Back of the napkin calculation of human emmission of CO2 and the toxicity level in contained space over time
Considering covid lockdown has the world quarentined in their houses. Some people who work from home has not left their room for weeks. I’m wondering if your room is air tight, how long can you stay in them till your production of CO2 becomes toxic.
Some reference link
(1) https://www.globe.gov/explore-science/scientists-blog/archived-posts/sciblog/2008/08/11/release-of-carbon-dioxide-by-individual-humans/comment-page-1/index.html
(2) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5380556/
(3) https://en.wikipedia.org/wiki/Density_of_air
First read the first link because most of the numbers comes from there and to understand how some of the figures are calculated.
Assumptions
Assuming my room is 4x3x2 m of volume. That’s 24 square meters Assuming air density of air is 1kg per cubic meter (1)(3)* My room thus has 24kg of air From results of link 1) we produce “0.9 kilograms of carbon dioxide for each day per human” (1) CO2 at levels greater then 5% starts to be toxic to humans (2) Moist air contains 0.038% of CO2 by volume 1)
Calculation
The quesion is how long till the room is at toxic level of CO2, assuming ~5% is toxic level. (2) From link (2), people have different tolorance for CO2 toxicity, but we’ll use 5% for this calculation
Air in my room contains 0.038% of CO2 by volume. By weight it’s 0.0006% grams of CO2 per gram of air. (1)
0.0006*24 = .0144 kg of CO2 per kg of air
If we use 5% toxicity by weight, then 1.2kg of CO2 is at toxic.
24*0.05 = 1.2 kg
Assuming the room is air tight, it’s not, then in 1.317 days the room will be at toxic level of CO2.
(1.2-0.0144)/0.9 = 1.317
If 5% toxiciity is by volume, …
From calories intake perspective, …
This is an aproximation. It’s so I know to open the window every other day as oppose to keeping it close the whole week to keep the moquito out and the heat.
*Density of air is actually 1.225 kg/m3 from wikipedia (3)
(1.2-0.0144)/0.9
1.3173333333333332
cube_meter = 24
((cube_meter*0.05) - (0.0006*cube_meter))/0.9
1.3173333333333335