1.
The first step is to realize that warm water will evaporate
more rapidly than cool water. You probably know that
already. If a cup of iced tea were set next to a cup of
hot tea you probably be able to tell which was which by just
looking at them. You wouldn't need to touch the cups or
taste the tea or look for ice cubes.
You might notice that one of
the cups of tea was steaming (the cup on the right
above). That would be the hot tea. The steam
that you see is not actually water vapor. Rather water
vapor is evaporating so quickly that it is filling the
cooler air above with more moisture than it can handle (the
relative humidity is over 100%). The excess water
vapor condenses (bringing the relative humidity down to
100%) and forms a cloud of very small drops of water.
That's what you are seeing.
Now we'll redraw the picture and cover both cups so that
water vapor can begin to buildup in the air above the water
in both cups.
Arrows represent the different rates of evaporation.
One arrow is shown evaporating from the cup of cold
water. We'll just assume the warmer water at right is
evaporating 3 times more rapidly. We've arbitrarily
assigned rates of evaporation of 10 and 30 to the water in the
two cups. The actual numbers aren't important, the
important point is that the warm water evaporates more quickly
than the cold water.
2.
Water vapor will start to buildup in the air above each
cup. And, even though it has just evaporated, some of
the water vapor will condense and rejoin the water at the
bottom of each cup. Let's just assume that 1% of the
water vapor molecules will condense (again just a made up
number).
The amount of water vapor in each glass will increase until it
reaches a point where
water evaporation rate =
water vapor condensation rate
for the cup of cold water
10 = 0.01 x water
vapor concentration
The 0.01 is 1% expressed in decimal form. Solving
this
equation
gives
you a water vapor concentration of 1000. The air is
saturated when you reach this point and the RH = 100%.
If you repeat the calculation for the cup at right with the
higher rate of evaporation you get a water vapor concentration
of 3000.
The air is saturated in both glasses (RH = 100% in both
glasses) but there is more water vapor in the warm glass.
3.
The fact that the rates of evaporation and condensation are
equal when air is saturated (RH = 100%) is something we'll be
using later when we study the formation of
precipitation. Here's a picture of how that would look
inside a cloud (the air inside a cloud is just like the air in
the covered glasses above)
The air inside the cloud is saturated. The rate of
evaporation from the cloud droplet (2 green arrows) is
balanced by an equal rate of condensation (2 orange
arrows). The RH = 100%. The cloud droplet won't
grow any bigger or get any smaller.
4.
Here's something to test your understanding of this
material. As a matter of fact I'll make it an Optional
Assignment. Turn in your answers to the questions below
at the start of class on Friday and you'll receive some extra
credit.
The assignment consists of 4 questions:
(i) Is the water in Glass A WARMER
or COLDER than in Glass B?
(ii) Is there MORE or LESS water vapor
in the air in Glass A than in Glass B?
(iii) Is the relative humidity in each glass MORE than 100%,
LESS than 100% or is it EQUAL to 100%.
(iv) The rates of evaporation and condensation aren't equal in
either glass, so the pictures will change with time.
What will the glasses look once they have reached
equilibrium?
We'll end this section with a table that shows the
dependence of saturation mixing ratio on air temperature.
Note that the value of the
saturation mixing ratio doubles for every 20 F increase in
temperature. The same data are shown in graphical
form below.