Fri., Feb. 2, 2007

The Practice Quizzes and the first Optional Assignment were returned in class today (note if you don't have a grade marked on your paper you received full credit).  Be sure to keep any graded work that is returned to you just in case an error is made inputting grade data into the computer used to calculate your grade for the class.  The Practice Quiz grades were not recorded, the optional assignment grades were recorded.

The Experiment #1 reports and the 1S1P Assignment #1 reports are due next Monday (Feb. 5).  Students signed up for Expt. #2 should expect to receive the experiment materials next week.

We learned about the ideal gas law before the quiz on Wednesday.  This was the first of three steps that would lead to a better understanding of why warm air rises and cold air sinks.  Today we will look at the 2nd and 3rd steps and finish that section.  The 2nd step is Charles' Law which is a special case of the ideal gas law (pressure stays constant).


Air in the atmosphere behaves like air in a balloon.  A balloon can grow or shrink in size depending on the pressure of the air inside. 

We start in the upper left hand corner with air inside a balloon that is exactly the same as the air outside.  The air inside and outside have been colored green.  The brown arrows show that the pressure of the air  inside pushing outward and the pressure of the air surrounding the balloon pushing inward are all the same. 

Next we warm the air in the balloon (Fig. 2).  The ideal gas law equation tells us that the pressure of the air in the balloon will increase.  The increase is momentary though. 

Because the pressure inside is now greater than the pressure outside, the balloon will expand.  As volume begins to increase, the pressure of the air inside the balloon will decrease.  Eventually the balloon will expand just enough that the pressures inside and outside are again in balance.  You end up with a balloon of warm low density air that has the same pressure as the air surrounding it (Fig. 3)

You can use the same reasoning to understand that cooling a balloon will cause its volume to decrease.  You will end up with a balloon filled with cold high density air.  The pressures inside and outside the balloon will be the same.

These associations: warm air = low density air and cold air = high density air are important and will come up a lot during the remainder of the semester.


Charles Law can be demonstrated by dipping a balloon in liquid nitrogen.  When you pull the balloon out of the liquid nitrogen it is very small.  It is filled with cold high density air.  As the balloon warms the balloon expands and the density of the air inside the balloon decreases.   Air temperature and air density (or volume) inside the balloon change in a way that keeps the pressure constant.
The last of the three steps (in trying to better understand why warm air rises and cold air sinks) is to look at the upward and downward pointing forces that act on a balloon and try to figure out why sometimes one force sometimes the other force is dominant.


Air has mass and weight   When an air parcel has the same temperature, pressure, and density as the air around it, the parcel will remain stationary.  With gravity pulling downward on the air, there must be another force pointing upward of equal strength.  The upward force is caused by pressure differences between the bottom (higher pressure pushing up) and top of the balloon (slightly lower pressure pushing down on the balloon).

If the balloon is filled with warm, low density air the gravity force will weaken (there is less air in the balloon so it weighs less). The upward pressure difference force (which depends on the surrounding air) will not change.  The upward force will be stronger than the downward force and the balloon will rise. 

Conversely if a balloon is filled with cold low density air, gravity will strengthen and the balloon will sink.
 


We modified the earlier demonstration somewhat (see bottom of p. 54 in the photocopied class notes).  We used a balloon filled with hydrogen instead of air.  Hydrogen is less dense than air even when the hydrogen has the same temperature as the surrounding air.  A hydrogen filled balloon doesn't need to warmed up in order to rise.

We dunked the hydrogen filled balloon in some liquid nitrogen to cool it and to cause the density of the hydrogen to increase.  When removed from the liquid nitrogen the balloon can't rise, the gas inside is denser than the surrounding air (the purple and blue balloons in the figure above).  As the balloon warms and expands its density decreases.  The balloon at some point has the same density as the air around it (green above) and is neutrally bouyant.  Eventually the balloon becomes less dense that the surrounding air (yellow) and floats up to the ceiling.

You might have a look at the material on Archimedes' Law on pps 53a and 53b in the photocopied Class Notes.  That explains this same material in a slightly different way, a way that you might be better able to relate to.
Now back to surface weather maps.  Weather data has been plotted onto the surface weather map below using the station model notation.


Plotting the surface weather data on a map is just the beginning.  For example you really can't tell what is causing the cloudy weather with rain and drizzle in the NE portion of the map above or the rain shower at the location along the Gulf Coast.  Some additional analysis is needed.  A meteorologist would usually begin by drawing some contour lines of pressure to map out the large scale pressure pattern.  We will look first at contour lines of temperature, they are a little easier to understand.


Isotherms, temperature contour lines, are drawn at 10 F intervals. They do two things: (1) connect points on the map that all have the same temperature, and (2) separate regions that are warmer than a particular temperature from regions that are colder.  The 40o F isotherm highlighted in brown above passes through one city reporting a temperature of exactly 40o (highlighted in yellow).  Mostly it goes between pairs of cities: one with a temperature warmer than 40o and the other colder than 40o.  Temperatures generally decrease with increasing latitude.

Now the same data with isobars drawn in.  Again they separate regions with pressure higher than a particular value from regions with pressures lower than that value.    Isobars are generally drawn at 4 mb intervals.  Isobars also connect points on the map with the same pressure.  The 1008 mb isobar (highlighted in brown) passes through a city where the pressure is exactly 1008.0 mb (highlighted in yellow).  Most of the time the isobar will pass between two cities.  The 1008 mb isobar passes between cities with pressures of 1006.8 mb and 1009.7 mb.  You would expect to find 1008 mb about halfway between those two cites, that is where the 1008 mb isobar goes.

Next Monday we'll look at what you can expect to see in the vicinity of centers of Low and High pressure.