Mon., Feb. 24, 2014

A couple of songs from Brandi Carlile before class today: "Helplessly Hoping" and "The Story".

The 1S1P Assignment #1 reports on stratospheric ozone have been graded and were returned today.  That leaves just the carbon dioxide topic left to grade.  The first of the Assignment #2 topics, the Surface Weather Map Analysis, is due Wednesday this week.

The Upper Level Charts Optional Assignment was collected today (that's the one that will earn you a Green Card if you do a good job on the assignment).  The Optional Assignment on the station model notation and surface weather maps (collected last Monday) was returned today together with the In-class Optional Assignment from last Friday.  Several students did have a look at the online lecture notes over the weekend (something everyone should be doing), found the assignment, and turned it in at the start of class today.  They'll receive credit for the assignment.





Here's a particularly photogenic storm system with a long cold front.  Pressure at the center of the storm (up near the Great Lakes) is about 980 mb.  Note the long line of cloudy weather stretching along the length of the cold front.

You may notice a couple of types of fronts that are unfamiliar.  First extending out from the low pressure center, in magenta, with both half circles and "points", is an occluded front. 

Occluded fronts form when a cold front, which typically moves at 15 to 25 MPH, overtakes a warm front, which move at 10 to 15 MPH.  This is shown in the sketch below.



The top figure shows crossectional views of a cold front and a warm front.  The advancing cold air mass has a rounded shape.  At a warm front warm air overtakes and overuns the back retreating edge of a cold air mass.  The back edge has a ramp like shape.

When the advancing edge of cold air (the cold front) catches the retreating edge of cool air at the warm front, the cold air wedges its way underneath the slightly less dense cool air.  There is no longer any warm at ground level - it has all been lifted by the colder air.  Because air is being lifted cloud formation and precipitation is found along occluded fronts.



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. (a picture from a previous semester).



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.

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.


This next figure might make clearer the difference between temperature (average kinetic energy) and heat (total kinetic energy).  This figure (p. 46a in the ClassNotes) wasn't shown in class.




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 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 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 change the total energy of the water in the pool, i.e. cool (or warm) all the water in the pool, than it would be to change the total energy of the water in the cup.

The difference between temperature and heat can be understood by considering groups of people and money (the people represent atoms or molecules and the money is analogous to kinetic energy).  Both groups above 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).


Energy transport by conduction
Conduction is the first of four energy transport processes that we will cover (and the least important transport process in the atmosphere).  The figure below illustrates this process.  Imagine heating the end of a piece of copper tubing just so you can visualize a hot object.  If you held the object in air it would slowly lose energy by conduction and cool off.



How does that happen?  In the top picture some of the atoms or molecules near the hot object have collided with the object and picked up energy from the object.  This is reflected by the increased speed of motion or increased kinetic energy of these molecules or atoms (these guys are colored orange). 

In the middle picture the initial layer of energetic molecules have collided with some of their neighbors and shared energy with them (these are pink).  The neighbor molecules have gained energy though they don't have as much energy as the molecules next to the hot object.

In the third picture molecules further out (yellow) have now gained some energy.  The random motions and collisions between molecules is carrying energy from the hot object out into the colder surrounding air.

Conduction transports energy from hot to cold.  The rate of energy transport depends first on the temperature gradient or temperature difference between the hot object and the cooler surroundings.  If the object in the picture had been warm rather than hot, less energy would flow and energy would flow at a slower into the surrounding air.

The rate of energy transport also depends on the material transporting energy (air in the example above).  Thermal conductivities of some common materials are listed.  Air is a very poor conductor of energy and is generally regarded as an insulator. 

Water is a little bit better conductor.  Metals are generally very good conductors (cooking pans are often made of stainless steel but have aluminum or copper bottoms to evenly spread out heat when placed on a stove).  Diamond has a very high thermal conductivity (apparently the highest of all known solids).  Diamonds are sometimes called "ice."  They feel cold when you touch them.  The cold feeling is due to the fact that they conduct energy very quickly away from your warm fingers when you touch them.


I brought a propane torch to class to demonstrate the behavior of materials with different thermal conductivities.  Because of time constraints I only actually demonstrated the rightmost picture in class.  I'll have the torch again in class on Wednesday and will demonstrate how much better a conductor copper is than glass.





A piece of copper tubing is held in the flame in the picture at left.  Copper is a good conductor.  Energy is transported from the flame by the copper and you must grab the tubing several inches from the end to keep from burning your fingers.  Part of a glass graduated cylinder is held in the flame in the center picture.  You could comfortably hold onto the cylinder just a couple of inches from the end because glass is a relatively poor conductor.  The end of the glass tubing got so hot that it began to glow (its is emitting radiant energy, the 4th of the energy transport processes we will discuss).  Air is such a poor conductor that it is safe to hold your finger just half an inch from the hot flame and still not feel any heat coming from the flame (but be careful putting your hand or fingers above the flame)

Transport of energy by conduction is similar to the transport of a strong smell throughout a classroom by diffusion.  Small eddies of wind in the classroom blow in random directions and move smells throughout the room.  For a demonstration you need something that has a strong smell but is safe to breathe.





Last semester I had great hopes for Vicks Vapo Rub which contains Camphor, Eucalyptus Oil and Menthol.  But that didn't work very well.  So this semester I again tried curry powder.
 


It didn't work very well either.  The classroom is too large and the ventilation system too efficient.  Though sometimes a demonstration that doesn't really work can be instructive.  I'll bring the curry powder to class again on Wednesday and we'll add a little change to the demonstration and hopefully get the smell to spread further out into the room.  

Because air has such a low thermal conductivity it is often used as an insulator.  It is important, however, to keep the air trapped in small pockets or small volumes so that it isn't able to move and transport energy by convection (we'll look at energy transport by convection on Wednesday).  Here are some examples of insulators that use air:




Foam is often used as an insulator.  Foam is filled with lots of small air bubbles, they're what provides the insulation.

You can safely hold onto a foam cup filled with liquid nitrogen (-320 F) because the foam does such a good job insulating your fingers from the cold liquid inside.




Thin insulating layer of air in a double pane windowI don't have double pane windows in my house.  As a matter of fact I leave a window open so my cats can get in and out of the house (that's not particularly energy efficient).

We really haven't needed winter coats much this winter in Tucson.



Hollow fibers (Hollofil) filled with air used in sleeping bags and ski coats.  Goose feathers (goosedown) work in a similar way.  Fiberglas insulation is another example.  It works so well as an insulator first because it is glass which has low thermal conductivity and also because it traps lots of little pockets of air.


We really didn't cover much material today because I wanted to leave time for an in-class experiment.  Three students from class volunteered to help.

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 water.  The water will cool as energy is taken from it and used to evaporate liquid nitrogen.

We'll be able to use a thermometer to measure how much the water cools and use that to determine how much energy was taken from the water.  This is illustrated below:





As we saw last Friday, adding energy to an object will cause it to warm up.  If you know how much energy you added, the object's mass and specific heat, you can calculate the temperature change that will result using the left equation above.

Now we'll just rearrange the terms in the equation so that we can use a measurement of temperature change to determine the amount of energy added or removed.  That's the equation at right.

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


The cup and the water together weighed 169.5 g of room temperature water.  The cup weighed 4.0 g, so we really had 165.5 g of water.  The students measured its temperature, 23 C.

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


We're going to evaporate 33.0 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 33.0 grams of liquid nitrogen into the cup containing 165.5 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 14 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 = 45.1 calories/gram (48.8 cal/g later in the day in the 10 am class).  A trustworthy student in the class informed us that the known value is 48 cal/g.  Our measurement was pretty darn close to the known value.