Showing posts with label physics. Show all posts
Showing posts with label physics. Show all posts

Tuesday, April 29, 2014

Feeling Cold



After a week away from school, I took the opportunity to catch up with spring on the campus for a half-hour during first period.  Walking out the door in shirt sleeves (having forgotten my jacket this morning), I was surprised at how comfortable it was compared to my arrival less than an hour before.  By the time I was headed back for the door, I was chilled.  Why?



We commonly predict our comfort outdoors by the air temperature.  This had not changed, but when I came out of the building I was in sunlight, so I benefitted from another source of heat than my own.  Further, the building sheltered me from the wind initially.  Then again, I began to warm up a little as I walked briskly back to the building, generating increased body heat.



So a better question than, "what's the temperature?" might be "how fast will my body lose heat?" or--even better--breeze, sunlight and exercise considered, "what will my body's net heat flow be?"



I returned from a boating trip a few days ago that reminded me of another lamentable (and embarassing) factor: wet clothing.  I had overturned my kayak in cold knee-deep water by a simple-minded error in climbing into it.  I spent the next half-hour wet and wind-blown, until I could get aboard the bigger boat, and get below and change.  Being wet in cool weather can be positively dangerous.  Worse still is staying in the water: you are out of the wind and its evaporative cooling power, but water is  so effective at removing heat from the body that even an hour in really cold water can be a death sentence.  Indeed, water robs heat so effectively that a person can die of hypothermia in New England waters even in high summer, if he stays in the water long enough.



In physics terms, you can think of your body as a container; inside the box thermal energy is generated by respiration fueled by the food you've eaten and enabled by the oxygen you inhale.  Clothing varies in its ability to insulate the box, slowing the flow of heat outward.  Outside the box are a variety of conditions that increase or decrease (on a very warm day, even reverse) heat flow.  The air itself is a fair insulator, but far less if it is moving air; water, by contrast, is an effective absorber of heat.  The idea of wind chill gets at just one of these conditions.  "Net heat flow" encompasses all the factors.



So it seems temperature is only one factor in comfort and safety outdoors.  Besides dressing for the weather, we must consider sun and exercise, and wind and water.  As your heat balance can change many times on even a single outing, the wisdom of dressing in layers becomes obvious, as well as the importance of being able to keep dry when shelter is not close by.



 And shivering, although uncomfortable, is one way your body automatically increases heat production when you're cold: you muscles vibrate, so increase energy output without actually going anywhere--like taking a brisk walk while standing still. 

Wednesday, April 2, 2014

Making a (very small) Virtue of Necessity



As I climbed to the third-floor classroom yesterday, I got to wondering how much energy I was burning.  I was predisposed to think of stair-climbing in term of calories (rather than, say, heart health) because I have put on a few pounds lately.  (Okay--more than a few.) 



This could be quite complicated as a biology question, but in terms of physics, it can be done--very roughly but adequately--in five minutes on the back of an envelope.  In fact, with some simplification it can be done in your head.



The first thing to realize is that height is a kind of energy (potential energy).  Consider a car about to roll down a hill in neutral: when that car steam-rolls you at the bottom, you will have experienced that potential energy converted into the form of motion (kinetic) energy.  By the same token, energy is "stored" in an object as it is raised to a height.  That means the energy I burn in walking up the stairs is roughly equal to the amount I gain in potential energy in going up two floors. 



A moment's thought will convince you that potential energy depends on both the mass of the object, and how high it is.  (An anvil falling on your head will affect you differently than a marble from the same height.)  It also depends on the "acceleration of gravity" (symbolized "g"), which describes how quickly a falling object on earth accelerates, and is equal to 9.8m/s2.  (This translates: a falling object increases its speed by 9.8 meters per second for each second that it falls.)  The actual equation for potential energy (Ep) is:


                                           Ep=mgh               



--where "m" is mass in kilograms, and "h" is height in meters.  (Ep is in Joules; a Joule is the amount of energy needed to accelerate a 1kilogram object by 1 meter per second every second.)



I'm guessing the floors of the school to be 4 meters apart, so 8m total height.  Taking g to be nearly 10, and my mass to be almost exactly 100kg, we have:



                               100kgX10m/s2X8m=8000J



Sounds like I'm burning a lot of energy on my climb!  Now to turn that into a more familiar unit: a calorie is four-point-something Joules--call it four even for simplicity.  Now I have burned about 200 calories on my climb.  But wait! in one of the stupider coincidences in science, there are two kinds of calories**: the regular sort used by physics, and the Calorie (big "C") used in considering food.  A Calorie is equal to 1000 calories.  So my climb actually only burned about 2 Calories. 



Bummer.



According to the sugar bag in my pantry, a teaspoon of sugar--not much more than I put in my coffee--has 15 Calories.  So every time I walk up to the third floor, I burn through only a few sips of my morning brew.**



Deep funk.



I suppose the take-home lesson is one I already knew: you can't exercise yourself into weight loss (unless maybe you're the athletic type, in which case you probably don't have to); you have to control your eating.  (Yes, there's more to it, but it's still unavoidable.)  Probably I should stop making hermit cookies, full of deadly brown sugar, molasses and butter.  From the scientific point of view, it's pretty cool (and scary) how much energy food contains. 






*Another definition: a calorie (small c) is the amount of energy needed to warm one gram of water by one degree Celsius.  Therefore a Calorie can warm a whole kilogram by the same one degree.


**Okay, so it isn't really that simple: since I am assuming our bodies are 100% efficient at converting chemical (food) energy--via muscles, joints, etc.--into potential energy.  What if our bodies were only 25% efficient? or 15%?  I still don't burn that whole cup of coffee!

Wednesday, February 5, 2014

No, the Universe Doesn't Hate Us (a little Snow Physics)

My wife called it, rather pointedly, heart attack snow.  It would be heavy and wet and accumulate all day.  Better to shovel several times--not letting it get too deep--than try to clear the driveway all at once at the end. 

So I reminded my wife that the issue is power, not energy.  It takes a certain amount of energy to clear the driveway, and the total amount of energy won't vary too much whether the driveway is cleared in stages, or all at the end.*  (I suppose most of that energy goes into lifting the snow against gravity, though some part goes into throwing it varying distances.)   The demand shoveling snow puts on your cardiovascular system is a matter of power.  Power is energy per unit time.  Any number of units could be used; I like Joules/second, which is the fundamental metric unit, but if you're interested in your use of food energy, or losing weight, you might use, say, Calories/minute. 

Let's imagine that clearing the entire driveway of six inches of  heavy, wet snow requires expending 500 Calories.  You could take it easy, take small bites with your shovel, do it over the course of two hours (don't forget to take breaks!) and exert an average power of 500 Calories/2 hours = 250 Cal/h.  Or you could do a rush job, finishing in one hour, and exert 500 Cal/h -- twice the power does the same job in half the time.  The oxygen to burn those calories (and the carbon dioxide that results) is delivered by your hard-working lungs, heart and blood vessels.  If you don't get much aerobic exercise between snowfalls, I'd recommend option A!  (Or take my wife's advice; or get a snow thrower.) 

You see the distinction between energy and power all the time once you become familiar with it.  It is the reason that my little Hyundai and a Porsche can both drive the speed limit on the highway--but the Porsche can get to that speed from the on-ramp a LOT quicker than I can!  It is also the reason my old dad can still climb the stairs in his house with his failing heart, but he has to take them more slowly than I do.

Now to the main question.  If you live in a snowier clime, you will have noticed that more snow falls where you have just shoveled than in the surrounding areas.  The effect is most noticeable at the edges.  In other words, when it comes to show shoveling the universe seems to punish virtue!  But I'm pretty sure the universe (Splendid though it is) doesn't care about us much one way or the other, and certain it doesn't care that--much less how--we shovel.  What's going on, then?

As I reached the bottom of the driveway on Tuesday morning, a clue appeared in the snow that had accumulated between the cars.

Only five inches between the cars, but eight by
my little Hyundai and a foot by the minivan.

Here's the secret.  Moving fluid carries more and bigger particles the faster it is moving.  That's it.  The rule is usually applied to rivers, but it applies equally to snow-laden air.  Snow falls slowly, so that even a slight breeze will keep some of it suspended until the air slows down.  This is why snow forms drifts: the air slows when it meets an obstacle, and more snow is deposited. (The cars in the driveway are Big obstacles.)  It explains why the snow is deeper at the edges of the driveway (close to the high curb) than it is in the middle of the driveway.  It explains why I will shovel more snow if I shovel more times--each time I shovel, I am making a new "wind shadow" that will slow the air, depositing some of its white load.

This also one reason it is so difficult to measure snowfall: small variations in the landscape--as well as obvious barriers--can lead to different amounts of accumulation.

Another application of the principle explains a lot about rivers.  As the speed of moving water increases, it picks up more and bigger particles of sediment, as it slows it deposits them, beginning with the largest and heaviest.  The lower reaches of the Mississippi River, flowing over nearly level land, meanders because it does: any slight random bend in the river causes the water to slow a bit on the inside of the bend, and speed up on the outside.  Sediments are eroded by the faster moving water on the outside, forming a cut bank, while they are deposited on the inside, forming a point bar.  This makes the river bend greater and greater, as the river digs farther and farther into its outside edge.  In other words, a river meanders because it does! 

By the same token, it explains why the highest land in New Orleans is (against all "common sense") on the banks of the Mississippi River itself.  The land all around the river was created by the river overflowing its banks in periodic floods.  As the sediment-laden water leaves the fast-flowing channel it immediately slows, dropping most of its load.  The water that floods farther into the countryside has less sediment and gains less new land.  The historic French Quarter is right on the bank, while lower areas farther from the river weren't settled until this marshy land could be efficiently drained.  (It's a little jarring to realize that the surface of the river may actually be above your head as you stand only a short distance away.)  By the same token, the flooding of New Orleans after hurricane Katrina left the French Quarter nearly untouched, while it did the most damage to the poorest neighborhoods in these less-desirable lowlands. 

Only the green areas  are actually above sea level; the white are at, the yellow are below, sea level.  Note that the RIVER did not flood after Katrina; the water came from Lake Ponchartrain via the canals.

Since the river is now confined behind high levees where it cannot escape to spread its sediments, the situation of New Orleans must become fundamentally worse with time, as sediment-built land sinks and sea levels rise.



*Actually, it will, but in a way that favors doing it all at once.  And soon you will know why.

Saturday, January 4, 2014

Domestic Science


The last 8ft or so of the first floor has a flat roof.  (Here already cleared.)

One end of my house has a flat "rubber" roof.  After a heavy snow, I worry about the accumulated weight, and usually go out an upstairs window with a snow shovel to clear it off.  Today, with the temperature rising into the tropical upper twenties (it bottomed out at 0oF last night), I decided it was time. 

As I sent cubic-foot blocks hurtling to the ground, I got to wondering just how much extra weight that roof was supporting.  How hard could it be to figure out, at least roughly?  If I knew the weight of a given volume of snow--i.e. its density, then I could multiply that by the volume of snow to get the total weight. 

If you care about the details, read on.  Otherwise, photos might be enough.

Estimating density would be a bit tricky: not only does snow differ in density from one snowfall to another, and as it changes temperature, it also differs with depth in the same snow: the deeper down you look, the more the snow will be packed down by the snow overlying it.  Finally, the density will change as you handle snow to measure it, whether you accidentally pack it down, or fluff it up.

Thinking about weighing snow on our old kitchen spring scale gave me an idea.  The lid of the scale, which doubles as the weighing pan, is a short cylinder with almost straight sides.  It reminds me a bit of a device soil scientists use to find the density of soil: a bulk density corer.  The idea is to drive the short, fat cylinder of the corer into a body of soil, removing it intact for measurement.  Measurements will be more true to the soil's natural state because the soil will be almost undisturbed, and neither loosened nor packed-down.

My son passed the scale to me through the window.  A shovel thrust straight down made a flat surface to push the scale pan into.  Once the pan was in flush with this surface, a big more careful work with the snow shovel got the core out intact for weighing.  Since I expected the density to vary with depth, I pushed the pan into the snow about halfway down, to make the core more "average." 

Snow cut straight vertically for sampling. 

Taking a bulk core with the scale pan, being careful not to disturb or pack it.

Weight full: 10.5oz.

Weight (approximately) empty: 5.5oz.

The scale pan with snow read 10 1/2 ounces, and 5 1/2 ounces empty.  Because it's easier to do math with metric units, I will call this 0.14 kg.*  The pan's volume can be found from its radius and height.  Since it's inside is 14cm (o.14m) in diameter and 8cm (0.08m) deep, the volume is the area of the circle times the height, or pi.r2.h=3.14X(0.075m)2X0.08m=0.0014m3.  Giving the snow a density of mass/volume=99kg/m3.  (That sounds like a lot, until you consider how big a cubic meter is!  In fact, pure water is about 1000kg/m3 --that's a bit over a ton per cubic meter, to mix my units a bit.)  It nicely fits the generalization that snow is typically 90% air. 




Now for the total volume of snow. I didn't think to get my son to pass me a tape measure, but the depth of snow varied from about two inches deeper than my foot-deep shovel blade to about two inches less deep. That's 0.36m down to 0.25m. Since these is back-of-the envelope calculations, I'll presume the snow depth varied smoothly for a roof width of 8ft (2.4m). Imagining this cross-section as a rectangle with a thin triangle on top gives it an area of (0.25mX2.4m)+(1/2X0.11mX2.4m)=0.73m2.  Since the roof is about 27ft or 8m long, the total volume of snow is roughly 0.73m2X8m=5.8m3.

Result:



At a density of about 100kg/m3, this gives a total snow mass of around 600kg, with a weight in English units of 1300lb. Impressive, but of course that weight is spread over a roof that's 2.4mX8m=19m2 in area, so it amounts to only 68lb per square meter. The guy shoveling it exerts 210lb on the much smaller area of his shoes--so it's high time he got the hell off the roof!


This little exercise isn't as time-consuming to do as it is to write about.  Even so, I don't plan to repeat it.  I could probably guesstimate future snowfall weights by comparing them to this one.

While I'm up here, I'll take a couple of photos of the Wild Place I often write about.
*A pet peeve of mine (yes, I've got a zoo-full) is the misconception that weight (e.g. pounds) and mass (e.g. kilograms) are the same thing.  They are not.  I sigh deeply when someone says that one kilogram "equals" 2.2 pounds.  It doesn't.  Mass is a measure of how much "stuff" something has, while weight is the force gravity exerts on that stuff.  We can, however, relate them safely provided the force of gravity remains constant.  Rather than "2.2lb=1kg,"  instead, think, "a mass of 1kg has a weight of 2.2lb at normal earth surface gravity."

Wednesday, October 30, 2013

For Spacious Skies -part 3

You now know that a cloud forms in moist air when that air cools below its dew point--the temperature at which the evaporation of water from cloud drops slows enough that the relatively greater condensation rate causes those drops to grow.  You also know why the temperature influences evaporation.

Now we attack the question of what cools the air in the first place.  The most common is that something lifts the air upward, resulting in adiabatic cooling (definition later).  This involves the structure of the atmosphere, plus a nifty bit of physics called the ideal gas laws.

First the atmosphere.  You probably know that the air is thinner as you go upwards, so that the air where commercial jets fly is too thin even to breathe successfully.  You can feel the difference even driving in hilly country as the changing pressure affects your eardrums.  The reason for this is simple: air is compressible.  The vertical structure of the atmosphere is a bit like a giant  stack of pillows: the topmost pillows are light and fluffy, but as you go downward they are compressed more and more under the weight of pillows above.  The bottom pillows will be squashed flat, dense, under a lot of pressure.   As you move upwards in in the atmosphere, air pressure AND air density decreases for the same reason.

 Now the perfect gas lawsIn a nutshell, three things are interrelated in any body of gas: its volume, its pressure, and its temperature.  Changing any one of these three things affects one or both of the others.  If a gas is compressed into a smaller volume, its pressure and/or temperature rise.  If the gas is allowed to expand, its temperature and/or pressure falls.  So if a mass of air rises upward, the lowered pressure causes its temperature to fall.  (This is called adiabatic cooling.)  If that temperature falls below its dewpoint, cloud droplets grow as condensation of water vapor onto particles in the air wins out over evaporation.  A cloud forms.  Conversely, sinking air warms, evaporating any cloud that is present.   Because the altitude at which air reaches its dew point is fairly constant in a given situation, clouds often have pretty flat bottoms, all of which line up; the illusion created is that the clouds are sitting on some sort of invisible surface.  (In reality, rising air is rising through a sort of boundary line where cloud drops begin growing rapidly.)
 
The next time you see light, fluffy cumulus clouds apparently floating in the sky, imagine air rising where the cloud is, and sinking in between, continuously creating the appearance you see.

Watch the low, passing clouds for signs of evaporation.  (Follow the small isolated bits.)

Well then: why does the gas rise?  Usually one of two reasons, and each results in a different basic cloud type.  First, air can be heated, and that warm air rises, buoyed up by the cooler, denser air around it.  This often happens to air in contact with the warm ground on a sunny day.  Each rising mass of air begins to form a cloud when it reaches the altitude at which its temperature drops below the dew point.  This results in the puffy, separate clouds called cumulus.  Second, an enormous area of air can be lifted all at once (for example, by an approaching front.  This results in a layer cloud called stratus.

 

 





Cumulus mediocris and congestus over Swifts Creek, Australia (Wikipedia Commons)


Stratocumulus stratiformis perlucidus over Galapagos, Tortuga Bay  (Wikipedia Commons)

Make your own cloud!  Take the label off a soda bottle (the bigger the better) so you can see inside more conveniently.  Get a match ready to light.  Put a little water (a tablespoon or two is enough) into the bottle and shake it.  Now light the match, let it burn a moment, then blow it out and drop it, still smoking, into the bottle.  Put your mouth to the open end of the bottle and blow, increasing the air pressure in the bottle.  After a few seconds--and while watching what is happening inside the bottle--release the air.  There: do you see it?  The air went cloudy the moment you released the pressure.  Clouds you make this way will sometimes last several minutes.

Can you explain what happened from what you have learned?  (Try on your own before reading on.)

Shaking the water in the bottle allowed as much as possible to evaporate quickly, increasing the humidity in the bottle to near-saturation.  The smoke particles from the smoldering match provided condensation nuclei.  When you forced additional air into the bottle, the pressure increased, causing the air to warm slightly, so more water could evaporate, raising the dew point.  When you released the pressure, the temperature in the bottle dropped below the dewpoint, the condensation rate overcame the evaporation rate, and water vapor condensed on the smoke particles forming tiny cloud droplets.  There!  A cloud of your own!

 
For nice (though small) photos of all the more common cloud types, see:
http://weather.about.com/od/cloudsandprecipitation/ig/Clouds-Types-on-a-Weather-Map/
 

It's worth mentioning that water vapor is a powerful carrier of energy in the atmosphere.  As water evaporates due to solar heating, potential energy becomes stored in the water vapor that results.  We think of this as potential energy because the rapid motion of the gas particles prevents (on the whole) their condensing back into clusters (drops) bound by their electrical attraction.  (This is analogous to a rock at the top of a cliff or hill: it has potential energy that it can give up as it falls or rolls downward due to the force of gravity.  In the case of water vapor molecules, the electrical attractions are the "gravity," while their rapid motion is the "height.")  Just as the water absorbs energy in evaporation, it gives off energy as it condenses. 

 Let's see how that energy can be a powerhouse.  The sun warms moist ground or a lake, causing water to evaporate and form a warm and humid body of air.  The warm moist air begins to float upward in the cooler air around it because warm moist air is lower in density.  As it rises, the drop in pressure causes that body of air to expand, lowering its temperature below the dew point.  If this warm air were dry, it would cool enough to be the same temperature as the cooler air around it, its density would match that of the surrounding air, and it would stop rising--end of story.  BUT because that air is humid, water vapor begins to condense into cloud drops.  The process of condensation produces heat (that potential energy is no longer just potential!) that prevents the air from cooling any further, so it continues to rise.  Condensation continues in the rising air, causing the cloud to tower higher and higher, until the supply of water vapor is small enough that condensation ceases, the air stops rising, and the cloud stops building.  If there is enough water vapor to build the cloud into a thunderhead, a thunderstorm may result.  And if there is enough warm, humid air (say, over the subtropical Atlantic Ocean in summer) then the energy of the condensing water vapor may power a hurricane--a kind of runaway freight train of condensation--and the most destructive of all storms. 

So when you see a cumulus cloud boil upward, increasing in height over time, you are seeing the power in water vapor.
 

More coming about particular clouds...


For more information:

source for "how do clouds form?" "that distinguishes convective vs stratiform process

In somewhat the same vein as above--five different situations that can cause cloud formation (though this page does refer to air "full of" moisture)

Here is one that has a little animation that gets it wrong

A nice diagram of adiabatic cooling, though it still mentions air's ability to hold moisture: http://www.vivoscuola.it/us/rsigpp3202/umidita/lezioni/form.htm

A nice, comprehensive look atclouds and their phenomona
 
The only (repeat: ONLY) site I've found that gives explanations for some particular cloud shapes

ExTREMELY cool time-lapse video of storm overspreading a city

The slower but larger high-def version takes much longer to load, but IS WORTH IT!

 

Tuesday, October 22, 2013

For Spacious Skies --part 2

Two posts ago, we began looking at the processes that form clouds at the molecular level.   A quick review, and then we'll get to something you can see more easily.  Molecules of both liquid water and gaseous water (water vapor) are in motion.  If the molecules of liquid water move fast enough, they evaporate (become gas), while if water vapor molecules slow enough, they condense (become liquid).  The "dynamic" part of this business is that both of these processes happen simultaneously pretty much wherever water exists.

Molecules of liquid water becoming water vapor is called evaporation, while the opposite process of molecules of gaseous water clinging to form a drop of liquid is called condensation.

Evaporation happens when molecule jostling in a liquid gain enough speed (really kinetic energy) to overcome the electrical forces that make them cling, so that they come loose and leave the water to become water vapor (gas) molecules.  Condensation happens when gas molecules zinging off each other slow down enough (lose kinetic energy) so that, instead of bouncing off each other, they cling to form liquid water.

(A nice, succinct explanation of most of today's topic can be found at: http://www.ems.psu.edu/~fraser/Bad/BadClouds.html  Even if you read on here, you would be well advise to look at this page.)

Now it's time to get concrete for a bit.

Put a bucket of water into a closet.  Put a window in this closet so you can closely watch what is going on.  Shut the door.  (Do not try this at home--your imagination will work just fine and be quicker.)  On a dry day, water molecules on the surface of the water in the bucket will be zinging off into the air as chance collisions with other water molecules give them enough energy to break loose from neighboring molecules to which they cling.  Over a period of time, more and more water molecules will be in the air as water vapor.  Some of these water molecules, in colliding with each other, will lose enough energy to cling back to the water in the bucket.  In the beginning, water will be evaporating from the bucket much faster than they condense from the air.  As you observe the bucket, the water level will be sloowwly dropping.  But as water vapor accumulates in the closet, the condensation rate will increase--simply because there are more molecules in the air that, by chance, slow enough to stick back to the liquid.  (If you could sample that air, you would find it more humid than when you began.)  At some point, these two processes will balance out--water evaporating out of the bucket and condensing back into it--and it will seem as if everything has stopped.  But you know the truth: both evaporation and condensation are still happening, but at equal rates.

We don't have a cloud yet (though we're getting closer); what we have is a dynamic process of evaporation and condensation in conditions which are not changing.  Now we change the temperature.  Remember that temperature is directly related to the average speed of a group of molecules: the higher the temperature, the faster they go.  It turns out that changing the temperature in the closet will not much alter the rate water vapor condenses back to liquid, but it WILL change the rate of evaporation from the bucket.  The warmer the water in the bucket, the faster the molecules move, the faster the rate of evaporation.  If we warm the closet, the result is more water evaporates until there is enough water vapor in the air to rebalance the rates.  At that point, the level in the bucket has dropped a bit again, and the air is more humid.*

What if we cool the closet?  You guessed it: the evaporation rate slows much more than the condensation rate does, and water condenses back into the bucket until there is less remaining water vapor so the condensation rate drops back into balance with the new evaporation rate of the cooler bucket.  The bucket has regained some of its water, and the air is drier.

By now, it might have occurred to you that the real world doesn't behave quite like this. For one thing, water condensing out of the air won't just condense inside the bucket, but on any surface--the walls, floor, ceiling, etc.  This often happens outdoors when the humidity is high enough and surfaces cool off during the night: water accumulates on these surfaces because the chilled water on them doesn't evaporate fast enough to equal the condensation rate.  We call this DEW.  It's fascinating to go out in the morning and observe the kinds of surfaces that do and do not collect dew.  (We'll save that discussion for a later post.)

It's important to note that condensation requires a surface to condense upon.  But clouds are in the air!  It turns out that there are all kinds of surfaces available in normal outdoor air: dust particles, soot, salt crystals, and even bacteria drifting in the air can serve as "condensation nuclei," so that "cloud droplets" form around them. 

We haven't quite gotten to clouds yet, but we know how to form them in principle: provide enough water vapor, surfaces for droplets to condense on, and then cool the environment.  For any given level of water vapor in the air, there is a temperature at which condensation will begin to win out over evaporation.  This temperature is called the DEW POINT.  The higher the level of water vapor present (called "absolute humidity") the higher the condensation rate and so the higher the dew point temperature.  When you feel damp, sweaty, and miserable, you might hear the weather forecaster name a dew point that is only a few degrees below the air temperature: the air is so humid that only a tiny temperature drop will cause net condensation.  Or the forecaster might say the relative humidity is nearly 100%--with 100% RH being the balance point between evaporation and condensation in that damp, uncomfortable air.

 By the way, the reason humid air is so uncomfortable is that our body loses excess heat by sweating: the evaporating sweat absorbs heat from your skin and makes you cooler.  If the air is very dry such evaporation happens so quickly that you may not even be aware you are sweating, but in humid air there will be so little net evaporation that--instead of cooling you--your sweat will simply accumulate.  Yuck!

One more point and then we'll close for today.  If surfaces cool below the dewpoint, you get dew.  But if cool ground chills the air above it so that water vapor condenses into cloud droplets near the ground, we have fog.  And of course if the air cools higher up, a cloud forms. 

One more piece will make the puzzle pretty complete: why does air cool and warm in the first place?  That will be next time.

 

I set out to show cloud in dynamic change.  (This despite my entry-level camera.)  Watch these passing low clouds especially for signs of evaporation: smaller whisps of cloud "disappear" as they evaporate.

 
*A site that debunks the misunderstanding that "warm air holds more water than cool air," so that "air is like a sponge" is Bad Clouds.