Friday Oct. 15, 2010
click here to download today's notes in a more printer friendly format

"No Sugar Tonight/New Mother Nature" from the Guess Who and "Magic Carpet Ride" from Steppenwolf seemed like reasonable music at the end of a busy week in NATS 101.

Experiment #3 materials were distributed before class today.  There are about 10 sets of materials left.  I'll bring them to class on Monday.

Quiz #2 has been graded and was returned in class today. 

Question #18 on the quiz (see below) was "thrown out" because it was clear when grading the quiz that the question was confusing and students weren't sure how to handle it.  An adjustment has been made in the formula used to determine the percentage grade on the quiz.

Here's what I was thinking

The electric field shows you the direction and gives you an idea of the strength of the electrical force that would act on a + charge.  The fact that the + charge in Fig. A is moving upward would seem to indicate that the electric field was pointing in the same direction.  If a - charge in Fig. B is moving downward, then probably a + charge would move upward (shown in red above).  Again the electric field would point upward. 

There was an In-class Optional Assignment today.  If you download the assignment, answer the questions, and then turn it in at the start of class on Monday you can receive at least partial credit for it.

Here's an idea of what we will be covering between now and the next quiz
(with maybe some emphasis on the items in bold)

humidity, measuring humidity, heat index
dew and frost, radiation and steam fog
condensation nuclei and cloud formation
identifying and naming clouds
satellite photographs
precipitation formation and types of precipitation

The following is an introduction to the first item: humidity (moisture in the air).  This topic and the terms that we will be learning and using can be confusing.  That's the reason for this introduction.  We will be mainly be interested in 4 variables: mixing ratio, saturation mixing ratio, relative humidity, and dew point temperature.  Our first job will be to figure out what they are and what they're good for.  Then we see what can cause the value of each variable to change.  You will find much of what follows on page 83 in the photocopied ClassNotes. 



Mixing ratio tells you how much water vapor is actually in the air.  Mixing ratio has units of grams of water vapor per kilogram of dry air (the amount of water vapor in grams mixed with a kilogram of dry air).  It is basically the same idea as teaspoons of sugar mixed in a cup of tea. 



The value of the mixing ratio won't change unless you add water vapor to or remove water vapor from the air.  Warming the air won't change the mixing ratio.  Cooling the air won't change the mixing ratio (one exception is when the air is cooled below its dew point temperature and water vapor starts to condense).  Since the mixing ratio's job is to tell you how much water vapor is in the air, you don't want it to change unless water vapor is actually added to or removed from the air.


Saturation mixing ratio is just an upper limit to how much water vapor can be found in air, the air's capacity for water vapor.  It's a property of air, it doesn't say anything about how much water vapor is actually in the air (that's the mixing ratio's job).  Warm air can potentially hold more water vapor than cold air.  This variable has the same units: grams of water vapor per kilogram of dry air.  Saturation mixing ratio values for different air temperatures are listed and graphed on p. 86 in the photocopied class notes. 


Just as is the case with water vapor in air, there's a limit to how much sugar can be dissolved in a cup of hot water.  You can dissolve more sugar in hot water than in cold water.

 The dependence of saturation mixing ratio on air temperature is illustrated below:


The small specks represent all of the gases in air except for the water vapor.  Each of the open circles represents 1 gram of water vapor that the air could potentially hold.  There are 15 open circles drawn in the 1 kg of 70 F air; each 1 kg of 70 F air could hold up to 15 grams of water vapor.  The 40 F air only has 5 open circles; this cooler air can only hold up to 5 grams of water vapor per kilogram of dry air.

Now we have gone and actually put some water vapor into the volumes of 70 F and 40 F air (the open circles are colored in).  The same amount, 3 grams of water vapor, has been added to each volume of air.  The mixing ratio, r, is 3 g/kg in both cases.


The relative humidity is the variable most people are familiar with, it tells you how "full" the air is with water vapor, how close it is to being filled to capacity with water vapor.

In the analogy (sketched on the right hand side of p. 83 in the photocopied notes) 4 students wander into Classroom A which has 16 empty seats.  Classroom A is filled to 25% of its capacity.  You can think of 4, the actual number of students, as being analogous to the mixing ratio.  The classroom capacity is analogous to the saturation mixing ratio.  The percentage occupancy is analogous to the relative humidity.
The figure below goes back to the volumes (1 kg each) of 70 F and 40 F air that could potentially hold 15 grams or 5 grams, respectively of water vapor.


Both the 70 F and the 40 F air that each contain 3 grams of water vapor.  The 70 F air is only filled to 20% of capacity (3 of the 15 open circles is colored in) because this warm air's saturation mixing ratio is large.  The RH in the 40 F is 60% even though it has the same actual amount of water vapor because the 40 F air can't hold as much water vapor and is closer to being saturated. 

Something important to note: RH doesn't really tell you how much water vapor is actually in the air.  The two volumes of air above contain the same amount of water vapor (3 grams per kilogram) but have very different relative humidities.  You could just as easily have two volumes of air with the same relative humidities but different actual amounts of water vapor.



The dew point temperature has two jobs.  First it gives you an idea of the actual amount of water vapor in the air.  In this respect it is just like the mixing ratio.  If the dew point temperature is low the air doesn't contain much water vapor.  If it is high the air contains more water vapor. 

Second the dew point tells you how much you must cool the air in order to cause the RH to increase to 100% (at which point a cloud, or dew or frost, or fog would form).


If we cool the 70 F air or the 40 F air to 30 F we would find that the saturation mixing ratio would decrease to 3 grams/kilogram.  Since the air actually contains 3 g/kg, the RH of the 30 F air would become 100%.  The 30 F air would be saturated, it would be filled to capacity with water vapor.  30 F is the dew point temperature for 70 F air that contains 3 grams of water vapor per kilogram of dry air.  It is also the dew point temperature for 40 F air that contains 3 grams of water vapor per kilogram of dry air.Because both volumes of air had the same amount of water vapor, they both also have the same dew point temperature.
Now back to the student/classroom analogy


The 4 students move into classrooms of smaller and smaller capacity.  The decreasing capacity of the  classrooms is analogous to the decrease in saturation mixing ratio that occurs when you cool air.  Eventually the students move into a classroom that they just fill to capacity. This is analogous to cooling the air to the dew point.



Next we'll try to answer the 2 questions above.

We first must understand the rate at which water evaporates depends on temperature (see p. 84 in the photocopied ClassNotes).  Hot water evaporates more rapidly than cold water.  Wet laundry hung outside on a hot day will dry much more quickly than it would on a cold day.

Before talking about water, have a look at the grade distribution below.  The average appears to be about 77%.  Students with grades equal to or greater than 90.0% are exempt from the final. 


If I added 5 pts to everyones grade,
Would the curve shift to the RIGHT  or the  LEFT?
Would the average grade  INCREASE,  DECREASE  or remain the  SAME?
Would the number of people that don't have to take the final  INCREASE,  DECREASE  or remain the  SAME?

 



It seemed like most everyone understood that the curve would shift to the RIGHT, the average grade would INCREASE, and the number of people getting out of the final exam would INCREASE.

The next question is very similar.  Instead of grades, the figure below shows the distribution of the kinetic energies of water molecules in a glass of water.  There's an average and some of the water molecules (the ones at the far right end of the curve) have enough kinetic energy to be able to evaporate (analogous to students that are exempt from the final exam).  You'll find this figure on p. 84 in the photocopied ClassNotes.


If the water were heated, would the curve shift to the  RIGHT  or the  LEFT.  Would the average kinetic energy of the water molecules  INCREASE, DECREASE  or  remain the  SAME?.  Would the number of water molecules, with enough kinetic energy to be able to evaporate  INCREASE,  DECREASE,  or remain the  SAME?  The new curve is shown below  




The value of the average kinetic energy would increase and more molecules would lie to the right of the threshold and be able to evaporate.  Thus we conclude that hot water evaporates more rapidly than cold water.  This is shown pictorially below (the number of arrows is a measure of the rate of evaporation).



This remaining material wasn't covered in class today.  We'll review it quickly on Monday.

And now a completely different type of question.  The situation is shown below.



When the front door is first opened people will start streaming into the Walmart.  The number of people in the store will start to increase.  At some point some fraction of the people inside will start to leave.  Eventually the number inside will grow to the point that the number of people leaving balances the number entering.  The question is how many people would have to be inside the Walmart in order for the two rates to be equal?

In the rate of people entering the store were higher, the number inside would increase.  If the rate were to decrease then the number of people inside would get smaller.

The "Walmart problem" is very similar to saturation of air with water vapor which is shown on p. 85 in the photocopied ClassNotes.


The evaporating water in Picture 1 is analogous to people entering a Walmart store just as the store opens in the morning.  There is initially no water vapor in the air in the covered glass but it will begin to buildup (Fig. 2).  Some fraction of the water vapor molecules will condense (even though they might have just evaporated), this is shown in Fig. 3.  The rates of evaporation and condensation aren't yet equal in Fig. 3 so the water vapor concentration will increase a little bit more until eventually the rate of condensation balances evaporation (Fig. 4).  The air is saturated at that point.  The water vapor concentration won't increase further.  Saturated air has a relative humidity (RH) of 100%. 

Cups filled with cold and warm water are shown at the bottom of the figure.  Because of different rates of evaporation (slow in cold, rapid in warm water) the water vapor concentrations at saturation will be different.

This would be like going back and redoing the Walmart problem assuming that people were entering the store at different rates:  10 people/minute, 20 people/minute, and 30 people/minute.  You'd end up with 100, 200, and 300 people in the store once the entering and exiting rates were equal.

One last thing to notice in the bottom part of the figure above.  The relative humidities in the cold and warm cups are the same (100%) even though the actual amounts of water vapor in the air are very different.  This is proof again that relative humidity really doesn't tell you how much water vapor is actually in the air.  It only tells you whether the air is full of water vapor or not.