Weighing air Etc.
Most recent answer: 10/22/2007
- Savannah (age 11)
Air has weight. If you weigh a vacuum-packed can of nuts (with most of the air removed) then open it so the air can rush in, you can weigh the air that went in. The result might be 0.1 gram or so, depending on the size of the can and how tightly packed it was.
Light also has weight, but very very little. The light in the room I'm in now weighs about 0.00000000000000000001 grams, not enough to notice even with a sensitive scale.
Sometimes we get picky and insist on calling heat 'thermal energy'. Whatever you call it, it also has weight but very little. All the thermal energy in my body accounts for about 0.000001 gram of my weight, not exactly a large percent of it, but big enough that it could be measured with very precise instruments.
One thing to worry about when you're weighing things, either with a scale or a balance, is the buoyant force in the surrounding air. Mike's example of weighing a vacuum can is a good one, since the can displaces the same volume of air when it's open and when it's closed, as long as it holds its shape. Some vacuum packages of nuts are plastic packages, and the plastic is sucked around the nuts -- letting air in increases the volume of the package and also the buoyant force on it, and the net effect may be that you don't see any change in weight. But the evacuated can displaces air and puts vacuum in its place, and when the air comes in, you can think of it either as a reduction in the buoyant force or the addition of the weight of the air.
You can weigh a soccer ball or a football when deflated and when inflated. The same argument holds -- if the pressure in the ball is 1 atmosphere, it should weigh the same as when it is completely flat, due to the change in the buoyant force. But when the air pressure goes over 1 atmosphere, it starts to push down on the scale more.
(published on 10/22/2007)
Follow-Up #1: light weight? heat weight?
- David I Bowling (age 66)
1. You're confusing the rest mass of a photon with the mass which is the source of the gravitational field. If you have a collection of photons traveling equally in all directions, their collective invariant mass is just given by m=E/c2. In other words, there's a mass associated with their energy, and that mass pulls gravitationally on everything else, just the same as any other mass. It is the same as any other weight, unless General Relativity is completely screwed up, which is unlikely. As we said, under ordinary circumstances this light weight is too tiny to matter.
As you say, the force of light pressure (due to its momentum) is not the same as the gravitational effect. It is indirectly connected, since momentum is the first three components of a relativistic 4-vector, and the energy is the fourth component.
2. You may be right that it's impractical to weigh the thermal energy in a human body. Its weight is big enough to measure, but as you say it would be very tricky to measure it against the background of our much larger total weight.
(published on 10/22/2007)
Follow-Up #2: The earth is an oblate spheroid
- Katharine Mullaney (age 13)
Let's hope that perhaps your teacher didn't explain that more carefully to you. The facts are that the shape of the earth has been very carefully measured by orbiting satellites. It turns out to be pretty close to a sphere but slightly flattened at the poles due to the spinning of the earth. This shape is called an oblate spheroid. See for an explanation.
(published on 10/28/2013)