Thursday Feb. 26, 2015

"Rhapsody in Blue" (16:24); "Bumble Boogie" (4:36); "I Got Rhythm" (6:08), "Bolivar Blues" (3:15) the last two songs featured Marcus Roberts at the Piano (and if you have some extra time you should wathc this 60 Minutes segment on Marcus Roberts)

A new Optional Assignment is now available.  You can receive up to 0.5 points of extra credit or points that will be added to your Quiz #2 score (the points earned on the assignment will be added to the points missed total; the points earned on the assignment will reduce the number of points missed on the quiz).  The assignment is due at the beginning of class on Thursday Mar. 5.

The station model notation/surface weather maps Optional Assignment was returned in class today.  Remember if your paper doesn't have a score you earned full credit.  That doesn't mean you answered all the questions correctly and you should check your answers with those posted online.  I was surprised by the number of people that got latitude and longitude mixed up.  I mentioned in class that the last question on this Optional Assignment will appear on this year's final exam.

We won't be spending much classroom time on upper level charts but there are a few features that you should be familiar with.

First the overall appearance is somewhat different from a surface weather map.  The pattern on a surface map can be complex but you generally find circular (more or less) centers of high and low pressure (see the bottom portion of the figure below).  You can also find closed high and low pressure centers at upper levels, but mostly you find a relatively simple wavy pattern like is shown on the upper portion of the figure below (sort of a 3-dimensional view).  The figures and text below come from Upper Level Charts pt. 1, which is required reading.
 

Trough and ridge features on upper level charts.
A simple upper level chart pattern is sketched below (a pure top view).  There are two basic features: wavy lines that dip southward and have a "u-shape" and lines that bend northward and have an "n-shape".

The u-shaped portion of the pattern is called a trough.  The n-shaped portion is called a ridge.

Troughs are produced by large volumes of cool or cold air (the cold air is found between the ground and the upper level that the map depicts).  The western half of the country in the map above would probably be experiencing colder than average temperatures.  Large volumes of warm or hot air produce ridges. 




The eastern 2/3 rds of the United States was under an upper level trough yesterday (Feb. 25, 2015).  There is a ridge off the west coast of the US.  It is a little hard to see because most of the ridge lies to the left of the edge of the map. (source of this image)
 This map shows how temperatures across the country yesterday compared with normal for this time of year a temperature departure from normal map).  The blue that covers the eastern 2/3rds of the country indicates colder than normal.  That is associated with the upper level trough.  The west 25% of the country is warmer than normal because it is associated with an upper level ridge. (source of this chart)

An actual example of an upper level map is shown above at left.   Temperature data is shown in the figure at right.  Colder than normal temperatures at right match up well with an upper level trough on the map at left.  The warmer than average temperatures along the western US are associated with the eastern edge of an upper level ridge.
We're done with weather maps for the time being.  Though if interesting weather appears imminent I'll try to mention it in class.

If we were using a textbook in this class we'd be moving into Chapter 2!  During the next couple of weeks we will be concerned with energy, temperature, heat, energy transport, and energy balance between the earth, atmosphere, and space.

It is easy to lose sight of the main concepts because there are so many details.  The following is an introduction to this new section of material and most of the figures are found on pages 43 & 44 in the photocopied ClassNotes.

1. Types of energy





Kinetic energy is energy of motion.  Some examples (both large and microscopic scale) are mentioned and sketched above.  This is a relatively easy to visualize and understand form of energy.




Radiant energy is a very important form of energy that was for some reason left off the original list in the ClassNotes (pps 43&44).  Electromagnetic radiation is another name for radiant energy.  Sunlight is an example of radiant energy.  It's something that we can see and feel (you feel warm when you stand in sunlight).  But everyone in the classroom is emitting light, infrared light, an invisible form of radiant energy.  And actually the walls, ceiling, floor and even the air in the classroom are also emitting infrared light.  We can't see it.  Because it's there all the time I'm not sure whether we can feel it or not.






Latent heat energy is an under-appreciated and rather confusing type of energy. The word latent refers to energy that is hidden.  That's part of the problem.  But it is also the fact that the energy is contained in water vapor and water.  That seems like an unlikely place for energy to be found.    The hidden energy emerges when water vapor condenses or water freezes.

In the bottom picture above, sunlight shining on a tropical ocean warms and evaporates ocean water.  The sunlight energy is stored in the resulting water vapor.  A hurricane derives much of its energy from the condensation of water vapor (it also gets heat energy from the warm ocean water).

Energy units
Now just brief mention of units of energy


Joules are the units of energy that you would probably encounter in a physics class.  We'll usually be using calories as units of energy.  1 calorie is the energy need to warm 1 gram of water 1 C (there are about 5 grams of water in a teaspoon).  Your electric bill shows the amount of energy that you have used in a month's time, the units are kilowatt-hours.

Here's a little miscellaneous information that you don't need to worry about remembering.  You've probably seen the caloric content of food on food packages or on menus in restaurants.  1 food calorie is actually 1000 of the calories mentioned above. 




A 150 pound person would burn almost 500 calories while sleeping during the night (8 hours x 60 minutes per hour x 1 food calorie per minute).  This is about the energy contained in a donut.

2. Energy transport processes



 
By far the most important process is at the bottom of the list above.  Energy transport in the form of electromagnetic radiation (sunlight for example) is the only process that can transport energy through empty space.  Electromagnetic radiation travels both to the earth (from the sun) and away from the earth back into space.  Electromagnetic radiation is also responsible for about 80% of the energy transported between the ground and atmosphere.

You might be surprised to learn that latent heat is the second most important transport process.  This term latent heat can refer to both a type of energy and an energy transport process.

Rising parcels of warm air and sinking parcels of cold air are examples of free convection.  Because of convection you feel colder or a cold windy day than on a cold calm day (the wind chill effect).  Ocean currents are also an example of convection. 

Convection is also one of the ways of rising air motions in the atmosphere (convergence into centers of low pressure and fronts are two other ways we've encountered so far) 

Conduction is the least important energy transport at least in the atmosphere.  Air is such a poor conductor of energy that it is generally considered to be an insulator.

3. Energy balance
The next picture (the figure in the ClassNotes has been split into three parts for improved clarity) shows energy being transported from the sun to the earth in the form of electromagnetic radiation.  On average about half of this sunlight passes through the atmosphere and is absorbed at the ground.  This causes the ground to warm (sunlight energy striking the ocean warms the oceans but is also used to evaporate ocean water).  Measuring the energy in sunlight arriving at the surface of the earth is the object of Experiment #3.




We are aware of this energy because we can see it (sunlight also contains invisible forms of light) and feel it.  With all of this energy arriving at and being absorbed by the earth, what keeps the earth from getting hotter and hotter?  If you park your car in the sun it will heat up.  But there is a limit to how hot it will get.  Why is that? 

It might be helpful when talking about energy balance to think of a bank account.  You open a bank account and start depositing money.  The bank account balance starts to grow.  But it doesn't just grow without limit.  Why not?  The answer is that once you find money in the bank you start to spend it.  The same is true of energy and the earth.  Once the earth starts to warm it also starts to emit energy back into space (the orange arrows in the figure below).  Radiant energy is emitted by the ground, the oceans, and the atmosphere. 



Energy is emitted by the earth in the form of infrared light, an invisible form of energy (to human eyes anyways).  A balance between incoming and outgoing energy is achieved and the earth's annual average temperature remains constant.

We will also look closely at energy transport between the earth's surface and the atmosphere (see the figure below). This is where latent heat energy transport, convection and conduction operate (they can't transport energy beyond the atmosphere and into outer space).





This is also where the atmospheric greenhouse functions.  That will be a important goal - to better understand how the atmospheric greenhouse effect works.

The atmospheric greenhouse effect



The greenhouse effect is getting a lot of "bad press".  If the earth's atmosphere didn't contain greenhouse gases and if there weren't a greenhouse effect, the global annual average surface temperature would be about 0 F (scratch out -4 F and put 0 F, it's easier to remember).  Greenhouse gases raise this average to about 60 F and make the earth a much more habitable place.  That is the beneficial side of the greenhouse effect.  That's mostly what we'll be concentrating on - how can the greenhouse effect cause this warming, how can it produce this much warming.

The detrimental side is that atmospheric greenhouse gas concentrations are increasing (no real debate about that).  This might enhance or strengthen the greenhouse effect and cause the earth to warm (some debate here particularly about how much warming there might be).  While that doesn't necessarily sound bad it could have many unpleasant side effects (lots of debate and uncertainty about this).  That's a subject we'll explore at different times during the semester.

Energy, temperature, and specific heat
When you add energy to an object, the object will usually warm up (or if you take energy from an object the object will cool).  It is relatively easy to come up with an equation that allows you to figure out what the temperature change will be (this is another equation I'll write on the board before  the next quiz if you ask me to - try to understand it, you don't have to memorize it).



The temperature change, ΔT,  will first depend on how much energy was added, ΔE.  This is a direct proportionality, so ΔE is in the numerator of the equation (ΔE and ΔT are both positive when energy is added, negative when energy is removed)

When you add equal amounts of energy to large and small pans of water, the water in the small pan will get hotter.  The temperature change, ΔT, will depend on the amount of water, the mass.  A small mass will mean a large ΔT, so mass should go in the denominator of the equation. 

Specific heat is what we use to account for the fact that different materials react differently when energy is added to them.  A material with a large specific heat will warm more slowly than a material with a small specific heat.  Specific heat has the same kind of effect on ΔT as mass.  Specific heat is sometimes called "thermal mass" or "thermal capacity."  You can think of specific heat as being thermal inertia - a substance with high specific heat, lots of thermal inertia, will be reluctant to change temperature.

Here's an important example that will show the effect of specific heat (middle of p. 45).





Equal amounts of energy (100 calories) are added to equal masses (100 grams) of water and soil.  We use water and soil in the example because most of the earth's surface is either ocean or land. Before we do the calculation, try to guess which material will warm up the most.  Everything is the same except for the specific heats.  Will water with its 5 times larger specific heat warm up more or less than the soil?

The details of the calculation are shown below.

With its higher specific heat, the water doesn't heat up nearly as much as the soil.  If we had been removing energy the wouldn't cool off as much as the soil would.

Water moderates climate
These different rates of warming of water and soil have important effects on regional climate.




Oceans moderate the climate.  Cities near a large body of water won't warm as much in the summer and won't cool as much during the winter compared to a city that is surrounded by land.  Water's ΔT is smaller than land's because water has higher specific heat.

The yearly high and low monthly average temperatures are shown at two locations above.  The city on the coast has a 30o F annual range of temperature (range is the difference between the summer and winter temperatures).  The city further inland (assumed to be at the same latitude and altitude) has an annual range of 60o F.  Note that both cities have the same 60o F annual average temperature. 

Growing tomatoes in the desert - practical application
 Here's another situation where you can take advantage of water's high specific heat to moderate climate on a smaller scale.




I was out planting tomatoes in my garden last weekend.   They need to go in the ground early in Tucson so that so that they can start to make tomatoes before it starts to get too hot in May.  In February it can still get cold enough to kill tomatoes so they need some protection (the broccoli and lettuce in the background can handle a light frost.




Here's one way of doing that.  You moderate the climate and surround each plant with a "wall o water"  -  a teepee like arrangement that surrounds each plant.  The cylinders are filled with water and they take advantage of the high specific heat of water and won't cool as much as the air or soil would during a cold night.  The walls of water produce a warm moist micro climate that the tomato seedlings love.  The plastic is transparent so plenty of sunlight can get through.


Adding energy to something will usually cause its temperature to change.  But not always.  What else could happen? 

You put a pan of water on the stove and turn on the burner.  The water will warm.  It will only warm to a certain point however.  Then what happens?

Phase changes



The water will warm to 212 F (100 C) and then it will start to boil.  Adding energy to ice will first cause it to warm to 0 C.  But then it will stop warming and will start to turn to water.  Adding energy to an object can cause the object or material to change phase.  The dry ice above is sublimating (changing directly from solid to gas).
It is very easy to calculate how much energy is needed to cause a phase change.


The energy needed depends on the amount of material present (the mass) and on the material itself (that's the Latent Heat term above).  It also depends on the specific phase change.  I.e. there are different Latent Heat values depending on whether the material changes from solid to liquid, liquid to gas, or solid to gas.

Measuring the latent heat of vaporization (evaporation) of liquid nitrogen
We had just enough to conduct an experiment.  I was able, with some difficulty, to get a student to assist.

Here's the object of the experiment:

The source of energy in our experiment will be the energy contained in a cup of room temperature water.  We'll pour some liquid nitrogen into the cup of water.




Energy will naturally flow from hot (the water) to cold (the liquid nitrogen).  As energy is taken from the water it will cool.  We'll assume that all of the energy taken from the water is used to evaporate nitrogen, no energy flows from the cup into the surrounding air (that's part of the reason we conduct the experiment in a Styrofoam cup.


Our earlier equations is shown above at left.  If you know how much energy is added to something you could determine the temperature change that would result.  We can turn the equation around so that is we measure the temperature change that any object undergoes we can calculate the amount of energy added or removed (the equation at right).

Here we put everything together.  We'll determine how much energy is taken from the water.  Then we'll assume all of that energy is used to evaporate nitrogen.  That's the right hand equation above.


We start with a large styrofoam cup filled about 1/3 full with room temperature water.



The cup and the water together weighed 152.7 g of room temperature water.  The cup weighed 3.9 g, so we really had 148.8 g of water.  The student measured its temperature, 20.0 C.

Next the student poured some liquid nitrogen into a second, smaller styrofoam cup.




We're going to evaporate 35 grams of liquid nitrogen.  The total amount of energy needed to do that, ΔE, is the mass of the liquid nitrogen times the Latent Heat of
vaporization of Nitrogen (LHvap). 

ΔE = mass x LHvap

LHvap is the energy needed per gram to vaporize (evaporate) liquid nitrogen.  That's the quantity we are trying to measure.


We poured the 35 grams of liquid nitrogen into the cup containing 148.8 g of water.  Energy flows naturally from hot to cold.  We assume that any energy lost by the water is used to evaporate nitrogen.
Once the liquid nitrogen was gone (it had evaporated) we remeasured the water temperature.  It had dropped to 8.0 C.  Now we're ready to calculate the latent heat of vaporization
We set up an energy balance equation (energy lost by the water = energy used to evaporate nitrogen) and plugged in all our measured values.  We obtained a measured value of LHvap = 51.0 calories/gram (52.1 cal/g later in the day in the 9:30 am class).  A trustworthy student in the class informed us that the known value is 48 cal/g.  Not a bad result at all.


Here's a very little bit of more material.  We'll go over it quickly at the start of class on Tuesday, especially the information on temperature scales next Tuesday.  None of this was covered in class today.

Temperature and heat
You add energy to something and its temperature usually increases.  The figure below (p. 46 in the ClassNotes) shows you what happens inside an object when it's temperature changes.



The atoms or molecules inside the warmer object will be moving more rapidly (they'll be moving freely in a gas, just "jiggling" around while still bonded to each other in a solid).  Temperature provides a measure of the average kinetic energy of the atoms or molecules in a material. 

You need to be careful what temperature scale you use when using temperature as a measure of average kinetic energy.  You must use the Kelvin temperature scale because it does not go below zero (0 K is known as absolute zero). The smallest kinetic energy you can have is zero kinetic energy.  There is no such thing as negative kinetic energy.

You can think of heat as being the total kinetic energy of all the molecules or atoms in a material.

Temperature scales
Speaking of temperature scales




You should remember the temperatures of the boiling point and freezing point of water on at least the Fahrenheit and  Celsius scales (and the Kelvin scale if you want to).  300 K is a good easy-to-remember value for the global annual average surface temperature of the earth.  Remember 300 K and also that temperature never goes below zero on the Kelvin scale.



You certainly don't need to try to remember all these numbers.  The world high temperature record value of 136 F above was measured in Libya at a location that was only about 35 miles from the Mediterranean coast.  Water, as we have seen, moderates climate so it seemed odd that such a high temperature would have been recorded there.  The World Meteorological Organization recently decided the 136 F reading was invalid and the new world record is the 134 F measurement made in Death Valley.

The continental US cold temperature record of -70 F was set in Montana and the -80 F value in Alaska.  The world record -129 F was measured at Vostok station in Antarctica.  This unusually cold reading was the result of three factors: high latitude, high altitude, and location in the middle of land rather than being near or surrounded by ocean (again water moderates climate, both hot and cold).  

Liquid nitrogen is very cold but it is still quite a bit warmer than absolute zero.  Liquid helium gets within a few degrees of absolute zero, but it's expensive and there's only a limited amount of helium available.  So I would feel guilty bringing some to class and I don't think it would look any different than liquid nitrogen.