Enthelpy of condensation and the global heat budget

[klimatos]

I am a retired climatologist, not a physicist. I am seeking the help of physicists to resolve a matter that has always puzzled me. I shall try to list my reasoning in what appears to me to be a logical order. I will number my statements so that you may isolate my errors more easily. 1. When water vapor in the free atmosphere condenses into either water or ice, the temperature of the remaining gaseous atmosphere increases. 2. This increase in the temperature of the remaining gaseous phase is usually explained as a consequence of the “release” of latent heat (enthalpy of condensation) into the gaseous phase. 3. The mechanism of this transfer of thermal energy from the condensate to the remaining air remains obscure. Is it radiation, conduction, or mass transfer? 4. Mass transfer would seem to be out, since the mass transfer is occurring in the opposite direction—from the gaseous phase to the condensate phase. 5. Conduction would seem to be a poor choice, since the atmosphere is a notoriously poor conductor of thermal energy. 6. If the transfer is via radiation, is there an equivalent burst of radiation from the condensate during the process of condensation? 7. Or is it possible that this temperature increase does not represent a gain in thermal energy by the remaining atmosphere at all, but represents what might be termed a “statistical anomaly”? 8. I have always assumed that when a water surface vaporizes, the water molecules with the highest kinetic energy of translation normal to and away from the surface have the highest probability of escaping the various attractive forces of the liquid and becoming vapor molecules. 9. The selective nature of this process accounts for the fact that vaporization causes a mean energy loss (enthalpy of vaporization) in the vaporizing phase, thus reducing its temperature. 10. Because of the nature of the kinetic energy distribution curve, most of the molecules in “capture” proximity to a condensing surface will have very low kinetic energies of translation. 11. By selectively removing low KET molecules from the ambient air, the mean of the remaining molecular KETs is increased, resulting in an increase in temperature but a decrease in thermal energy content. 12. If true, this would have a significant impact on global heat budget studies. 13. If true, of course. That’s the sticker. 14. Where am I going wrong?

 

[Bystander]

One, two, okay. Three, four, five, six; "Not obscure, yes, wrong, unknown."

Seven, . Eight, okay. Nine, ten unnecessary embroidery. Leading to eleven which has to be called "wild speculation."

 

[DrClaude]

In point 3 (and 4,5,6), you seem to have things backwards: the condensation occurs because energy has been transferred from the water to the remaining air.

 

[jim hardy]

1. When water vapor in the free atmosphere condenses into either water or ice, the temperature of the remaining gaseous atmosphere increases.

I'm certainly no expert.
Dad was an aviation forecaster for US Weather Bureau
He taught me a couple basics.

To nitpick your #1
As you've worded it seems to me to imply heat flow from cold to warm,
Since there's no temperature change during a phase change
i'd say instead "condensation or freezing arrests cooling ..."
as evidenced by watching cumulus clouds grow vertically -
rising air wants to cool as it expands but condensing moisture keeps the air warm making a thermosiphon hence the columns one sees in summertime. Almost as if the expansion departs from adiabatic...

At night when air reaches the dew point by radiation cooling, dew must form before the air-water mix can cool further. Almost as if there's a discontinuity in specific heat...
So how does one describe that?

Not challenging your science, sir, for as you see I'm ill equipped,
but perhaps there's improved wording that'd lead the mind naturally to the right concepts.

In correcting their language they reason better.

Does what i say make any sense?

old jim

 

[dlgoff]

Dad was an aviation forecaster for US Weather Bureau
He taught me a couple basics.

How cool is that?

Almost as if the expansion departs from adiabatic...

Latent heat being the reason.

Pic from http://eesc.columbia.edu/courses/ees/climate/lectures/atm_phys.html
Sorry for the large pic size.

 

[256bits]

Does what i say make any sense?

Perfect sense.

To nitpick your #1
As you've worded it seems to me to imply heat flow from cold to warm

I agree.

 

[jim hardy]

Thanks Don, i'd completely forgotten about "lapse rates"

And a picture is well worth a kiloword..

old jim

 

[D H]

14. Where am I going wrong?

Here:

3. The mechanism of this transfer of thermal energy from the condensate to the remaining air remains obscure. Is it radiation, conduction, or mass transfer?

Here:

5. Conduction would seem to be a poor choice, since the atmosphere is a notoriously poor conductor of thermal energy.

And most definitely here:

12. If true, this would have a significant impact on global heat budget studies.

13. If true, of course. That’s the sticker.

There are two problems with your point #3. One is that you haven't covered all the possibilities; I'll get to that a bit later. The other is that it on a macroscopic level it doesn't really matter what the microscopic mechanism is. It happens. That's one of the nice features of using conservation laws. The easiest solution is to just say it happens; who cares how? That latent heat certainly exists, and growing cloud droplets don't get ever warmer as they grow from sub-micron level (the size of a cloud condensation nucleus) to 10 microns (the size of a smallish cloud droplet).

Your point #5 is incorrect. While air is a lousy conductor of heat at a macroscopic level, it's anything but lousy at the micron-level scale that encompasses cloud condensation nucleus and small cloud droplets. This is an extremely low Reynolds number regime. Molecular collisions are very important in this regime. The very small size of those cloud condensation nucleus and small droplets that the cloud droplets will be at more or less the same temperature as ambient.

I mentioned above that you missed a possibility. Looking at the molecular scale as opposed to mere microscopic, a cloud droplet simultaneously gains water molecules by condensation and loses water molecules by vaporization. Which rate dominates determines whether the droplet grows or shrinks. While the condensation rate exceeds the vaporization rate in a saturated atmosphere, vaporization still occurs, and this transfers some heat from the droplet to the surrounding atmosphere.

Your point #10 is one thing you did get right. Condensation selectively removes the lower kinetic energy water molecules from the air. The flip side, however, is also true: Vaporization from the surface selectively removes the higher kinetic energy water molecules from the droplet.

Collectively, the conductive and selective heat transfers will very quickly transfer the heat of condensation from the water droplet back to the air. There's no impact on global heat budget studies.

 

[jim hardy]

There's no impact on global heat budget studies.

I've long wondered what is the global effect on nighttime radiative heat loss from atmosphere caused by moving so much heat so far up.
At 18,000 ft one is above half the atmosphere and its noncondensible greenhouse gases, and above way more than half of the atmospheric water vapor.
So infrared starting from up there stands a better chance of escape thanks to its having hitch-hiked up as latent heat..

Pardon the amateurish speculation. I am after all, an amateur.
Dad gave me an appreciation for the scale of hurricanes and I've been fascinated by heat engines since.

A hurricane moves something like 5E19 joules/day.
http://www.aoml.noaa.gov/hrd/tcfaq/D7.html

Subject: D7) How much energy does a hurricane release?

Contributed by Chris Landsea (NHC)

Hurricanes can be thought of, to a first approximation, as a heat engine; obtaining its heat input from the warm, humid air over the tropical ocean, and releasing this heat through the condensation of water vapor into water droplets in deep thunderstorms of the eyewall and rainbands, then giving off a cold exhaust in the upper levels of the troposphere (~12 km/8 mi up).

One can look at the energetics of a hurricane in two ways:

1. the total amount of energy released by the condensation of water droplets or ...
2. the amount of kinetic energy generated to maintain the strong swirling winds of the hurricane (Emanuel 1999).

It turns out that the vast majority of the heat released in the condensation process is used to cause rising motions in the thunderstorms and only a small portion drives the storm's horizontal winds.

Method 1) - Total energy released through cloud/rain formation:

An average hurricane produces 1.5 cm/day (0.6 inches/day) of rain inside a circle of radius 665 km (360 n.mi) (Gray 1981). (More rain falls in the inner portion of hurricane around the eyewall, less in the outer rainbands.) Converting this to a volume of rain gives 2.1 x 1016 cm3/day. A cubic cm of rain weighs 1 gm. Using the latent heat of condensation, this amount of rain produced gives

5.2 x 1019 Joules/day or
6.0 x 1014 Watts.
This is equivalent to 200 times the world-wide electrical generating capacity - an incredible amount of energy produced!

old jim

 

[Bystander]

Your point #10 is one thing you did get right. Condensation selectively removes the lower kinetic energy water molecules from the air. The flip side, however, is also true: Vaporization from the surface selectively removes the higher kinetic energy water molecules from the droplet.

Are you saying that water droplets involved in atmospheric phenomena are not at local equilibrium with water vapor in the atmosphere?

 

[D H]

Are you saying that water droplets involved in atmospheric phenomena are not at local equilibrium with water vapor in the atmosphere?

I'm saying exactly the opposite. I specifically said that the tiny water droplets in a cloud are more or less at the the same temperature of the surrounding air.

The exact mechanism that makes this happen -- does it matter? ( I also said (or better, wrote) this.) While it is an interesting problem from the perspective of cloud physics, looking too closely can be a distraction.

That condensation releases heat is an undisputed physical fact. This heat has to go somewhere. But where?

**If** the air and the tiny little droplets that comprise a cloud are in thermal equilibrium, this energy is split between the air and the tiny little droplets that comprise the cloud. That the tiny little droplets are in thermal equilibrium with the local environment is an observed fact. Scientists did study this, but they did so long before the internet and arxiv.org existed. The results were as expected. The tiny droplets in a cloud are at the same temperature as the air in the immediate vicinity of the droplet.

 

[Chestermiller]

I am a retired climatologist, not a physicist. I am seeking the help of physicists to resolve a matter that has always puzzled me. I shall try to list my reasoning in what appears to me to be a logical order. I will number my statements so that you may isolate my errors more easily.transfer?

If you really want to get an understanding of this stuff, get yourself a copy of Microphysics of Clouds and Precipitation: by Prupacher and Klett.

Chet