When you try to leave your room you learn that the only door out is locked. Assuming there is no air flow into the room (air tight with no ventilation system) how long can you survive in the room
(5 meters long, 5 meters wide, 5 meters high)
-Human tidal volume (volume of air that moves in and out of the lungs during normal quiet respiration) is about 500 mL for an adult
-Resting respiratory rate for adults is 12-18 breaths per minute (bpm) under stressful conditions, we would expect to be at the high end of that, so let's use 18 ppm for our problem
-For a human adult breathing normal air, inhaled air is about 20.8% O2
-The density of normal air is about 1.2g/L
an interesting question
will probably make for a lively class discussion
a couple of pertinent facts
... normal exhaled air is about 15% O2
... humans can "survive" in air down to about 6% O2
To calculate how long you can survive in the room, we need to consider the volume of the room, the volume of air you breathe with each breath, the rate at which you breathe, and the percentage of oxygen in the air.
1. Calculate the volume of the room:
The volume of a rectangular room is calculated by multiplying its length, width, and height. In this case, the room is 5 meters long, 5 meters wide, and 5 meters high, so the volume would be 5m x 5m x 5m = 125 cubic meters.
2. Calculate the volume of air you breathe with each breath:
Given that the tidal volume, i.e., the volume of air that moves in and out of the lungs during normal quiet respiration, is about 500 mL, we need to convert it to cubic meters. Since there are 1000 mL in a liter, we divide 500 mL by 1000 to get 0.5 L. Then, since there are 1000 cubic centimeters in a liter, we divide 0.5 L by 1000 to convert it to cubic meters. Therefore, the volume of air you breathe with each breath is 0.0005 cubic meters.
3. Calculate the rate at which you breathe:
The resting respiratory rate for adults is typically between 12-18 breaths per minute. Since we want a conservative estimate, we'll use the higher value of 18 breaths per minute.
4. Calculate the oxygen concentration in the room:
Inhaled air typically contains about 20.8% oxygen (O2).
5. Calculate the total oxygen available in the room:
The density of normal air is about 1.2 g/L. Since there are 1000 L in a cubic meter, the density of normal air is 1.2 g/L * 1000 = 1200 g/m3.
To calculate the total oxygen available in the room, we multiply the volume of the room by the density of air and the oxygen concentration: 125m3 x 1200 g/m3 x 20.8% = 312,000 grams (or 312 kg) of oxygen.
6. Calculate the oxygen consumption rate:
To calculate how long the available oxygen will last, we need to determine how much oxygen you consume per minute. Using the volume of air you breathe with each breath (0.0005 cubic meters) and the breathing rate (18 breaths per minute), the total volume of air you breathe per minute is 0.0005 cubic meters x 18 breaths = 0.009 cubic meters per minute.
Given that the inhaled air contains 20.8% oxygen, you consume 20.8% of 0.009 cubic meters of oxygen per minute.
7. Calculate the survival time:
Now, divide the total oxygen available in the room (312,000 grams) by the oxygen consumption rate per minute (20.8% of 0.009 cubic meters) to get the survival time in minutes: 312,000 grams / (0.208 x 0.009 cubic meters) = 179,961 minutes.
Therefore, you would be able to survive approximately 179,961 minutes in the room, assuming all the conditions and calculations are accurate.
Note: This calculation does not account for potential variation in individual breathing rates due to stress or other factors. It's also important to remember that this is a theoretical calculation and not an actual scenario.