Physics Question Time!

[penk]

So I'm running a dehumidifier in my basement due to the ridiculous humidity levels in the last week or so. In an hour of running, it extracted about a half gallon of water from the air.

Which got me thinking.

Given:
1) Basement air volume of approximately 4500 cubic feet (20x30 basement with an 7.5' ceiling)
2) A relative humidity of between 50 and 60% (based on current forecasts. It's occasonally spiking up to 80%)
3) Ambient temperature at the start of this process at 84 degrees fahrenheit. Current indoor temperature is 76 degrees.

How much water is actually IN the air now?

If I cool down to 72 degrees, how much water will be extracted - ie, how often do I have to change the tank out?

I've been S'ingTFW, and have gotten a lot of physics chattering, but haven't been able to suss out the actual values.

Any ideas?

Comments

[dsrtao]

http://www.engineeringtoolbox.com/moisture-holding-capacity-air-d_281.html

Find the two points on the graph, do the subtraction, then the multiplication.

[dancingwolfgrrl.livejournal.com]

Search term fail! Here's an approximation in chart form; in this thread, a guy reverse-engineers the formula.

[randysmith]

I found the graph about half way down on

http://en.wikipedia.org/wiki/Relative_humidity

useful for this issue, at least in concept.

[starphire.livejournal.com]

Are you assuming that the room is sealed from outside air?
I would assume that it isn't, and that there is a constant inflow of more humid air coming into the room while the dehumidifier is working. My experience with portable dehumidifers is that in humid basements in the summertime they are pretty much running flat out all the time, and the extraction rate of water is related to the humidity and temperature of the room. So as the air dries out, it will collect water more slowly, which complicates the answer.

When you say "cool down to 72 degrees", I'm not sure what you mean - that there is a central air conditioner in addition to the dehumidifier? Because the dehumidifier is actually increasing the air temperature, due to the inefficiency of the machine. The cooling coil is very cold, almost freezing, so air that comes in direct contact with it is able to give up almost all of its water. But then the air passes over the other condenser, which is adding heat overall to the air coming into the unit. Overall, you don't notice the increasing temperature because of the improved comfort from the lower humidity.

But assuming for a moment that there is no infiltration from outside the room, then my estimate says you've got about 1.8 kg of water vapor in the air at 76F, 60%RH. Or only about half a gallon of water.

Given that it only took an hour to collect that much water from the air, I would suggest that there is a replenishing source of more humid air and/or a source of water evaporating from the basement walls & floor.

In a real basement, as you remove water vapor from the air the

Cooling the room will automatically increase the RH

[starphire.livejournal.com]

As a related empirical note, I've removed about 2 gallons of water from a portable dehumidifier in about 12 hours of basement usage, day in and day out. Even from smaller spaces than yours.

[penk.livejournal.com]

Thanks for all the answers... here's a few details...

The unit i'm using is a combination AC / dehumidifer. It's venting to the outside now (though it's a craptastic install - it'll be done better shortly). So the temperature change is because it's running as an AC now.

Air infiltration is happening, but not a lot. Super-insulated housing and all that :) but I know the inerface to the outside for the vent is full of holes (I just needed to get things started and cooled- and it's absolutely done that).

Half a gallon sounds about right... the container I've emptied I misjudged... it's probably about 1/3 of a gallon. so I've pulled a half gallon so far in about 6-7 hours. I'm probably down to 40% humidity in here now - it's noticeably dryer.

The goal here is to prevent mustyness/mold int he basement during these days. I think this'll do it.

Thanks :)

[metahacker.livejournal.com]

You'll also pull a lot of humidity out of the walls/floor/etc. to start with. That'll taper off eventually.

[metahacker.livejournal.com]

Others have more complete answers; I just want to use the word "psychrometrics". :)

[keyne.livejournal.com]

Seriously. I thought it was a typo in the first few references, till I went to the Wikipedia page :)

[frobzwiththingz.livejournal.com]

At the humidity level we are currently dealing with, I'd suspect that you can forget about thinking about "how much water is in the air" at all, and assume that your limiting factor is actually "How much heat can the compressor move from the cooling coils". So you need to know how "efficient" the your dehumidifier is, or its COP value; the ration of much heat it moves from the cold side to the hot side, divided by the power input from the AC outlet. The manufacturer may tell you this on the spec sheet of the unit. From there, you use the heat of vaporization of water, 540 cal/g, and directly calculate the amount of condensed water produced per unit time, given the power the unit takes in from the wall.

[antoniseb.livejournal.com]

I get that the air in your basement at 84F can hold 2.6kg of water (100% humidity). At 72F it can hold about 1.8kg.

I suspect that part of the matter of emptying the bucket has to do with new water vapor coming into the basement.

I got this number by saying there were about 5600 molar volumes of air in your 4500 cubic foot basement, and that at 84F, about 2.5% of the molecules can be water, which weighs 18 grams per mole.

[penk.livejournal.com]

That's a great summary, thank you! So a gallon of water is 8-ish lb, or about 3.78 kg, so about a half a gallon in the air itself (assuming a sealed environment).

I'm pulling between a quart and a half gallon out every 4-6 hours now, that's likely coming from wall and other items saturation, as well as leaking air.

Definitely time for the foam expansion stuff, and construction of a better mount for the exhaust.

Thanks again!