Friday Feb. 17, 2012
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"Nothing Else Matters" from Apocalytica before class this afternoon.

Quiz #1 has been graded and was returned in class today.  Please check carefully to see that your quiz was graded correctly and hang on to this quiz and any other work that is returned to you during the semester.  Don't throw anything away until you've received and agree with your final grade at the end of the semester.

A new Optional Assignment is online.  You can earn extra credit and even a green card (see the fine print on the assignment itself).  The assignment is due at or before the start of class next Friday (Feb. 24).

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.  Most of the following figures are found on pps 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.



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 in the ClassNotes.  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.

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 is a common form of electromagnetic radiation) 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.

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 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 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 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).  I've changed the numbers from the example shown in class.



Equal amounts of energy (1000 calories, note that calories are units of energy) are added to equal masses (500 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 water?

Here are the details of the calculation.

With its higher specific heat, the water doesn't heat up nearly as much as the soil.  If we had been removing energy the soil would have cooled off more than the water also.

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."



I did plant some of my young tomato plants last weekend (this is a picture from a previous year).  It still can get 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 them.



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 microclimate that the tomato seedlings love.  The plastic is transparent so plenty of sunlight can get through.

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.  We hurried through this a little bit in class.


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.  We'll stick a thermometer into the object and measure any changes in temperature that occur.


If you know the mass and specific heat of an object and measure a change in temperature you can use the equation above to calculate how much energy was added to or removed from the object.

And on to the in-class experiment.  A couple of groups of students from the class were nice enough to volunteer to perform the experiment (an offer of a green card might also have had something to do with it).


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.
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.





So here's a step by step explanation of what the students did:
(a)


Some room temperature water poured into a styrofoam cup weighed 190.0g.  The cup itself weighed 3.7 g, so they had 186.3 g of water.  The water's temperature was measured with the thermometer and was 22.5 C  (room temperature).

(b)
Some liquid nitrogen was poured into a second smaller styrofoam cup.  That weighed 58.5 g.  Subtracting the 2.4 g weight of the cup means we had 56.1 g of liquid nitrogen. 

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.

(c)
After the liquid nitrogen had evaporated the water's temperature was remeasured.  It had dropped to 6.9 C. 


We started out with water that was 22.5 C, so that is a temperature drop of 15.6 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 (56.1 g) and the water (186.3 g).  We measured the ΔT (15.6 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:

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