Maximum amount of water a 40x40x10 sq ft space can hold without it precipitating out?

[astro]

Assume a house is 40 x 40 x 10 feet high or 16,000 cubic feet in size. Under ideal humidity and temperature conditions for air holding water what is the maximum amount of water in gallons a space like that could hold before it began to precipitate out?

I ask because I was doing some washing of large items in the bathtub the day (too large for the washer) and the air had to absorb several gallons in water from the drying articles in the small bathroom space while drying which it did easily. I want to know how much water air can hold in small scale terms like the interior of a house.

[watchwolf49]

I picked up 0.03 ounce per cubic foot in Wikipedia, or about 3-3/4 gallons at 86ºF, for fully saturated air.

[astro]

@watchwolf49

I picked up 0.03 ounce per cubic foot in Wikipedia, or about 3-3/4 gallons at 86ºF, for fully saturated air.

Really? That sounds way lower than what I would have thought.

[watchwolf49]

That’s the static calculation … at any given moment in time … you still have air exchange, motion and condensation all going on as time passes.

[Xema]

@astro

… the air had to absorb several gallons in water from the drying articles in the small bathroom space

This hasn’t much to do with how much water the air within your house can hold. As watchwolf notes, there’s always gas exchange going on between the house and the atmosphere outside.

[Isilder]

@Xema

This hasn’t much to do with how much water the air within your house can hold. As watchwolf notes, there’s always gas exchange going on between the house and the atmosphere outside.

Yes it does, the OP already knows that airing the house with air from outside will change things,

Also if water is precipitating out already then thats not the situation where “maximum” is relevant, the OP asked about the maximum which implies the air started off at 0% humidity and the only source of humidity was the subject source… Well anyway it also calibrates so that he knows that if its 50% relative humidity, then thats about half the max… you see ?

[Chronos]

There is no ideal temperature conditions. The hotter it gets, the more water vapor, without limit. There’s doubtless some practical limitation before we get to that point, but we don’t know what it is: The hottest it gets in your climate at this time of year? The hottest it ever gets anywhere on Earth? The hottest that won’t instantly kill a human, at 100% humidity? Boiling point?

[watchwolf49]

Good points … my answer above is at one atmosphere pressure and 30ºC … and I guess this is less an ideal state and more of a standard state (or close to).

Also true is that at one atmosphere and temperatures above 100ºC, then the amount of water vapor is unlimited, indeed it should be all the water will be in it’s vapor state.

Just wanted to add that at one atmosphere, water decomposes at around 17,000ºC into Hydrogen and Oxygen, though probably a less than ideal temperature for your bathroom.

[core]

This may be a silly question, but why is humid air less dense than dry air? This seems counter intuitive to me.

[am77494]

Think it this way :

Dry Air consists of (rough percentages) 80 % Nitrogen (Molecular Weight 28) and 20% Oxygen (Molecular Weight 32).

Now - take a space that is occupied by 100 molecules of air. The weight of this volume (or in other words density) will be 80x28+20x32 = 2880 units

Now take away 8 of the Nitrogen molecules and 2 of the oxygen molecules and replace them with water. So now you have 72 molecules of Nitrogen, 18 Molecules of Oxygen and 10 molecules of water, total 100 molecules and they require the same volume as before. Since the weight of a water molecule is 18, the new weight now is :

72x28+ 18x32 + 10x18 = 2772 units . See how it weighs less than before ?

[core]

@am77494

total 100 molecules and they require the same volume as before

This was the fact my brain was missing. I did not know that 100 molecules of x always occupy the same volume as y regardless of what they are. That was probably taught to me in junior high school and I forgot… chemistry never was one of my strengths. They give us pilots nifty formulas and rules of thumb without explaining the reasons, and sometimes you find yourself questioning the most basic things when the topic comes up.

[iceiso]

Here’s another way to think of it:

Molecular weight of water vapor, H2O = 18
Molecular weight of dry air (mostly N2) = ~29

As you can see, pure water vapor is the lightest while dry air is the heaviest. If a given volume of water vapor and dry air were competing for space (without mixing), dry air would sink to the bottom and water vapor would rise to the top.

Humid air is just a mixture of dry air and water vapor so its weight would be somewhere between the two.

[am77494]

@core

This was the fact my brain was missing. I did not know that 100 molecules of x always occupy the same volume as y regardless of what they are. That was probably taught to me in junior high school and I forgot… chemistry never was one of my strengths. They give us pilots nifty formulas and rules of thumb without explaining the reasons, and sometimes you find yourself questioning the most basic things when the topic comes up.

Yeah - that’s my gripe too. They do not do a good job teaching chemistry. Anyways, glad it helped.

[Chronos]

If it’s any comfort, it’d be high school chemistry, not junior high.

[LSLGuy]

@core

This was the fact my brain was missing. I did not know that 100 molecules of x always occupy the same volume as y regardless of what they are. That was probably taught to me in junior high school and I forgot… chemistry never was one of my strengths. They give us pilots nifty formulas and rules of thumb without explaining the reasons, and sometimes you find yourself questioning the most basic things when the topic comes up.

@iceiso

Here’s another way to think of it:

Molecular weight of water vapor, H2O = 18
Molecular weight of dry air (mostly N2) = ~29

As you can see, pure water vapor is the lightest while dry air is the heaviest. If a given volume of water vapor and dry air were competing for space (without mixing), dry air would sink to the bottom and water vapor would rise to the top.

Humid air is just a mixture of dry air and water vapor so its weight would be somewhere between the two.

Pilot-relevant tie-in …

The fact water vapor is lighter than air is what drives weather. Clouds, especially convective clouds, couldn’t form & precipitate if water vapor was heavier than air. It’s not the same details as ice floating in liquid water, but it has equally huge impacts on how the ecosphere works.

The confusing thing is when we hear “water vapor” we tend to think “water” as in liquid water. And obviously liquid water is much heavier than gaseous air. But that’s a total red herring.

[watchwolf49]

@LSLGuy

Pilot-relevant tie-in …

The fact water vapor is lighter than air is what drives weather. Clouds, especially convective clouds, couldn’t form & precipitate if water vapor was heavier than air. It’s not the same details as ice floating in liquid water, but it has equally huge impacts on how the ecosphere works.

The confusing thing is when we hear “water vapor” we tend to think “water” as in liquid water. And obviously liquid water is much heavier than gaseous air. But that’s a total red herring.

I’m not so sure about this, generally temperature is considered the driving force in weather … as temperature goes up so does buoyancy, hot air rises … I’m not saying humid air’s lighter density doesn’t help, but the primary mover of the vertical motion is temperature.

The crux of the matter is when the water vapor starts precipitating out of the air. This releases energy of which some is added to the temperature of the air, thus making it more buoyant as it rises. Whereas buoyancy is decreasing as the water bleeds out making the air more dense.

I found this information that presents am77494 posting in some more depth using the Ideal Gas Law.

[Chronos]

It depends on what you mean by “weather”. Temperature differences are key for driving the winds, but without water vapor being lighter than air, we wouldn’t have rain.

[Carl_Pham]

@LSLGuy

Pilot-relevant tie-in …

The fact water vapor is lighter than air is what drives weather. Clouds, especially convective clouds, couldn’t form & precipitate if water vapor was heavier than air. It’s not the same details as ice floating in liquid water, but it has equally huge impacts on how the ecosphere works.

The confusing thing is when we hear “water vapor” we tend to think “water” as in liquid water. And obviously liquid water is much heavier than gaseous air. But that’s a total red herring.

That is not the case. Water vapor, like any gas, has an equilibrium distribution with respect to height under the influence of gravity, at any nonzero temperature. The reason it rises in general is simply that it is removed from high altitudes because the temperature drops below the dew point, it condenses, and falls to Earth as rain or snow. Since the water is continually being removed from high altitudes, it continually diffuses upward from lower altitudes to restore (or attempt to restore) the equilibrium distribution. This would happen even if water molecules were heavier than N2 or O2. I can’t think of any terrestrial example off the top of my head, but you can consider Jupiter, where there is plenty of water, ammonia et cetera clouds and weather, even though the atmosphere is something like 90% hydrogen.

[LSLGuy]

@Chronos

It depends on what you mean by “weather”. Temperature differences are key for driving the winds, but without water vapor being lighter than air, we wouldn’t have rain.

In strict meteorology-speak “weather” means just clouds and precip. All the rest of fronts, temperatures, jet streams, Hadley cells and all the rest are not “weather”.

[Ruken]

@Carl_Pham

That is not the case. Water vapor, like any gas, has an equilibrium distribution with respect to height under the influence of gravity, at any nonzero temperature. The reason it rises in general is simply that it is removed from high altitudes because the temperature drops below the dew point, it condenses, and falls to Earth as rain or snow. Since the water is continually being removed from high altitudes, it continually diffuses upward from lower altitudes to restore (or attempt to restore) the equilibrium distribution. This would happen even if water molecules were heavier than N2 or O2. I can’t think of any terrestrial example off the top of my head, but you can consider Jupiter, where there is plenty of water, ammonia et cetera clouds and weather, even though the atmosphere is something like 90% hydrogen.

This covers diffusion, but wet (or hot) air can lead to convection.