How long does it take to reach harmful CO2 levels in a room?

[Airbreather]

TL;DR Summary

How long it takes to reach from 400 to 1000 ppm in a room?

• I exhale 1 kg of CO2 per 24 hours = 41.67g/h (average)
• Co2 indoors after ventilation = outdoors = 400 ppm (world average)
• Co2 indoors threshold = 1000 ppm (cognitive effect)
• Room volume = 32.5 m³
• Details to neglect: window and door closed tight, no HVAC system or other ventilation.

How long it takes to reach from 400 to 1000 ppm in the room? So I need to ventilate again.

 

[DrClaude]

In the PhysicsForums way of doing things, I will try and guide you to the solution.

• I exhale 1 kg of CO2 per 24 hours = 41.67g/h (average)

How many molecules/moles is that?

• Room volume = 32.5 m³

Setting a temperature, you can use the ideal gas law to convert that to a number of molecules/moles. You can then compare with the number above (we can assume that all that breathing is doing to the air in the room is converting O₂ to CO₂ in a 1:1 ratio).

 

[Baluncore]

How long it takes to reach from 400 to 1000 ppm in the room? So I need to ventilate again.

I guess a small, closed room like that would feel stuffy after about an hour.

 

[Airbreather]

In the PhysicsForums way of doing things, I will try and guide you to the solution.How many molecules/moles is that?Setting a temperature, you can use the ideal gas law to convert that to a number of molecules/moles. You can then compare with the number above (we can assume that all that breathing is doing to the air in the room is converting O₂ to CO₂ in a 1:1 ratio).

41.67g of CO2 = 0.9468410229609557 mol

I added:
• 60pa for pressure
• 20°C for temperature
• molar 44.01 for mass of CO2
to omnicalculator.com/physics/ideal-gas-law and got 0.666698 mol for an amount of substance.

I read it as the room is supposed to be fully filled with CO2 in less than an hour, but It's not as I'm alive.

 

[DrClaude]

41.67g of CO2 = 0.9468410229609557 mol

I added:
• 60pa for pressure
• 20°C for temperature
• molar 44.01 for mass of CO2
to omnicalculator.com/physics/ideal-gas-law and got 0.666698 mol for an amount of substance.

I read it as the room is supposed to be fully filled with CO2 in less than an hour, but It's not as I'm alive.

Atmospheric pressure is 101325 Pa. The room will contain about 1300 moles of gas. Even with these numbers, I get that 1000 ppm of CO₂ will be reached in less than 1 hour. But in anything but a sealed room, air exchange with the outside will be important.

 

[gleem]

A simple calculation. There are 42 kgs of air in a 32.5 cu. m room. if 41.67 gm/hr is introduced to get 1000 ppm by weight it takes one hour.

 

[Vanadium 50]

First, the premise seems odd. There is no ventilation, but there is some air exchange.

Second, you don't know the amount of CO2 you produce to four digits, You just don't.

Third, the more CO2 you have the faster you lose it, So 400 ppm/hour irresepctive of concentrayion is unrealistic.

@DrClaude and @gleem made some good calculations, I do not see the impact of the air exchange.

I have 1300 moles of gas ro start. CO2 is 400ppm or 23g, In an hour, 42g comes in and 23 g leave, dor a net increase of 19g,, So just under 2 hours to hit 1000 ppm.

HOWEVER, if you remove 400 ppm every hour, snd since you start out ar 400 ppm, a more realistic model is that you exchange a volume of air every hour, In that case, you will never hit 1000.

 

[Baluncore]

Details to neglect: window and door closed tight, no HVAC system or other ventilation.

First, the premise seems odd. There is no ventilation, but there is some air exchange.

What is the air exchange you assert, after the room is sealed?

 

[Vanadium 50]

You're right; I misread,

 

[Airbreather]

Atmospheric pressure is 101325 Pa. The room will contain about 1300 moles of gas. Even with these numbers, I get that 1000 ppm of CO₂ will be reached in less than 1 hour. But in anything but a sealed room, air exchange with the outside will be important.

My bad for mistaking Psi with Pa.
So now I know I can't neglect the ventilation. Is there a way to calculate when I'll reach 1000ppm in a room with one closed door and window 61x61 cm. Temperature and pressure outside are the same as in a room.

 

[Drakkith]

My bad for mistaking Psi with Pa.
So now I know I can't neglect the ventilation. Is there a way to calculate when I'll reach 1000ppm in a room with one closed door and window 61x61 cm. Temperature and pressure outside are the same as in a room.

Yes, you'll need to know the rate of diffusion of CO2 between the inside and the outside based on the difference in concentrations, which means you need to know the area the gas can diffuse through between the cracks and gaps in the doors and the windows. And then you need to plug that into a differential equation of some type. Unfortunately I failed that class once before passing it and haven't dealt with different equations since...

 

[jbriggs444]

Yes, you'll need to know the rate of diffusion of CO2 between the inside and the outside based on the difference in concentrations,

It seems unlikely that diffusion will be the dominant transfer mechanism. Convection will likely transport more CO2. But how much convection will there be?

Do we have a temperature gradient to promote a circulation? In at the top of the window and out at the bottom. Or vice versa.

Is the wind blowing, either through a leaky structure or tangentially across the open window?

Is the door opposite the window an interior door (very leaky) or an exterior door with good quality weather seals? What about ducts for heating, cooling and the associated returns?

My expectation would be that an interior room with one open outside-facing window will exchange plenty of air with the outside world except, perhaps, on the calmest of days with a negligible temperature gradient. But I have no real world expertise to back that up.