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.)
see above.
To solve this problem, we need to use the given information and make some calculations.
First, let's find out at what altitude people start to become light-headed, which is at an oxygen partial pressure of 0.10 atm. We know that the usual partial pressure of oxygen at sea level is 0.20 atm, which is a fifth of the total air pressure at sea level (1 atm), so we can calculate the total air pressure at the point where people start to become light-headed.
1/5 * 1 atm = 0.20 atm
Since people become light-headed at an oxygen partial pressure of 0.10 atm, we can set up the equation:
0.20 atm - 0.10 atm = air pressure at light-headed altitude
Therefore, the air pressure at the altitude where people become light-headed is 0.10 atm.
Next, we can determine the change in air pressure per thousand feet of altitude. The problem states that the air pressure decreases by one inch of mercury for every thousand feet of altitude.
To convert inches of mercury to atmospheres, we can use the conversion factor:
1 inch of mercury = 0.0334211 atm
Therefore, the change in air pressure per thousand feet of altitude is:
0.0334211 atm per thousand feet
Now, we can figure out at what altitude airplane cabins should be pressurized. We want to find the altitude where the air pressure decreases to 0.10 atm, which is the same as the point where people become light-headed.
We know that:
Change in air pressure per thousand feet of altitude = 0.0334211 atm per thousand feet
Atmospheric pressure at light-headed altitude = 0.10 atm
Setting up the equation:
0.0334211 atm per thousand feet * altitude = 0.10 atm
Solving for altitude:
altitude = 0.10 atm / 0.0334211 atm per thousand feet
altitude = 2.985 thousand feet
Therefore, airplane cabins should be pressurized up to an altitude of approximately 2.985 thousand feet above Mean Sea Level (MSL).
Finally, let's determine the maximum altitude where unpressurized pure oxygen can be used. Since the partial pressure of oxygen required to avoid becoming light-headed is 0.10 atm, we can set up the equation:
0.10 atm = (1/5) * total air pressure at altitude X
Solving for the total air pressure at altitude X:
total air pressure at altitude X = 0.10 atm * 5
total air pressure at altitude X = 0.50 atm
To convert from atmospheres to inches of mercury, we can use the conversion factor:
1 atm = 29.9213 inches of mercury
Therefore, the total air pressure at altitude X is:
0.50 atm * 29.9213 inches of mercury per atm = 14.9607 inches of mercury
Since the air pressure decreases by one inch of mercury per thousand feet of altitude, we can determine the maximum altitude where unpressurized pure oxygen can be used by setting up the equation:
14.9607 inches of mercury - 1 inch of mercury per thousand feet * altitude = 0 inches of mercury
Solving for altitude:
1 inch of mercury per thousand feet * altitude = 14.9607 inches of mercury
altitude = 14.9607 thousand feet
Therefore, you should be able to use unpressurized pure oxygen up to approximately 14.9607 thousand feet above Mean Sea Level (MSL).
In summary:
- Airplane cabins should be pressurized up to approximately 2.985 thousand feet above MSL.
- Unpressurized pure oxygen can be used up to approximately 14.9607 thousand feet above MSL.