Friday Feb. 21, 2014


Xavier Rudd "Better People",   "Time to Smile" before class because I'm feeling a lot better after having graded 80+ experiment reports and (together with my TAs) having looked at 280+ quizzes.

Quiz #1 has been graded and was returned in class today.  The average score was 75%.  The calculation below shows what sort of final grade you might expect if you were to score 76% on the remaining quizzes (the 76% was the average grade for the other section of the class and I didn't want to redo the figure, the end result would be nearly the same if 75% were used in the calculation).

The average of three quiz scores (pt. 1) and your writing grade (pt. 2) would be computed.  1.5 pts of extra credit (pt. 3) would be added to the average.  You'd end up with a before the final exam average of 83.5%, a solid B (pt. 4).  Note we've assumed a writing grade of 100%.  You'd get that by scoring 35 out of 40 on the experiment report and earning 45 1S1P pts. 

We'll assume you're happy with a B in the class (especially since you got Cs on all the quizzes).  We calculate in the 2nd equation how low of a score you could get on the Final Exam and still preserve the B.  The 80% at pt. 5 shows the desired grade.  Your current average (pt. 6) is 80% (pt. 7) of your overall grade.  Your final exam score (pt. 8) will count as 20% of your overall grade (pt. 9).

You'd only need 66% on the Final Exam to keep a B in the class (69% if the 75% average were used throughout).

How is it possible that with Cs on the quizzes and a D on the Final Exam you would end up with a B in the class?  The answer is the writing grade.  There is no reason not to get 100% on the writing grade and doing so can have a big effect on your overall grade.

This is about as much math as you'll ever have to do in this class.

An In-class Optional Assignment was collected at the end of today's class.  Students provided answers to 5 questions asked during the course of the class.  If you weren't in class but are reading these online notes you can turn in answers to the question embedded in the notes and receive at least partial credit.

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.

Types of energy
We will learn the names of several different types or forms 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 that we can see and feel (you feel warm when you stand in sunlight).  Everyone in the classroom is emitting 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. 




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 (the energy had been added earlier when ice was melted or water was evaporated).

Here's the 1st of the In-class Optional Assignment questions:
1.  Can you think of any additional types/forms of energy?




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)

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.

Here's another In-class Optional Assignment question
2.  What's the difference between energy & power?

Energy transport
Four energy transport processes are listed below


 

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 a 3rd way of causing 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.

The next In-class Optional Assignment question is
3.  The Gulf Stream is a well known ocean current.  Where is it?  What do you know about it?  Is it a warm or cold current?  What direction does it move?  Can you see or appreciate how it is able to transport energy?

Energy balance and the atmospheric greenhouse effect

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.




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.  If you periodically deposit money into your account why doesn't the balance just grow without limit.  The answer is that you also take money out of the account and spend it.  The same is true of energy and the earth.  The earth absorbs incoming sunlight energy but also emits energy back into space (the orange and pink arrows in the figure below).  Energy is emitted by both the surface of the earth and the atmosphere.




Energy emitted in the form of infrared light is an invisible form of energy (it is weak enough that we don't usually feel it either).  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).




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

The next to last question on today's assignment pertains to the figure above.
4.  How is energy transported back and forth between the earth's surface and atmosphere?







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 also).  That's a subject we'll explore later in the semester.


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 small pan will heat up more quickly.  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 (500 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.

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. 

Here's another situation where you can take advantage of water's high specific heat to moderate climate on a smaller scale.




This is what I'll be doing about this weekend, planting tomatoes.  I do this 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 can 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.

Now in anticipation of an in-class experiment planned for next Monday.

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




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.   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.

Here's the last of the In-class Optional Assignment Questions
5.  Can you name the three phase changes shown in the figure above.