minimum size breathing hole

Factual Questions
1

Let’s say we put a human in a perfectly sealed box. The box is large enough that he cannot create any significant air currents. What is the minimum size hole we need to cut in the wall for enough molecular oxygen to diffuse into the box for our subject to survive indefinitely? Assume normal atmospheric conditions outside the box.
(Yes, I admit I’m planning on the live capture and transport of a human to Omicron Persei VIII for the new Earth Zone™ exhibit at the Imperial Zoo.)

2

Shh! Don’t give away the plan.

3

The more I think about it, the more interesting this question gets. Several points to consider:

  1. For every liter of O2 consumed, somewhere between 0.7 and 1.0 liter of CO2 is produced, depending on diet and metabolic activity. The ratio of CO2:O2 is the ‘respiratory quotient’.

  2. The carbon dioxide level in fresh air ranges from 0.03% to 0.06% by volume. Exhaled breath has a CO2 level of about 5%. Inhaling CO2 at concentrations above 5% is immediately dangerous, and OSHA limits longer-term levels to 0.5%, although many people develop symptoms such as headache above 0.1%.

  3. Room air has an abundance of oxygen, and if it weren’t for the CO2 buildup you could rebreathe the same air many times before you had any problems with hypoxia. So the limiting step here is going to be the carbon dioxide buildup, not the oxygen consumption.

  4. The normal VCO2, or CO2 production rate, is 90-130 ml/min/m2. So, given an ‘average’ human with a body surface area of 1.7 m2, you get 153 to 221 ml of CO2 produced per minute.

Let’s assume that you want the dude in the box to be relatively comfortable, not hovering on the brink of consciousness. So you don’t want the CO2 level inside the box to go above 0.5%. So, we can define some values: CO2 inside box at 0.5% (partial pressure ~3.8 mm Hg); outside box at 0.03% (partial pressure ~0.3 mm Hg), and total CO2 flux must be about 200 ml/min, or about 0.008 mol/min. Molecular weight of CO2 is 44 g/mol. Assume that the concentrations are steady-state.

I don’t know how to make the final calculation, though.