Discuss scuba diving and mountain climbing using the gas laws. Compare volume, temperature, and pressure.?

Answer 1

So many ways to go with this - physics, athletics, medicine, technology, etc.

PV=nRT means Volume (V) = a constant/Pressure(P). Double the pressure and you half the volume.

Doubling the pressure in SCUBA means going down 32 feet. Each breath you take down there has twice as much gas in it. Twice the pressure of O2 and N2. More O2 is good (to a limit of about one atmosphere partial pressure*) but more N2 means it dissolves into your blood but can come out solution (painfully and sometimes fatally called "the bends"). That's why SCUBA divers do "decompression" on the way up.

Going down another 32 feet to a depth of 64 feet and you add another atmosphere of pressure (three times the absolute pressure).

*Below 100-foot depth or so, the increased pressure of oxygen actually becomes toxic and SCUBA divers used gas mixtures with less oxygen in them.

Halving the pressure, doubles the volume. For mountain climbers and pilots, that happens at 18,000 feet of elevation. Other datapoints that stuck in my head include:

14,495' on top of Mt Whitney, CA = 58% sea level pressure.
20,320' on top of Denali ("Mt McKinley") = 45%
29,028' on top of Everest = 33%.

People have survived (heck, climbed) at 29,000' but there's no permanent habitation about 18,000-18,500' because there's not enough partial pressure of oxygen for our bodies to growth and heal.

Pilot are required to use supplemental oxygen above 12,000' in an unpressurized plane, which seems very low to a mountaineer. But pilots are sea level creatures momentarily at alititude and they really need their wits about them.

As gases expand, they get cooler. "Adiabatic expansion" means the volume gets bigger without heat being added or subtracted to the volume. Air pushed up 1000 feet will cool 3.5F or 2C. If it is 70F at the beach, it will be 35F at 10,000 on a nearby mountain. Hence it can be raining and 50F in the flats during the same storm that dumps snow in the mountains.

Hope that helps. I could prattle on about other aspects of diving/mountaineering, etc but I'm not sure which direction you are going with it.

Some things to google:
SCUBA decompression
SCUBA oxygen toxicity
Mountaineering HAPE
Mountaineering HACE
supplemental oxygen pilot
adiabatic expansion weather