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How would you convince people that air has volume and that volume can change without mass changing? Because the measurement of volume is taught in the maths curriculum, there are people who think that air doesn’t have volume because it doesn’t have a boundary (no values to substitute into a formula), or that its volume is conserved because its mass is conserved (and also because in 2D, when we cut up a shape, ‘area’ is conserved).
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There are some profound questions in there!
I think volume changing without mass changing is the easier one. You could demonstrate that with a sponge. If the class doesn’t like that because ‘It’s only shrinking because you’re squeezing out all the air’, you could try putting a piece of sponge inside a syringe and blocking up the end of the syringe with hot glue or something.
For the ‘air has volume’ question, a soft drink bottle full of air is not bad. If you have a second, crumpled bottle, half-full of air,you might be able to make some comparisons. I guess you need to make sure your examples involve air that is in a completely sealed container.
I guess you could have a demo with a fishtank full of oil, and two beakers on the bottom. Fill one of them with water – how much water is in that beaker? How much oil is in the other?
I guess the fundamental piece to the puzzle is the gas law PV=nRT. Maybe showing them a gas formula with volume in it will help, even if they don’t need to learn it just yet.
I suspect that every student you have has a different problem, so you’ll probably need several different strategies, but hopefully one or more of these is helpful in some way.
Good luck!
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Simple demonstration of different volumes at different pressures:
Try using a hand pump (you know, the old kind you hold still with your foot while pushing a handle down with both hands) to pump up a car tyre. How much volume is in the cylinder of the pump? What is the change in volume of the car tyre as it is pumped up? (not much!)
The pump cylinder (around one litre?) fills with air at normal atmospheric pressure, which is then squeezed into the tyre whose volume hardly changes.
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