Wednesday Oct. 22, 2008
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The music today by Fishtank
Ensemble seems to have been reasonably well received both in the
MWF class and the T Th section.
The Experiment #2 reports have been graded and were returned in class
today. You are allowed to revise your report. Revised
reports are due in two weeks, on or before Wed., Nov. Nov. 5. You
only need to redo sections where you want to earn additional
credit. Please return your original report with your revised
report.
The revised Experiment #1 reports were due today.
Some students chose to prepare a report on a Scientific Paper instead of doing an
experiment report. The Scientific Paper that I had in mind is
available online (I will bring you a copy of the paper and report
guidelines if you send me a request by email).
I hope to have the Expt. #4 materials
available in class on Friday. There are not enough materials for
everyone on the signup sheet, so it will be first come first
served.
I mentioned having visited one of the other NATS 101 sections on
Wednesday morning. Many of the students weren't paying any
attention at all to the lecture but were working on homework from other
classes, surfing the internet, or working on a crossword or Sudoku
puzzle. I didn't want anyone in my class to find themselves
without anything to keep themselves occupied so I handed out a
"humidity puzzle." This isn't an assignment.
You'll find answers to these questions at the end of today's notes.
We can use
results from humidity problems #1 and #2 worked in class on Monday to
learn a useful rule.
In the first
example the difference between the air and dew point
temperatures was large (45 F) and the RH was low.
In the 2nd problem the difference between the air and dew point
temperatures was
smaller (20 F) and the RH was higher. The easiest way to remember
this
rule is to remember the case where there is no difference between the
air and dew
point temperatures. The RH then would be 100%.
Next we
will use what we have learned about humidity
variables (what they tell you about the air and what causes them to
change value) to learn something new. The figure below is on p.
87 in the photocopied ClassNotes. The figure was redrawn after class.
At Point 1 we start with some 90 F air with a relative
humidity of 25%, fairly dry air (these data are the same as in Problem
#4 on Monday). Point 2 shows the air being cooled to the dew
point, that is
where the relative humidity would reach 100% and a cloud would form.
Then the air is cooled below the dew
point, to
30 F. Point 3 shows the 30 F air can't hold the 7.5 g/kg of water
vapor that
was originally found in the air. The excess moisture must
condense (we will assume it falls out of the air as rain or
snow). When air reaches 30 F it contains 3 g/kg, less than half
the
moisture (3 g/kg) that it originally did (7.5 g/kg). Next, Point
4, the 30
F air is warmed back to 90 F, the starting temperature, Point 5.
The air
now
has a RH of only 10%.
Drying moist air is like wringing moisture from a wet sponge.
You start to
squeeze the sponge and nothing happens at first (that's like cooling
the air, the mixing ratio stays constant as long as the air doesn't
lose any water vapor). Eventually water will start to drop from
the sponge (with air this is what happens when you reach the dew point
and continue to cool the air below the dew point). Then you let
go of the sponge and let it expand back
to its orignal shape and size (the air warms back to its original
temperature). The sponge (and the air) will be drier than when
you started.
This sort of process ("squeezing" water vapor out of moist air by
cooling the air below its dew point) happens all the time. Here
are a couple of examples (p. 87 again)
In the
winter cold air is brought inside your house or apartment and
warmed. Imagine 30 F air with a RH of 100% (this is a best case
scenario, the cold winter air usually has a lower dew point and is
drier). Bringing the air inside and warming it will cause the RH to
drop from 100% to 20%.. Air indoors during the winter is often
very dry.
The air in an
airplane comes from outside the plane. The air outside the plane
can be very cold (-60 F perhaps) and contains very little water
vapor (even if the -60 F air is saturated it would contain essentially
no water vapor). When brought inside and warmed to a
comfortable
temperature, the RH of the air in the plane will be very close
0%.
Passengers often complain of becoming dehydrated on long airplane
flights. The plane's ventilation system probably adds moisture to
the
air so that it doesn't get that dry.
Here's a very important example, the rain shadow effect (the figure, p.
88 in the ClassNotes, was
redrawn after class for clarity).
We start with some moist but unsaturated air (RH is about
50%) at Point
1.
As it is moving toward the right the air runs into a mountain and
starts to rise (see the note below). Unsaturated air
cools 10 C for every kilometer of altitude gain.
This is known as the dry adiabatic lapse rate. So in rising 1 km
the air will cool to 10 C which is the dew point.
The air becomes saturated at Point 2, you would see a cloud
appear. Rising saturated air cools at a slower rate than
unsaturated air. We'll use a value of 6 C/km (an average
value). The air cools from 10 C to 4
C in next kilometer up to the top of the mountain. Because the
air is being cooled below its dew point at Point 3, some of the water
vapor will condense and fall to the ground as rain.
At Point 4 the air starts back down the right side of the
mountain. Sinking air is compressed and warms. As soon as
the air starts to
sink and warm, the relative humidity drops below 100% and the cloud
evaporates. The sinking air will warm at the 10 C/km rate.
At Point 5 the air ends up warmer (24 C vs 20 C) and drier (Td =
4 C vs Td = 10 C) than when it started out. The downwind side of
the mountain is referred to as a "rain shadow" because rain is less
likely there than on the upwind side of the mountain. Rain is
less likely because the air is sinking and because the air on the
downwind side is drier than it was on the upslope side.
Most of the year the air that arrives in Arizona comes from the Pacific
Ocean. It
usually isn't very moist by the time it reaches Arizona because it has
travelled up and over the
Sierra Nevada mountains in
California and the Sierra Madre mountains further south in
Mexico. The air loses much of its moisture on the western slopes
of those mountains.
NOTE: The figure
above illustrates orographic or topographic lifting.
It is one of 4
ways of causing air to rise. We have already run into the other
three in class this semester. They were: convergence
(surface winds spiral into centers of low pressure), convection (warm
air rises), and fronts. Rising air is important because rising
air expands and cools. Cooling moist air raises the relative
humidity and a cloud might form.
The next topic in our potpourri of topics today was measuring
humidity. One of the ways of measuring humidity is to use a sling
(swing might be more descriptive) psychrometer.
A sling
psychrometer consists of two thermometers mounted
side by side. One is an ordinary thermometer, the other is
covered with a wet piece of cloth. To
make a humidity measurement you swing the psychrometer around for a
minute or two and then read the temperatures from the two
thermometers. The dry - wet thermometer (dry and wet bulb)
temperature difference can be
used to determine relative humidity and dew point (see the tables on
pps. 139 and 140 in the textbook). The figures below show some additional
details not covered in class.
The evaporation is shown as blue arrows because this will cool the
thermometer. The same thing would happen if you were to step out
of a swimming pool on a warm dry day, you would feel cold. Swamp
coolers would work well on a day like this.
The figure at upper left also shows one arrow of condensation.
The amount or rate of condensation
depends on how much water vapor is
in the air surrounding the thermometer. In this case (low
relative humidity) there isn't much water vapor. The
condensation arrow is orange because the condensation will release
latent heat and warm the thermometer.
Because there is more evaporation (4 arrows) than condensation (1
arrow) the wet bulb thermometer will drop.
The wet thermometer will cool but it won't cool indefinitely. We
imagine that the wet bulb thermometer
has cooled to 60 F. Because the wet piece of cloth is cooler,
there is less evaporation. The wet bulb thermometer has cooled to
a temperature where the evaporation and condensation are in
balance. The thermometer won't cool any further.
You
would measure a large difference (20 F) between the dry and wet bulb
thermometers on a day like this when the air is relatively dry.
The air temperature is the same in this
example, but there is more
water vapor in the air.
You wouldn't feel as cold if you stepped out of a pool on a warm humid
day like this. Swamp coolers wouldn't provide much cooling on a
day like this.
There are four arrows of evaporation (because the water temperature is
still 80 F just as it was in the previous example) and three arrows now
of
condensation (due to the increased amount of water vapor in the air
surrounding the thermometer). The wet bulb thermometer will cool
but won't get as
cold as in the previous example.
The wet bulb thermometer might well only cool to 75 F. This might
be enough to lower the rate of evaporation (from 4 arrows to 3 arrows)
enough to bring it into
balance with the rate of condensation.
You would measure a small difference (5 F) between the dry and wet bulb
thermometers on a humid day like this.
There won't be any difference in
the dry and wet bulb temperatures when
the
RH=100%. The rates at which water is evaporating and water vapor
is condensing are equal. That's one of the things that happens
when air is saturated. The dry and wet bulb thermometers would
both read 80 F.
The last thing we covered was the formation of dew, frost, and
something called frozen dew. The
figures below were redrawn after class to make them clearer.
It might be a little hard to figure out what is being
illustrated
here. Point 1 is sometime in the early evening when the
temperature of the air at ground level is 65. By the next morning
the air has cooled to 35 F. When the air temperature reaches 40
F, the dew point, the relative humidity reaches 100% and water vapor
begins to condense onto the ground. You would find your newspaper
and your car covered with dew the next morning.
The next night is similar except that the nighttime
minimum
temperature drops below freezing. Dew forms and first covers
everything on the ground with water. Then the water freezes and
turns to ice. This isn't frost, rather
frozen dew. Frozen dew is often thicker and harder to scrape off
your car windshield than frost.
Now the dew point and the nighttime minimum temperature are both
below
freezing. When the RH reaches 100% water vapor turns directly to
ice (deposition). This is frost.
What happens on this night (what important point is not reached?
You'll find the answer at the very bottom of today's notes)
Here are the answers to the handout distributed at the beginning of
class.
The air temperature never reaches the dew point (or frost point) and
the RH nevers reaches 100%. So nothing forms. This is
sometimes called "black frost" (frost that you can't see ...
because it isn't there)
