Calculating the exact time it would take for a person to consume enough oxygen or exhale enough carbon dioxide to make the environment unsuitable for respiration in a sealed room is a complex task that depends on several variables, including the person's metabolic rate, lung capacity, and the initial concentration of oxygen in the room. However, I can provide a rough estimate based on some general assumptions.
1. **Volume of the Room:** The room's volume is 7' x 12' x 7' = 588 cubic feet (assuming you're talking about a room with standard atmospheric pressure and temperature).
2. **Oxygen Consumption:** On average, a person at rest consumes about 250 milliliters (ml) of oxygen per minute. For simplicity, we'll assume this person is at rest.
3. **Carbon Dioxide Production:** A person exhales about 200 ml of carbon dioxide per minute at rest.
4. **Initial Oxygen Concentration:** We'll assume the room starts with a normal atmospheric oxygen concentration of about 21%.
Now, let's calculate how long it would take for a person to deplete the oxygen in the room to a level that becomes dangerous (below 18%) and accumulate enough carbon dioxide to be harmful (above 5%).
- The room volume is 588 cubic feet.
- Initial oxygen volume in the room: 588 cubic feet x 0.21 (21%) = 123.48 cubic feet of oxygen.
Let's calculate the time it takes for the person to consume this initial oxygen volume:
\(Time_{oxygen} = \frac{Initial\;Oxygen\;Volume}{Oxygen\;Consumption\;Rate} = \frac{123.48\;cubic\;feet}{0.25\;cubic\;feet/min} = 493.92\;minutes\)
So, it would take approximately 493.92 minutes or about 8 hours and 14 minutes for a person at rest to consume enough oxygen to lower the oxygen concentration in the room to a potentially dangerous level.
Now, let's calculate how long it takes for the person to produce enough carbon dioxide to reach a potentially harmful concentration:
- Initial carbon dioxide volume in the room: 0 cubic feet (assuming the room starts with no carbon dioxide).
\(Time_{CO2} = \frac{Room\;Volume \times CO2\;Threshold\;Concentration}{CO2\;Production\;Rate}\)
\(Time_{CO2} = \frac{588\;cubic\;feet \times 0.05}{0.2\;cubic\;feet/min} = 147\;minutes\)
It would take approximately 147 minutes or about 2 hours and 27 minutes for a person to produce enough carbon dioxide to reach a potentially harmful concentration.
Therefore, it would take longer for oxygen depletion to become a concern than for carbon dioxide buildup in this scenario. However, please note that these calculations are based on simplified assumptions and actual results could vary significantly depending on many factors, including the person's activity level, health, and the initial room conditions. In reality, oxygen levels below 18% and carbon dioxide levels above 5% are already dangerous and can lead to unconsciousness or death. It's essential to prioritize safety and ensure proper ventilation in enclosed spaces.