## How long can we survive in a sealed enclosure?

 B. Geerts 12/'97

The average concentration of oxygen in the atmosphere is 21.0% by volume, but in polluted environments it may be lower. The US Occupational Safety and Health Administration has adopted a lower acceptable limit of oxygen in the workplace of 19.5%. At 12% a loss of consciousness is likely, although people with medical conditions may lose consciousness at 15% or even more.

Question: How long can 10 healthy adult people survive in a sealed room of dimensions 3m x 4m x 2.5m before they run out of oxygen (i.e. the oxygen concentration drops to 12%)? An adult of average weight consumes about 3.33 10-6 m3 s-1 of oxygen while at rest. The typical volume of an adult is 0.1 m3.

Answer: The equation for rate of change of oxygen concentration in an enclosure without oxygen replacement (neglecting the buildup of carbon dioxide) is:

(total oxygen consumption rate) = (volume of oxygen consumed) / (total time lapsed)

or

nC = {Vr - nVp}{Li - Lf}/t

Where:

t = time lapsed from initial time to time of loss of consciousness (s)

Vr = volume of enclosure (m3)

Vp = volume of a person (about 0.1 m3)

Li = initial oxygen concentration (21% or 0.21)

Lf = final oxygen concentration (12% or 0.12)

n = number of people in enclosure

C = per capita rate of oxygen consumption (3.33 10-6 m3 s-1)

Therefore:

t = {Vr - nVp}{Li - Lf} / nC

Now plug in the numbers:

t = (30-1)(0.21-0.12)/( 3.33 10-5) s = 7.8 104 s

So the people are likely to have suffocated after 7.8 104 s or 21 hours and 47 min. In reality this period may be shorter, because people exert more energy and (demand more oxygen) when the CO2 content of the air increases, because they need to breathe more heavily. Also if there is any panic.