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Hi Stephen

Sorry to eat into your time, but I *think* I have the answer to my CO2 question. I calculated it in 1% increments, starting at the previous base and adjusting breathing changes at the appropriate points in the formula (3% and 5%).

I know this is very approximate and subject to a lot of different variables in the two people, but can you let me know if the below looks correct in terms of how it would play out, moving from 0.4% to 7% in 1% increments?

Approximate time to reach 1% Carbon Dioxide from 0.4% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.588 Hours  (35 minutes)
(2)  x  (1.7)          3.4

Approximate time to reach 2% Carbon Dioxide from 1% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.588 Hours  (35 minutes)
(2)  x  (1.7)          3.4

Approximate time to reach 3% Carbon Dioxide from 2% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.588 Hours  (35 minutes)
(2)  x  (1.7)          3.4

Approximate time to reach 4% Carbon Dioxide from 3% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.294 Hours  (17 minutes)
(2)  x  (3.4)          6.8

Approximate time to reach 5% Carbon Dioxide from 4% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.294 Hours  (17 minutes)
(2)  x  (3.4)          6.8

Approximate time to reach 6% Carbon Dioxide from 5% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.147 Hours  (8 minutes)
(2)  x  (6.8)          13.6

Approximate time to reach 7% Carbon Dioxide from 6% base

(200)  x  (.01)          2
T=    ———————    =    ——    =   0.147 Hours  (8 minutes)
(2)  x  (6.8)          13.6

TOTAL:    Approximately 2 Hours 35 Minutes    (155 minutes)

If this were Mythbusters, I'd be aiming for at least a 'Plausible', so I'm trying to make the piece more science than fiction.

Also, you mentioned that Nitrogen would play no part in the scenario? So, any percentage of CO2 would deduct from the total percentage of O2 only? Nitrogen would remain at approximately 78% (780,000 ppm) the whole time?

The vessel itself is a personal submersible at surface pressure (14.7 PSI) with a failed life support system, if the context makes any difference.

I really do appreciate your help a great deal.

Kind Regards

Pete

Not quite.  The first equation would use 0.006 instead of 0.01 for your "base" of 0.004 CO2 concentration.  So that number is off.  IF you want to account for that, just plug in the equation using 0.066 instead of doing these 1% advancements.  I also have no idea why you suddenly had them expelling double, and then quadruple the volume of CO2 every two time steps, that makes no sense.  From looking around, it also seems to me that 5% (therefore using 0.046 as your number up top) is really the toxic limit that would put people down with exposure on the time scale of hours...so I'd use that.  Gives you 2.7 hours to reach 5%.

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#### Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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