at the same pressure and temperature, the air does not have a net weight (as it cancels with its buoyancy.)

So in summary, if you're at the airport, trying to crush down your bags so they have less air in them so you're less likely to tip the scales and pay excess baggage, you're wasting your time and perhaps you shouldn't have cut it so close in the first place.

In this example I am completely ignoring things like: The fact that air is warmer when it is exhaled from the body, which would increase pressure for a short period until the temperature normalises, and the fact that exhaled air has less oxygen and more carbon dioxide in it, and as such may be heavier particles, however these are negligible factors which don't have a significant effect on this argument.