How do I solve this?
The usual partial pressure of oxygen that people get at sea level is .20 atm, that is, a fifth of the usual sea level air pressure. People used to 1 atm air pressure begin to become light headed at about .10 atm oxygen. As a rule of thumb, the air pressure decreases one inch of mercury each thousand feet of altitude above seal level. At what altitude should airplane cabins be pressurized? Up to about what altitude should you be able to use unpressurized pure oxygen? (Express your answer in feet above Mean Sea Level, or MSL.)
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If passengers are ok at 0.2 atm oxygen (1 atm normal pressure) and light headed at 0.1 atm oxygen (0.5 atm air pressure) then cabin pressure must not be as low as 0.5 atm total pressure. I assume that means cabin pressures could be as low as say 0.7 or 0.8 atm and passengers would feel ok. If we take 0.75 as a good guess, then 0.75 x 760 mm Hg = 570 mm and the difference is 760-570 = 190 mm. If the pressure decreases 1 inch for each 1000 feet, that is 25.4 mm/1000 ft. Therefore, 190 mm/25.4 mm = about 7.5 or 7,500 feet. Thus cabins should be pressurized in the neighborhood of 7,500 feet. I flew a small (single engine--two seat) private plane for several years at altitudes of 5,000 and 6,000 feet and they were not pressurized, and it didn't affect be a bit--a bit--a bit -- a bit. :-).
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