Thursday Sep. 29, 2011
click here to download today's notes in a more printer friendly format

A couple of songs from Dire Straits this morning ( "Brothers in Arms" and "Down to the Waterline")

After a monumental effort, the Expt. #1 reports have been graded and were returned in class today.  You are allowed to revise your reports if you want to (you don't have to).  The revised reports will be due in 2 weeks, on or before Thu., Oct. 13 (the date of Quiz #2).  You only need to rewrite portions where you want to earn additional credit.  Please return your original report with your revised report.

And to encourage people to read through the Online Notes, I'm likely to bury a link to an Optional Assignment or maybe embedding questions in the Online Notes.  So keep an eye out for that.

During the next couple of weeks we will be moving into a completely different topic and 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 (found on pps 43&44 in the photocopied Class Notes) is meant to introduce some of what we will be covering in class.  (some of the figures that follow are from a previous semester and may differ somewhat from what we did in class)


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.

Latent heat energy is perhaps the most underappreciated and most confusing type of energy. The word latent refers to energy that is hidden in water and water vapor.  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).

Radiant energy is a very important form of energy that was for some reason left off the original list.  Sunlight is an example of radiant energy that we can see and feel (you feel warm when you stand in sunlight).  There are many types of radiant energy that are invisible (such as the infrared light that people emit).  Electromagnetic radiation is another name for radiant energy.



Water vapor is effectively a particularly important form of invisible energy.  When water vapor condenses to produce the water droplets (or ice crystals) in a cloud, an enormous amount of latent heat energy is released into the atmosphere.  This then might get turned into the violent winds in a tornado or a hurricane. 

It is hard to visualize or appreciate the amount of energy released into the atmosphere during condensation.  You can imagine the work that you would need to do to carry a gallon of water (8 pounds) from Tucson to the top of Mt. Lemmon.  To accomplish the same thing Mother Nature must first evaporate the water and (if my calculations are correct) that requires about 100 times the energy that you would use to carry the 8 pounds of water to the summit of Mt. Lemmon.  And Mother Nature transports a lot more than just a single gallon.

Hurricanes derive their energy from the heat in warm ocean water and from latent heat in water vapor that condenses while forming the clouds of the hurricane.

Energy transport
Four energy transport processes are listed below.

 

By far the most important process is energy transport in the form of electromagnetic radiation (sunlight is a common form of electromagnetic radiation).  This 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.

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.  Ocean currents are also an example of convection.  Ocean currents transport energy from the warm tropics to colder polar regions.  Not all of these details were mentioned in class.

Convection is a 3rd way of causing rising air motions in the atmosphere (convergence into centers of low pressure and fronts are other 2 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.

Energy balance and the atmospheric greenhouse effect
The next picture (the figure drawn in class 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 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. 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 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.

The detrimental side is that atmospheric greenhouse gas concentrations are increasing.  This might enhance or strengthen the greenhouse effect and cause the earth to warm.  While that doesn't necessarily sound bad it could have many unpleasant side effects.  That's a subject we'll explore briefly later in the semester.

When you add energy to an object, the object will usually warm up (conversely when 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 (one of those equations I'll probably write on the board during 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. 

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, note that calories are units of energy) are added to equal masses (50 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. Water has a higher specific heat than soil, it only warms up 2o C.  The soil has a lower specific heat and warms up 10o C, 5 times more than the water (the specific heat of the soil is 5 times smaller than that of water).

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.
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.  We'll see a much more dramatic example of the moderating effect of water on climate in a couple of weeks.

Here's another situation where you can take advantage of water's high specific heat to moderate "micro climate."



If this were the Spring semester I would probably already have planted some tomatoes in my vegetable garden.  The start of my summer vegetable garden.  It still gets plenty cold enough at night in February or early March to kill tomatoes (the brocolli and lettuce in the background can handle a light frost) so you have to protect the them.




Here's one way of doing that.  You can surround each plant with a "wall of water"  -  a tent 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 microclimate that the tomato seedlings love.

This being the Fall semester I will probably be planting my winter vegetable garden soon, maybe even this coming weekend.  I mention it because if something bad happens to the young seedlings I'm likely to get very mad.  If you hear of a freak hailstorm, torrential rains, or something like that it might be a good idea to sit in the back of the classroom until you see what kind of a mood I'm in.

Adding energy to an object will usually cause it to warm.  But there is another possibility (bottom p. 45),  the object could change phase (change from solid to liquid or gas).  Adding energy to ice might cause the ice to melt.  Adding energy to water could cause it to evaporate. 

The equation at the bottom of the figure above allows you to calculate how much energy is required to melt ice or evaporate water or sublimate dry ice.  You multiply the mass by the latent heat, a variable that depends on the particular material that is changing phase.  The latent heat of vaporization (evaporation) is the energy required to evaporate 1 gram of a material.

If you add energy to or remove energy from an object, the object will usually change temperature.  You can calculate the temperature change if you know the object's mass and its specific heat.  That's the equation we used in the example calculation above.  It's shown again below.

We conducted an experiment in the last part of the class and we needed to be able to measure ΔE.


It's not that hard to do.  If you are able to measure the ΔT that occurs when energy is added to or removed from an object we can write the same equation in slightly different form and use it (and the measurements of ΔT) to compute ΔE.

A couple of groups of students from the class were nice enough to volunteer to perform the experiment.

The students that are doing Experiment #2 are doing something similar, they are measuring the latent heat of fusion of ice, the energy needed to melt one gram of ice. 

You'll find the following figure on p. 45a in the photocopied Classnotes.  This is pretty confusing even after I neatened it up a little bit after class.  And to make matters even worse, I think I made a couple of calculation mistakes when we were working through this.  I'll point them out as we work through this step by step below.



So here's a step by step explanation of what the students did:
(a)
Some room temperature water poured into a styrofoam cup weighed 180.1g.  The cup itself weighed 3.5 g, so they had 176.6 g of water.


(b)
The water's temperature was measured with the thermometer and was 23.8 C  (room temperature).

(c)
Some liquid nitrogen was poured into a second smaller styrofoam cup.  That weighed 55.0 g.  Subtracting the 2.8 g weight of the cup means we had 52.2 g of liquid nitrogen.  Here's the first mistake: I'm pretty sure I forgot to subtract the 2.8 g while working through this in class.

We don't need to measure the temperature of the liquid nitrogen (doing so would probably destroy the thermometer).  It had already warmed as much as it can ( to -320 F or something like that).  Any additional energy added to the liquid nitrogen will cause it to evaporate.

(d)
After the liquid nitrogen had evaporated the water's temperature was remeasured.  It had dropped to 7.5 C. 


We started out with water that was 23.8.0 C, so that is a temperature drop of 16.3 C.

It takes energy to turn liquid nitrogen into nitrogen gas.  The energy needed will be taken from the water (the red arrow below, energy naturally flows from hot to cold). 


Because the experiment was performed in an insulated sytrofoam cup we will assume all of the energy taken from the water is used to evaporate nitrogen.  No energy flows into the room air or anything like that.  We will set the two equations above equal to each other.  This is an energy balance equation.

We know the mass of the nitrogen (45.8 g) and the water (172.3 g).  We measured the ΔT (14.5 C) and we know the specific heat of water (1 cal/g C).  We substitute them into the equation above and solve for LH, the latent heat of vaporization of liquid nitrogen.  Here are the details of the calculation:

This is where I found the 2nd mistake.  I wrote down 2875.6 calories in class (probably misread the number in the dim light at the front of the room).

A responsible & trustworthy student in the class (though not a Buddhist monk) informed us that the known value is 48 cal/g, so this measurement was pretty close to the known value.

A second group of students also conducted an independent measurement of LH.  Their data are shown above, see if you can calculate LH.  Once you've given it a try (and only after you've spent some time on it) click here to see if you did the calculation correctly.



Here's the equation again that allows you to determine how much of a temperature change will occur when energy is added to or removed from an object. 

What exactly is happening inside an object when it's temperature changes?


The figure above is on p. 46 in the photocopied Class Notes.  Temperature provides a measure of the average kinetic of the atoms or molecules in a material.  Kinetic energy is energy of motion, so the atoms or molecules in a cold material will be moving more slowly than the atoms or molecules in a warmer object.

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.

Speaking of temperature scales, there are three of them that you should be familiar with.

You should remember the temperatures of the boiling point and freezing point of water on the Fahrenheit, Celsius, and perhaps 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.  That's a number you should remember.



You certainly don't need to try to remember all these numbers.  They're mostly just for informational purposes and to help with questions on hidden optional assignments.  The world high temperature record was set in Libya, the US record 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 (water moderates climate).     Liquid nitrogen is 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.

This next figure might make clearer the difference between temperature (average kinetic energy) and heat (total kinetic energy).




A cup of water and a pool of water both have the same temperature.  The average kinetic energy of the water molecules in the pool and in the cup are the same.  There are a lot more water molecules in the pool than in the cup.  So if you add together all the kinetic energies of all the molecules in the pool you are going to get a much bigger total number than if you sum the kinetic energies of the molecules in the cup.  There is a lot more stored energy in the pool than in the cup.  It would be a lot harder to cool (or warm) all the water in the pool than it would be the cup.

In the same way the two groups of people shown have the same $10 average amount of money per person (that's analogous to temperature).  The $100 held by the larger group at the left is greater than the $20 total possessed by the smaller group of people on the right (total amount of money is analogous to heat).