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re: furnace humidifiers; was re: not needed--pyjamas
22 dec 2001

>>it could be interesting to find the relative importance of a short
>>heating cycle in a 10 x 20 x 50 foot uninsulated box...

that's 10k ft^3 of air. 

>what's the equilibrium rh, with 4 humans inside an airtight box with
>a large hole at the top and a 15 minute 10 f cycle and 0% rh outdoors?

outdoor air at 0% rh corresponds to "extremely cold outdoor air."

if the equilibrium indoor humidity ratio is w, and every 15 minutes the
temp rises from 70 to 80 f, and the air expands to 10k(460+80)/(460+70)
= 10,189 ft^3, 189 ft^3 of air flows out, removing 60/15x189x0.075w
= 56.7w pounds per hour of water vapor...

meanwhile, the humans add 16/24h = 0.667 pounds per hour of water vapor.

if the water flow rate into the box equals the flow rate out of the box,
0.667 = 57.6w, so w = 0.0116 pounds of water per pound of dry air, and
pa = 29.921/(1+0.62198/w) = 0.547 "hg, vs 0.748 "hg at 70 f and 100% rh,
so the equilibrium rh is 100(0.547/0.748) = 73%.

but this temp-induced breathing only moves 189/15 = 12.6 cfm vs ashrae's 
60 cfm standard, so it appears we need a few green plants and a small vent
fan, or (more frugally and efficiently) a latent air-air heat exchanger,
eg an interior partition with a reversible fan and lots of tiny wall
crevices in both chambers, vs a big hole in the top of an airtight box. 


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