RESET Volunteer David McInnis: Lessons From The Atmosphere

From RESET Volunteer David McInnis:

This week’s lesson was about condensation, the atmosphere, and PV=nRT (without the equation).

I started listing the 3 states of matter (yeah, yeah, there’s really 4, let it go) on the board.  I got as far as solid before students started calling out, “liquid”, “gas”.   I was impressed.  So I asked them for examples, and quizzed them on different materials.  Pudding is a stumper.
Next each table grabbed a cup of water and put ice in it, then we talked about condensation a bit.  To keep things simple and clear I kept condensation limited to water in the atmosphere.  After talking we looked at the cups, where water had condensed on the outside of the cup.
No one was impressed!
However, I asked them where the condensation came from.  This puzzled most of them.  Others answered, “from the water” or “from the ice”.  “So the water went through the cup?”, I asked and then explained what had really happened.
We talked about the atmosphere, starting with how thick or high it might be.   I asked if you could breathe in outer space: “Noooo!”, said everyone.  So then, there had to be some height at which we transitioned from atmosphere to no atmosphere.   We talked about Mt. Everestand how even the most fit climbers had trouble breathing at 5 miles above sea level.  So what guesses did they have about the atmosphere’s thickness.
There’s a bit of a problem I glossed over here.  Namely that somewhere around 6 miles up no one would have enough oxygen to survive, but where space starts is a soft number.  For space flight, 60 miles is considered to be the point where you would become an astronaut.  For most orbital analyses 100 miles is considered a minimal orbit.   For easy math I went with 100 miles,  I should have gone with 10.
Physicist routinely use simple approximations to examine possibilities and provide quick insight to how things work.  Usually this is called order of magnitude approximations or back of the envelope calculations.  It’s an extremely valuable thing to learn, especially for checking to see if your answers or ideas are in the ball park.
We talked about the size of Earth, which required a small detour into circumference and diameter.  I claimed that it’s 24,000 miles to go all the way around Earth and its diameter is 8000 miles…   close enough.  Then I tried, with questionable success, to explain idea of not being too accurate, of making a quick approximation.  I grabbed a 14″ globe and claimed it was 8″ in diameter.   Holding up a 12″ ruler I asked if this was accurate or a rough approximation…  they stumbled for a sec, but then got it.   Annnndd I introduced the concept of ratios (they did know about fractions).
Phew!  At this point I had knew I was really pushing how much material we could cover, but surprisingly there weren’t any squirmers or any acting out.  They seemed both intrigued and straining to grasp what all was going on.
With ratios in their heads I said we wanted to figured out, roughly how thick the atmosphere would be on the globe.  Guesses generally ranged between 2 to 4 inches.
So Earth is 8000 miles in diameter and the globe was 8″ in diameter.  Our guess at the atmosphere’s thickness was 100 miles.  So how thick was it on the globe?
I started with the ratios and Ms. Haynes jumped in.  It turned out that this coincided with their current math lessons perfectly.  They came up with 1/10 inch.    I found a piece of cereal box and draped it on the globe.  The atmosphere is a lot thinner than most people imagine.
Mostly as a quick fun point we then did a demo showing that air pressure works in all directions.  Over a bucket, students took a mostly full cup of water and placed a piece of paper over the top.  They quickly  inverted the cup while holding the paper in place and then ‘released’ the paper once upside down.  The paper stays in place and the water (mostly) doesn’t spill.
If you try this note that it’s a huge hit on the fun-meter.  Every student will have to try it.  Warning: you will need some large sponges to clean up spilled water.  Also, they will try to use completely soaked paper, so tell them 1 paper per try.  We used small disposable plastic or waxed cups.
After cleaning up I took an empty 2 liter soda bottle and put an empty balloon on it.  The classroom had a sink, so I ran hot water over the bottle, explaining that this would heat the air inside.   The balloon inflates (modestly).
Shocking to me, the students were thrilled by this.
So I asked, what would happen if I then ran cold water over the bottle?
“It’ll shrink” and “the balloon will get sucked into the bottle” were common answers.    ‘Nice!”, I thought.
For the last experiment…  and I can’t believe we got through all of this in an hour!    … we made clouds.   An empty 2 liter bottle with a little  (~1 cup) of hot-ish water gets pumped by a bicycle pump with a ball needle poked through a wine cork on it.   When the pressure builds up a bit the cork pops out, with a bang, and the rapid decompression causes water vapor to form in the bottle, like a cloud.  We had 2 sets of equipment.  Three students at a time are needed;  1 to hold the bottle, 1 to pump, and 1 to hold the hose near the pump nozzle.
Beware!  The pop is quite loud and will startle everyone watching, including you, no matter how many times you see it (it’s a timing thing).  I explained and exclaimed repeatedly that there would be a loud boom but it wouldn’t hurt anyone.  The students absolutely love this and everyone wants a turn pumping.  They also forget to look in the bottle for the cloud, or to clear the cloud out before trying again.  Considering how many ideas they were exposed to during this lesson, a little play time was clearly earned.
Lots of excitement, lots of ideas in this one.   :-)

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