Thursday, Sept. 12, 2019

Jenny and the Mexicats "Frenetico Ritmo" (0-2:50), "The Song for UV House Mouse" (3:05 - 8:15 = 5:10), appearing on NPR Tiny Desk Concert, "La Noche" feat. Sandoval (4:24), "Llueve en el Mar" feat. Juan Solo (0:45 - 5:39 = ~5:00).  Jenny and the Mexicats will be appearing tomorrow (Fri., Sept. 13) at the Rialto Theatre in downtown Tucson.

We'll be using page 49, page 50, and page 51 from the ClassNotes today.


We were able to just get started on this topic at the end of class on Tuesday (Sept. 10)
Trying to understand why warm air rises & cold air sinks
                                                        












Hot air balloons floating over the Rio Grande river during the 2013 Albuquerque Balloon Fiesta (source of the photo)
 Photograph of a microburst, a localized intense thunderstorm downdraft, that hit Wittmann Arizona in July 2015.  Surface winds of 55 MPH were measured. (source of the photo)
 Cold sinking air.  The air was cooled by coming into contact with a piece of dry ice. (image source)

A full understanding of these rising and sinking motions is a 3-step process (the following is found on page 49 in the photocopied ClassNotes).




We will first learn about the ideal gas law.  It's is an equation that tells you which properties of the air inside a balloon work to determine the air's pressure. 

Next we will look at Charles' Law, a special situation involving the ideal gas law (air temperature volume, and density change together in a way that keeps the pressure inside a balloon constant).  Then we'll learn about the 2 vertical forces that act on air.  I'm pretty sure you know what the downward force is and suspect that you don't recall what the upward force is (hint we talked about it in class on Tuesday ).

The ideal gas law - a microscopic scale explanation of air pressure




We've spent a fair amount of time learning about pressure.  We first began with the idea that pressure is determined by the weight of the air overhead.  Air pressure pushes down against the ground at sea level with 14.7 pounds of force per square inch.  That's a perfectly sound explanation.

We then went a bit further and tried to imagine the weight of the atmosphere pushing down on a balloon sitting on the ground.  If you actually do push on a balloon you realize that the air in the balloon pushes back (and sideways) with the same force.  Air pressure everywhere in the atmosphere pushes upwards, downwards, and sideways.

These are large scale, atmosphere size, ways of thinking about pressure.  Next we are going to forget the atmosphere and focus in on just the air in the balloon. This is more of a microscopic view of pressure.
We'll probably start at this point in class on Thursday

Imagine filling a balloon with air.  If you could look inside which picture below would be more realistic?



The view on the left is incorrect. 
The air molecules do not fill the balloon and
do not take up all the available space. 


This is the correct representation. 
The air molecules are moving around at 100s of MPH
but actually take up little or no space in the balloon.




The air molecules are continually colliding with the walls of the balloon and pushing outward (this force divided by area is the pressure).  Wikipedia has a nice animation.  An individual molecule doesn't exert a very strong force, but there are so many molecules that the combined effect is significant.


We want to identify the properties or characteristics of the air inside the balloon that determine the pressure and then put them together into an equation called the ideal gas law.


The ideal gas law equation
You're not going to have to be able to figure out or remember the ideal gas law equation.  I'll give it to you.  Here is is:



You should know what the symbols in the equation represent.  Probably the most obvious variable is N the number of air molecules.  It's the motions of the air molecules that produce pressure.  No air molecules (N = 0) means no pressure.  The more air molecules there are the higher the pressure.

Number of gas molecules or atoms



Pressure (P) is directly proportional to Number of air molecules (N).  If N increases P increases and vice versa.



Here's an example.  You're adding air to a tire.  As you add more and more air to something like a bicycle tire, the pressure increases.  Pressure is directly proportional to N; an increase in N causes an increase in P.  If N doubles, P also doubles (as long as the other variables in the equation don't change).

Temperature
Here's what I think is the next most obvious variable.



You shouldn't throw a can of spray paint into a fire because the temperature will cause the pressure of the gas (propellant) inside the can to increase and the can could explode.  So T (temperature) belongs in the ideal gas law equation



Increasing the temperature of the gas in a balloon will cause the gas molecules to move more quickly (kind of like "Mexican jumping beans").  They'll collide with the walls of the balloon more frequently and rebound with greater force - that will increase the pressure.



We've gotten a little bit ahead of the story.  The variable V (volume) has appeared in the equation and it's in the denominator.  A metal can is rigid.  It's volume can't change (up until the moment the can explodes).  When we start talking about air in balloons or in the atmosphere volume can change.  A change in temperature or a change in number of air molecules might be accompanied by a change in volume.  Balloons and cans of spray paint are sealed, so N also stays constant.

At this point we did a quick demonstration to show the effect of temperature on the pressure of the gas in a rigid sealed container (N and V in the ideal gas law equation stay constant, just as in a can of spray paint).

The container was a glass flask, sealed with a rubber stopper.  A piece of tubing with a valve was connected to the flask.  The valve was opened at the start of the demonstration to be sure the pressures inside and outside the flask were equal.  The valve was then closed.  The manometer is a U-shaped tube filled with a liquid (transmission oil) that can detect differences in pressure.  Pressure from the air inside the flask could enter one end of the manometer tube.  The other end was exposed to the pressure of the air outside the flask. 

Green in the figure indicates that the temperatures of the air inside and outside the flask were equal.  The manometer is showing that the pressure of the air inside and outside the flask were equal.


I wrapped my hands around the flask to warm the air inside very slightly.  The increase in air temperature caused a slight increase in the pressure of the air inside the flask.  The air outside didn't change.  Note the change in the levels of the liquid in the manometer indicating the increase of the air pressure inside the flask.

The valve was opened momentarily so that the pressures inside and out would again be equal.  The valve was then closed and some isopropyl alcohol (rubbing alcohol) was dribbled on the outside of the flask.  As the alcohol evaporated it cooled the flask and the air inside the flask.  This caused the air pressure inside the flask to drop.  This change in air pressure was again indicated by the liquid levels in the manometer.

Volume
The effect of volume on pressure might be a little harder to understand.  Just barely fill a balloon with air, wrap your hands around it, and squeeze it.  It's hard to compress the balloon, you can't really compress it very much at all.


Think of the bottom layer of the atmosphere being squished by the weight of the air above.  As the bottom layer is compressed and its volume shrinks it pushes back with enough force to eventually support the air above.



A decrease in volume causes an increase in pressure, that's an inverse proportionality. 



It might take three or four breaths of air to fill a balloon.  Think about that.  You add some air (N increases) and the balloon starts to inflate (V increases).  Then you add another breath of air.  N increases some more and the balloon gets a little bigger, V has increased again.  As you fill a balloon N and V are both increasing.  What is happening in this case is that the pressure of the air in the balloon is staying constant.  The pressure inside the balloon pushing outward and trying to expand the balloon is staying equal to (in balance with) the pressure of the air outside pushing inward and trying to compress the balloon.

Here's the same picture again except N and V are decreasing together in a way that keeps pressure constant.  This is exactly what occurs during Experiment #1.

 
Experiment #1 - P stays constant, N & V both decrease

Here's a little more detailed explanation of Expt. #1



The object of Experiment #1 is to measure the percentage concentration of oxygen in the air.  An air sample is trapped together with some steel wool inside a graduated cylinder.  The cylinder is turned upside down and the open end is stuck into a glass of water sealing off the air sample from the rest of the atmosphere.  This is shown at left above.  The pressure of air outside the cylinder tries to push water into the cylinder, the pressure of the air inside keeps the water out.

Oxygen in the cylinder reacts with steel wool to form rust.  Oxygen is removed from the air sample which causes N (the total number of air molecules) to decrease.  Removal of oxygen would ordinarily cause a drop in Pin  and upset the balance between Pin  and Pout .  But, as oxygen is removed, water rises up into the cylinder decreasing the air sample volume.  The decrease in V is what keeps Pin  equal to Pout .  N and V both decrease together in the same relative amounts and the air sample pressure remains constant.  If you were to remove 20% of the air molecules, V would decrease to 20% of its original value and pressure would stay constant.  It is the change in V that you can see, measure, and use to determine the oxygen percentage concentration in air.  Those of you doing the experiment should try to explain this in your experiment report.

You might think that the mass of the gas molecules inside a balloon might affect the pressure (big atoms or molecules might hit the walls of the balloon harder and cause higher pressure and vice versa).


The mass of the air molecules doesn't matter.  The big ones move relatively slowly, the smaller ones more quickly.  They both hit the walls of the balloon with the same force.  A variable for mass doesn't appear in the ideal gas law equation.

The ideal gas law equations
The figure below shows two forms of the ideal gas law.  The top equation is the one we've been looking at and the bottom is a second slightly different version.  You can ignore the constants k and R if you are just trying to understand how a change in one of the variables would affect the pressure.  You only need the constants when you are doing a calculation involving numbers and units (which we won't be doing).



The ratio N/V is similar to density (mass/volume).  That's where the ρ (density)  term in the second equation comes from.