B Understanding the Science Behind Water Vapor and Cloud Formation

[Edison Bias]

Hi!

I wonder how water vapour can reach the sky while its temperature is far from the boiling point? I have learned that water is lighther than air and this is said to be the reason for water vapour to reach the sky. The trick question is however, how does water become vapour in the first place? I have also learned from Wikipedia that temperature is an average concept. So what we have is an average temperature, meaning some molecules has a higher temperature some a lower temperature.

Considering

E_k=\frac{mv^2}{2}\propto kT

we then have different speeds of the sitting water molecules and some of them actually has a temperature (or speed) higher than the boiling point so things then "dry up" in the sense that water is vaporized. Let't take an example: if the temperature on the ground is 25C, molecules with just twice of that average speed actually get vaporized. I may be far from the truth but what is then the true explanation of water becoming vapour so much that it can rise to the clouds?

Edison

 

[PeroK]

It's evaporation you should read up about, rather than boiling:

https://en.wikipedia.org/wiki/Evaporation

 

[Edison Bias]

That article was just bla, bla, bla like most Wikipedia articles.

If you know something, why not simply tell it?

Edison

 

[davenn]

That article was just bla, bla, bla like most Wikipedia articles.

If you know something, why not simply tell it?

Edison

you would do well to play nice if you expect people to help you !

so what was it about that article that didn't answer you Q on how surface water becomes a vapour ?Dave

 

[ProfuselyQuarky]

Evaporation is all about the energy level of individual molecules--not the average energy level of the entire mass of water. That's why evaporating water turns to vapor slower than boiling water does.

If the Wikipedia article was too hard for you, maybe this is better: http://www.chem4kids.com/files/matter_evap.html

 

[Edison Bias]

Actually, I did not get that far. I read everything in the first pargraph and it kind of confirmed my theory but I am not sure because Wiki-articles tend to have lots of information that really do not explain things in a manner that ordinary people can understand. This is also the reason why I am here, I wish for competent people like you to explain things, that's why it's called a forum, right? And I'm sorry, I really do not think it is a good forum if people just serve links. If I ask a question I expect an answer, wouldn't you? And I do not expect to have to read Wiki-articles of several pages where most of it is academic. I just want a rough explanation.

Edison

 

[ProfuselyQuarky]

Actually, I did not get that far. I read everything in the first pargraph and it kind of confirmed my theory but I am not sure because Wiki-articles tend to have lots of information that really do not explain things in a manner that ordinary people can understand. This is also the reason why I am here, I wish for competent people like you to explain things, that's why it's called a forum, right? And I'm sorry, I really do not think it is a good forum if people just serve links. If I ask a question I expect an answer, wouldn't you? And I do not expect to have to read Wiki-articles of several pages where most of it is academic. I just want a rough explanation.

You're right, a forum is a place to discuss. However, one should always learn to research for oneself and then ask questions after. Why have somebody here answer a question for you here if the question has already been answered elsewhere?

Now, this is a science forum, so back to the science. What else don't you understand, given the links provided?

 

[Edison Bias]

Evaporation is all about the energy level of individual molecules--not the average energy level of the entire mass of water. That's why evaporating water turns to vapor slower than boiling water does.

If the Wikipedia article was too hard for you, maybe this is better: http://www.chem4kids.com/files/matter_evap.html

This was interesting to hear! This is a textbook way of answering a forum question. But does this not confirm "my" theory?

Edison
PS
I have not read the link yet...

And maybe I should explain why I think this a textbook way of answering a forum question. This guy has made a short attempt into explaining things while at the same time supplying a link for further studies. It's the combination of trying to answer AND supplying a link that is A+

 

[ProfuselyQuarky]

This was interesting to hear! This is a textbook way of answering a forum question. Very interesting! But does this not confirm "my" theory?

Let't take an example: if the temperature on the ground is 25C, molecules with just twice of that average speed actually get vaporized. I may be far from the truth but what is then the true explanation of water becoming vapour so much that it can rise to the clouds?

First of all, read the link

Secondly, what exactly is you're "theory"? What theory is there to be had?

 

[micromass]

I wish for competent people like you to explain things, that's why it's called a forum, right? And I'm sorry, I really do not think it is a good forum if people just serve links. If I ask a question I expect an answer, wouldn't you?

The mentality of a science student would not be one where (s)he expects to be spoonfed the answer. It is one where (s)he would be content with a good link to an explanation. (S)he would then read the link and ask further questions if necessary.

If you're going to be lazy, entitled and spoiled, then science is not for you.

 

[ProfuselyQuarky]

This guy

correction: this *girl*

 

[Edison Bias]

Evaporation is all about the energy level of individual molecules--not the average energy level of the entire mass of water. That's why evaporating water turns to vapor slower than boiling water does.

If the Wikipedia article was too hard for you, maybe this is better: http://www.chem4kids.com/files/matter_evap.html

Wikipedia, throw youself into a wall :D

This was about the most simple and interesting link I have ever read, I have even made it a bookmark in my browser because I saw there's more to read.

As I understand it, I am actually right. The only difference is that this link talks about energy instead of kinetic energy or kT and that is actually the same. I have by the way learned that kT is related to kinetic energy in a way that depends on number of freedom degrees (in a gas anyway).

Edison

 

[Edison Bias]

correction: this *girl*

Sorry, how could I know?

A future madame Curie?

Edison

 

[ProfuselyQuarky]

Wikipedia, throw youself into a wall :D

This was about the most simple and interesting link I have ever read, I have even made it a bookmark in my browser because I saw there's more to read.

I read the Wiki article myself and it's very understandable, as well. I don't know how old you are, but if you're old enough to ask the question that you did, you should have been able to understand it, too. The link I gave you is a website meant for children (the word "child" being subjective, I suppose). I'm glad you like the link, but try to make more of an effort to understand articles for more "older" audiences, too.

Cheers,
PQ

 

[Edison Bias]

I read the Wiki article myself and it's very understandable, as well. I don't know how old you are, but if you're old enough to ask the question that you did, you should have been able to understand it, too. The link I gave you is a website meant for children (the word "child" being subjective, I suppose). I'm glad you like the link, but try to make more of an effort to understand articles for more "older" audiences, too.

Cheers,
PQ

So I'm a child it seams :D

Actually, I'm 47 but as you have understood I do not like academic Wiki-links that really do not give me a notch of more understanding other than fancy words. They only consumes time reading and I still think that if there's a simpler way of explaining things in a rough way, why not do so when you are sitting on the knowledge?

But I like and cheerish your answer, thank you very much!

Edison

 

[ProfuselyQuarky]

So I'm a child it seams :D

Actually, I'm 47

I'm sorry! I'm only 15 and I guess I'm just used to the way the adults I know write . . .

 

[Edison Bias]

I'm sorry! I'm only 15 and I guess I'm just used to the way the adults I know write . . .

Fifteen, and knows more about physics than me at 47.

Interesting, to say the least :D

Edison
PS
I hold a Master Degree in Electronic Engineering to make things even more pathetic :D

 

[russ_watters]

I'm sorry! I'm only 15 and I guess I'm just used to the way the adults I know write . . .

Color me impressed.

 

[Ophiolite]

That article was just bla, bla, bla like most Wikipedia articles.

If you know something, why not simply tell it?

In many cases the wikipedia articles are superior to what a forum member could produce in a reasonable time frame. I do agree with you that the combination of a very simple explanation accompanied by one or more references is the preferred route. However, I think the presumption here is that most members will be academically oriented and would be accustomed to studying appropriate material once it had been identified for them. in that regard I was taken aback to learn you have a Masters degree. . . . .and yet you characterise wikipedia articles as being bla, bla, bla. You might want to rethink that approach.

 

[Edison Bias]

Back to science (or at least an attempt into being scientific).

I think that all matter, regardless of state, gets it temperature due to particle speed, right? Both PQ's science article for children and the short Wikipedia article I found tells about vaporization as a consequence of some particles having a higher (kinetic) energy than others. This got me thinking "what is the limit of this Ek deviation?". Suddenly it struck me "Maxwellian distribution" might tell it.

The Maxwellian distribution may be written:

f(v)=e^{-\frac{Ek}{kT}}=e^{-\frac{mv^2/2}{kT}}=e^{-\frac{T_{k}}{T_{av}}}

where the last expression is just me thinking aloud.

For general purposes the expression for v is actually

v=v'-v_0

because we have a distribution of v around a certain vo or average temperature (Tav).

Now, the Maxwelllian distribution (MD) is not just taken from the air. It is a well-known fact that many things follow the natural logarithm (e). One thing is how the voltage of a capacitor decreases with a load of a resistor, another thing is that solutions to many differential equations follow e. So why may not the deviation of Ek to kT follow e?

Just as reference we may state that 1/e=37% and 1/(3e)=5%

If we consider MD and the hypothetical fact that Ek=kT we have that 37% of the particles has a higher Ek (and if Ek=3kT only 5% has a higher Ek).

Considering a "state-jump" from 300K to 400k (the boilingpoint, roughly) this gives a Ek/kT need of 4/3, speed then only need to change sqrt(4/3)=15%

I think I totally understand now :)

I didn't calculate with absolute temperatures (thus needed a factor of 4 times 25C to reach 100C) while going from 300K to 400K is totally different. In other words, the change in Ek need not be so large to give the particles enough "temperature" to vaporize.

A bit shorter than a Wikipedia link, don't you think? :)

Edison

 

[ProfuselyQuarky]

Ah, I got a bit confused when you said "Maxwellian distribution". I know the same thing as "Boltzmann distribution", but it's the same. Glad you got yourself a "eureka" moment, though!

 

[Edison Bias]

May I interpret what you say that I'm at least partly right?

Best Regards, Edison

 

[rootone]

One simple answer that immediately addresses the title question is that air is composed of a number of gases, one of which is water vapour.
At any given temperature there is a maximum amount of water vapour that can be present, warmer air can contain more.
If a mass of air cools it's 'relative humidity' will rise until that maximum is reached.
After that point any further cooling will result in some of the vapour condensing - turning back to the liquid phase of water, thus rain.
If the temperature gets low enough it will turn directly from vapour into ice crystals, so snow instead.

 

[Edison Bias]

I very much appreciate your answer, thanks!

However, it does not help me so much to know how things are, I want to know why it is that way. How water can turn into vapour (below the boiling point) in the first place I however think I understand now, or? Finally, if you feel like it, you may explain "warmer air can contain more" and the concept of humidity. Throw in some formulas while you are at it :)

Edison

 

[rootone]

Water does not need to be boiling for evaporation to occur.
Some of it will vaporise at a lower temperature if the air it exposed to has capacity to absorb it.
Leave a plate of water in a comfortably warm room and it will all evaporate eventually.

Relative humidity as a concept is fairly easy.
It's a percentage scale where 100% means the air is fully saturated and can contain no more water vapour.
Your plate of water will not evaporate if relative humidity of the air is at 100%.
There is a simple instrument called a hygrometer which is used to measure relative humidity.

 

[sophiecentaur]

@Edison Bias If you don't like Wiki, then demand your money back and never darken their door again. Wiki is not compulsory reading and you can always add your views / corrections to articles.

 

[rootone]

If you don't like Wiki ...

Personally I think the mods or whatever they are called at wiki do a pretty good job of running a website in a manner that the internet (well the web bit) was originally intended for.
If I wanted to have a moan I'd nuke farcebook first, then conspiracytoob.

 

[houlahound]

Hardened Steel would have a vapour pressure, everything has a vapour pressure. Seems you are confusing vapour pressure and boiling point causing gas vapours.

 

[sophiecentaur]

To find evidence of that sort of thing, just read about the problems of very high vacuum working. Everything really does evaporate; it's just a matter of how fast.

 

[Khashishi]

At some temperature, some particles will have higher energy and some lower. As you increase the temperature, more molecules will have enough energy to escape the liquid phase and fewer molecules in the gas phase will get captured into the liquid. At any temperature, you can have an equilibrium where as many molecules are escaping the liquid into gas as there are being absorbed by the liquid from the gas. At equilibrium you are at a relative humidity of 100%. Since the temperature and pressure keep changing, the water is generally not in equilibrium. In areas where relative humidity is less than 100% you have evaporation, and in areas where relative humidity is greater than 100% the water vapor will condense into clouds, fog, and dew. Cloud droplets can eventually collect and become heavy enough to fall.

 

[Edison Bias]

@Edison Bias If you don't like Wiki, then demand your money back and never darken their door again. Wiki is not compulsory reading and you can always add your views / corrections to articles.

I have never said I don't like Wiki, I have just said that I do not like when people only supply a link while not even trying to answer my question. Part II of my irritation is that Wikipedia tends to be too detailed in their articles which I think is good if you want to dig deep but to get the often much simpler answer you are searching for, you could actually spend days reading all blue links and this while still not get the answer you want. So if anyone here sits on the knowledge, why make me read for days?

This might seem lazy but as I see it, this is a forum where people discuss things and don't throw books in people's faces.

By the way, I have written over a hundred Wikipedia articles most of them from scratch. I have also written two or even three books on Wikibooks.

Wikipedia is amazing!

Edison

 

[Edison Bias]

Hardened Steel would have a vapour pressure, everything has a vapour pressure. Seems you are confusing vapour pressure and boiling point causing gas vapours.

This amazes me! Do you really mean that Hardened Steel dimnishes in time? I'm sorry for the expression, my english is not so good. I mean that the amount of steel lessens over time due to the fact that it also evaporates? In a tiny way I might understand, due to my earlier calculations i.e that there are kinetic energies exceeding Tav. I'm probably far from understanding because then we also have pressure and what is pressure really? In an ideal gas it is p=nkT or rho*gh but in solids?

Edison

 

[ProfuselyQuarky]

Cloud droplets can eventually collect and become heavy enough to fall.

Dust is also required for rain to fall. Additionally, there was a paper from PRL two years back that said that small vortices within clouds literally spin the saturated dust particles into rain drops. I can't find the original publication, but here's an the story about it:

http://physics.aps.org/story/v7/st14

 

[ProfuselyQuarky]

By the way, I have written over a hundred Wikipedia articles most of them from scratch. I have also written two or even three books on Wikibooks.

You should become a PF Insights writer!

(Also, is your real name "Edison"?)

 

[Khashishi]

Iron and carbon can technically evaporate or sublimate from steel but the rate so slow it might as well not happen.

As an aside, evaporation and condensation occur next to the phase boundary between liquid and gas. Under some conditions the climate is near the phase boundary between solid and vapor, and you get sublimation if the relative humidity is <100% and frost or snow if the relative humidity is >100%.

 

[Edison Bias]

At some temperature, some particles will have higher energy and some lower. As you increase the temperature, more molecules will have enough energy to escape the liquid phase and fewer molecules in the gas phase will get captured into the liquid. At any temperature, you can have an equilibrium where as many molecules are escaping the liquid into gas as there are being absorbed by the liquid from the gas. At equilibrium you are at a relative humidity of 100%. Since the temperature and pressure keep changing, the water is generally not in equilibrium. In areas where relative humidity is less than 100% you have evaporation, and in areas where relative humidity is greater than 100% the water vapor will condense into clouds, fog, and dew. Cloud droplets can eventually collect and become heavy enough to fall.

This is an extremely interesting reply, thanks! Let's think step by step. At Tav there are particles with higher and lower Tk. Increasing temperature Tk(max) gets so high that the particles escapes the liquid phase because Tk is now higher than T(liquid/gas)=Tboil. To me this sounds like what I think I now understand according to my former calculations. It evaporates because Tk>Tboil. I can't understand it in another way. The liquid is of course not boiling but some particles still reaches a temperature that is higher than boiling temperature (Tboil). Then you say that as some escapes the liquid phase, fewer gets recaptured. Why (relative humidity <100%)? Or is it perhaps due to the higher temperature where the matter approaches a gas, so to speak? The equliblium speak is interesting and obviously due to 100% humidity which I think can be called saturation. <100% humidity =evaporation, this I think I understand (room for more water excist in the air). But how can humidity >100%? You must mean that as a figure of speach because at the moment you hit 100% humidity everything must condense, right?

Edison

 

[Khashishi]

Close, but you should refer to the energy of a particle, not the temperature. The temperature refers to the whole distribution of all the energies of all the particles. Some molecules have more energy than the "work function" of the liquid. The work function is the energy it takes to escape the liquid (or solid). It is the work function, not the billing point, which you should be comparing to at the microscopic level. Humidity>100% means the air is supersaturated with vapor and will condense if there are enough nucleation sites. It doesn't immediately condense.

 

[sophiecentaur]

That article was just bla, bla, bla like most Wikipedia articles.

If you know something, why not simply tell it?

Edison

I have never said I don't like Wiki,

Which of your posts am I supposed to take seriously?
You may have committed a Trumpism.

 

[Edison Bias]

Close, but you should refer to the energy of a particle, not the temperature. The temperature refers to the whole distribution of all the energies of all the particles. Some molecules have more energy than the "work function" of the liquid. The work function is the energy it takes to escape the liquid (or solid). It is the work function, not the billing point, which you should be comparing to at the microscopic level. Humidity>100% means the air is supersaturated with vapor and will condense if there are enough nucleation sites. It doesn't immediately condense.

Another extremely interesting reply, thanks! I thought it was easier to see Ek as a temperature but obvioulsy I was wrong. The bold part is especially interesting for my misunderstanding. And I repeat for I find this profoundly educational: The temperature refers to the whole distribution of all the energies of all the particles.

It is also interesting that (I write this just because I love Tex):

n=\int_{-\infty} ^ {\infty} e^{-\frac{mv^2/2}{kT}}dv

Which, according to my Plasma Physics student litterature gives the particle density (note that the Maxwellian distribution came from that same book which I however did not consult, I remembered!).

Anyway, n is here the particle density (not the molar density as in p=nRT).

In my mind today I thought very much about this integral, to me it became known as a way of determining N (not n) and thus the number of particles. But n is almost the same, all you have to consider is that it is N/V and thus of more general use.

I really like the concept of "work function", it especially tells me how thermal emission in a tube is done, that is exceeding the work function by heat.

Finally, please explain the last bald sentence. Especially "nucleation sites" is hard to understand.

Edison

 

[houlahound]

Nucleation sites are typically impurities ie a physical scratch or some fur from string or dust that particles can "meet and chillax" and form an "island" and grow on.

I have used all of the above to promote nucleation in crystal growth .

 

[houlahound]

There is a lot of deep physics around nucleation, one can assume I feel the net result is it takes less energy to be together than free.

All I know is dipping some string in some copper sulphate solution or use a dirty beaker causes crystals to start.

Edison when you get bored with Boltzmann/Maxwell move onto Bose and prepare for a good mind blowing.

 

[Khashishi]

In the sky, dust particles act as nucleation sites.

n=\int_{-\infty} ^ {\infty} e^{-\frac{mv^2/2}{kT}}dv

Something is missing in your equation. I think it should look something like
n=\frac{n_0}{\sqrt{2\pi kT/m}} \int_{-\infty}^{\infty} e^{-\frac{mv^2}{2kT}}dv

<Moderator's note: fixed the LaTeX>

 

[houlahound]

Something went horribly wrong in the last post or my cell phone has a virus.

 

[DrClaude]

That integral should definitely not start from -∞

 

[Edison Bias]

In the sky, dust particles act as nucleation sites.

Something is missing in your equation. I think it should look something like
n=\frac{n_0}{\sqrt{2\pi kT/m}} \int_{-\infty}^{\infty} e^{-\frac{mv^2}{2kT}}dv

<Moderator's note: fixed the LaTeX>

Thank you for correcting me! I missed a constant in the Maxwellian distribution (MD) to be determined by my integral above, let's say this constant is A then MD' becomes

f(v)=Ae^{-\frac{mv^2/2}{kT}}

With the use of this along with my integral above the result for A is tedious but

A=\frac{n}{\sqrt{2\pi kT/m}}

which makes MD' equal to

f(v)=\frac{n}{\sqrt{2\pi kT/m}}e^{-\frac{mv^2/2}{kT}}

Integrating this with respect for v gives your result. However, n_o is kind of new to me, what does it mean? Is it perhaps the density at Ek_av? Because this distribution just tells that the density lessens for both higher and lower speed where I think speed should be vritten v=v'-v_o where v_o is related to Ek_av(?) I'm sorry, I still don't understand other than perhaps this: while there are fewer particles with a higer/lower speed in the same volume, desity has to be smaller for them, right?

Edison

 

[Edison Bias]

There is a lot of deep physics around nucleation, one can assume I feel the net result is it takes less energy to be together than free.

All I know is dipping some string in some copper sulphate solution or use a dirty beaker causes crystals to start.

Edison when you get bored with Boltzmann/Maxwell move onto Bose and prepare for a good mind blowing.

This is interesting, I will however not ask why due to deep physics, as you say :)

Edison

 

[Edison Bias]

Dust is also required for rain to fall. Additionally, there was a paper from PRL two years back that said that small vortices within clouds literally spin the saturated dust particles into rain drops. I can't find the original publication, but here's an the story about it:

http://physics.aps.org/story/v7/st14

Hi PQ!

I have now read your article, very interesting, short and easy to read too :)

And as Khashishi talks about "nucleation sites" for supersaturated air (humidity>100%) to condense this with dust for rain to condense/fall kind of feel related. Especially when houlahound talks about nucleation sites as impurities. I probably oversimplify too much but all these statements seem related and are very interesting.

Edison

 

[Edison Bias]

Let's consider a related natural phenomena:

If we have a puddle of water and the temperature outside is 300K and the pressure is 1atm, how long will it take for that puddle to dry up i.e vaporize totally if the amount is 1L and humidity is 50%?

Does evaporation depend on shape of water, i.e does it differ in time if the water is inside a tube or in a puddle?

I don't think so, it seems like there's a mass evaporation, regardless of shape, right?

So it seems like:

-\frac{dm}{dt}

is constant given a fixed temperature and pressure, right?

Let's rewrite that

-n\frac{dV}{dt}

or better

-V\frac{dn}{dt}

where n is the density, and the expression is constant.

Now, n is according to PF:

n=\frac{n_0}{\sqrt{2\pi kT/m}}\int_{-\infty}^{\infty}e^{-\frac{mv^2/2}{kT}}dv

But the temperature is constant so n does not vary even though it is interesting :)

So what makes -dV/dt?

To be continued...

Edison
PS
The only thing I have going for me is the Maxwellian Distribution and I have already calcylated that some 27% reach 400K (Tk) at 300K (Tav) but I kind of understand that that way of thinking is wrong.

Edit: Added humidity=50%, struck me as important before Khashishi told me below but it is because of Khashishi that I understand the importance of this.

 

[Khashishi]

Of course it depends on shape, and on humidity. Evaporation will be faster if the exposed surface area of the water is higher.

 

[Edison Bias]

Here I feel stupid to not understand this because intuition tells me you are right. But why is it shape-dependent? Do I dare to guess? It isn't more photons per area because water evaporates regardless of sunlight (even though sunlight heats the surface and speed up the process but we are talking 300K here). Maybe simply more air-molecules to "connect with" if the area is large? Thus more water molecules evaporates, right?

I have corrected for humidity above.

Edison