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.)
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. :-).
To solve this problem, we need to calculate the altitude at which airplane cabins should be pressurized and the maximum altitude at which unpressurized pure oxygen can be used. Let's break it down step-by-step:
Step 1: Convert the given partial pressure of oxygen to atmospheres.
- The usual partial pressure of oxygen at sea level is 0.20 atm.
- Convert one fifth to a decimal: 1/5 = 0.20 atm.
Step 2: Determine the altitude at which people become light-headed.
- People start to become light-headed at approximately 0.10 atm oxygen pressure.
Step 3: Calculate the decrease in air pressure per thousand feet of altitude.
- The rule of thumb states that air pressure decreases by one inch of mercury per thousand feet of altitude.
- The conversion factor between inches of mercury and atmospheres is 1 atm = 29.92 inches of mercury.
Step 4: Convert inches of mercury per thousand feet to atmospheres per thousand feet.
- 1 inch of mercury per thousand feet = (1/29.92) atmospheres per thousand feet.
Step 5: Determine the altitude at which airplane cabins should be pressurized.
- Set up a proportion to find the altitude:
(0.20 atm - 0.10 atm) / (1/29.92 atm per thousand feet) = (Altitude above sea level - 0 feet) / (1000 feet)
- Simplify the proportion and solve for the altitude.
Step 6: Calculate the maximum altitude for using unpressurized pure oxygen.
- This is the altitude at which the partial pressure of oxygen drops to 0.10 atm.
- Set up a proportion to find the altitude:
(0.20 atm - 0.10 atm) / (1/29.92 atm per thousand feet) = (Altitude above sea level - 0 feet) / (Maximum altitude)
- Simplify the proportion and solve for the maximum altitude.
By following these steps, you will be able to solve the problem and find the altitude at which airplane cabins should be pressurized and the maximum altitude for using unpressurized pure oxygen.
To solve this problem, we need to understand the relationship between altitude, air pressure, and partial pressure of oxygen.
Let's break it down step by step:
Step 1: Determine the altitude at which airplane cabins should be pressurized.
To find the altitude at which airplane cabins should be pressurized, we need to determine the air pressure at which people start to experience light-headedness due to low oxygen levels. We are given that this happens at a partial pressure of oxygen of 0.10 atm.
The air pressure decreases by one inch of mercury per thousand feet of altitude. Since 1 atm is equivalent to approximately 29.92 inches of mercury, we can convert the partial pressure of oxygen to inches of mercury by multiplying it by 29.92.
0.10 atm * 29.92 inHg/atm = 2.992 inHg
So, when the pressure drops to 2.992 inches of mercury, people experience light-headedness.
Now, we need to determine the corresponding altitude. Since the air pressure decreases by one inch of mercury per thousand feet of altitude, we set up the following proportion:
1 inch of mercury / 1000 feet = 2.992 inches of mercury / x feet
Cross-multiplying and solving for x, we get:
x = (2.992 inches of mercury * 1000 feet) / 1 inch of mercury
x ≈ 2992 feet
Therefore, the altitude at which airplane cabins should be pressurized is approximately 2992 feet above Mean Sea Level (MSL).
Step 2: Determine the altitude at which unpressurized pure oxygen can be used.
To determine the altitude up to which unpressurized pure oxygen can be used, we need to find the altitude at which the partial pressure of oxygen drops to 0.20 atm (one-fifth of the usual sea level air pressure).
Using the same method as in step 1, we can set up the following proportion:
1 inch of mercury / 1000 feet = 29.92 inches of mercury / x feet
Cross-multiplying and solving for x, we get:
x = (29.92 inches of mercury * 1000 feet) / 1 inch of mercury
x ≈ 29920 feet
Therefore, up to an altitude of approximately 29920 feet MSL, unpressurized pure oxygen can be used.
In summary:
- Airplane cabins should be pressurized around 2992 feet above MSL.
- Unpressurized pure oxygen can be used up to approximately 29920 feet MSL.