Understanding Survival in a Sealed Container: A Comprehensive Analysis

To estimate how long a person can survive in a sealed container filled with fresh air, we need to consider several critical factors, including the volume of the container, the volume of air required per person, and the rate of oxygen consumption. This article delves into the calculations and theoretical limits, discussing both oxygen consumption and carbon dioxide buildup as potential limiting factors.

Calculating the Volume and Oxygen Content of the Container

Consider a sealed container with dimensions of 40 feet (length) by 8 feet (width) by 8.5 feet (height). Let's calculate the volume of this container and the amount of oxygen it would contain.

Step 1: Calculate the Volume of the Container

The volume V of the container can be calculated as:

V Length × Width × Height

First, we need to ensure all dimensions are in the same unit. Since the width and height are given in feet, and the length is also given in feet, we can proceed with the calculation in feet:

V 40 ft × 8 ft × 8.5 ft ≈ 2720 ft3

Step 2: Calculate the Amount of Oxygen in the Container

Air is approximately 21% oxygen. Therefore, the volume of oxygen in the container is:

text{Volume of Oxygen} 0.21 × 2720 ft3 ≈ 571.2 ft3

Step 3: Determine the Oxygen Consumption Rate

An average adult at rest consumes approximately 0.5 liters of oxygen per minute. To convert this to cubic feet:

1 liter 0.0353147 cubic feet

Thus, the oxygen consumption rate is:

0.5 liters/minute 0.5 × 0.0353147 cubic feet/minute ≈ 0.01765735 cubic feet/minute

Calculating the Survival Time

With the understanding of oxygen content and consumption, we can now calculate how long the oxygen in the container will last:

text{Time} frac{text{Volume of Oxygen}}{text{Oxygen Consumption Rate}} frac{571.2 ft3}{0.01765735 ft3/minute} ≈ 32300 minutes

text{Time in hours} frac{32300 minutes}{60} ≈ 538.33 hours ≈ 22.4 days

Theoretical Limits and Real-World Factors

While the calculations above provide a theoretical survival time, in practice, other factors like carbon dioxide (CO2) buildup and psychological stress can significantly affect survival. Here's a more detailed analysis:

Factor 1: Carbon Dioxide Buildup

According to additional calculations, the limiting factor in a room would more likely be CO2 or water rather than oxygen, despite a considerable amount of oxygen remaining. An average person breathes around 10 liters (0.353 cubic feet) of air per minute, and exhales approximately 4 liters (0.0141 cubic feet) of CO2 per minute:

CO2 exhale rate 4 liters/minute × 0.0353147 ft3/liter ≈ 0.1412588 cubic feet/minute

Given the air volume of the container (2720 cubic feet), the lethal CO2 concentration is 8%. The lethal CO2 volume can be calculated as:

Lethal CO2 volume 2720 ft3 × 0.08 ≈ 217.6 ft3

At the rate of exhalation, it would take:

text{Time to reach lethal CO2 concentration} frac{217.6 ft3}{0.1412588 ft3/minute} ≈ 15400 minutes ≈ 10 days

Factor 2: Psychological Stress

Psychological stress and the inability to sustain physical and mental functions over prolonged periods also contribute to the overall survival time. In addition to CO2 buildup, factors such as the psychological impact of being trapped and the potential for panic and anxiety can significantly reduce the effective survival time.

Conclusion

In conclusion, an individual could theoretically survive for about 22.4 days in a 48x86 sealed container filled with fresh air, assuming no other factors affect survival like carbon dioxide buildup. However, in a real-world scenario, the survival time would likely be shorter due to CO2 buildup and psychological stress.

Therefore, it is crucial to consider multiple factors when assessing survival in a sealed environment, and the limitations of oxygen and CO2 levels must be carefully monitored.