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30 November 2009

Live PV diagrams!

It’s time to teach the ideal gas law, heat engines, and PV diagrams in AP physics. A lot of AP teachers are a bit intimidated by these topics. They’re more abstract than mechanics, and are farther divorced from our experience than, say, electricity and magnetism or waves and optics. I hope this next series of posts can help out.

Certainly your students have studied the ideal gas law in chemistry. But chances are, all they did (in their minds) was plug numbers into the equation PV=nRT. A major first step in teaching this unit is to give your class a firm understanding of the physical meaning of each of these variables.

You may or may not have seen Pasco’s heat engine / gas law apparatus. It consists of a low-friction piston that attaches to a metal cylinder – see the picture above. I use it to demonstrate the ideal gas law and PV diagrams with live data collection.

The three variables to measure are pressure, volume, and temperature of the gas in the cylinder. I attach a Vernier pressure probe to one of the ports on the front to measure, um, pressure. Temperature can be taken care of with a Vernier temperature probe inserted into the hole in the stopper on top of the metal cylinder. It’s only volume measurement that’s truly tricky.

If you can measure the height of the piston, then the volume of the gas under the piston and in the cylinder can be calculated. Pasco provides an instruction packet that suggests the use of a rotary motion sensor or smart pulley to get the piston’s position. I don’t do that, though it should work fine.

Instead, I mount a motion detector above the piston. By measuring the height of the detector above the piston’s lowest point, I can set the Logger Pro software to calculate the volume of the gas automatically from the motion detector reading. Thus, I’m collecting volume, temperature, and pressure data as many as 20 times per second.

In the picture to the right, you can see me using this apparatus to demonstrate PV diagrams at last summer’s AP Summer Institute at the University of Georgia. (Thanks to Laura Englebert, a physics teacher from the Atlanta area, for sending me the pictures. Woo-hoo!) I told Logger Pro to graph pressure on the y-axis and volume on the x-axis. Then, I slowly raised the piston, taking care not to let my hand get in the way of the motion detector. The graph showed a nicely hyperbolic curve – an isothermal process. But then I let the piston compress the gas rapidly. When gas compresses (or expands) quickly enough that there’s not enough time for heat to flow into or out of the gas, the process is adiabatic. Adiabatic compression on a PV diagram should jump to a higher isotherm, because the temperature goes up. Sure enough, while the process happens too fast to define the adiabatic curve, you can see that the graph ends up at a higher product of PV.

If you’re a bit lost in that last paragraph, don’t worry, it will make more sense once you get a chance to study the four major types of thermodynamic process that are tested on the AP exam – isothermal, adiabatic, isobaric, and isovolumetric. The 5 Steps book (now in a new and much-edited edition!) gives a good, short, readable treatment of these processes.

But note anyway that ANY portion of the ideal gas law can be tested experimentally! The linear relationship between pressure and temperature at constant volume? Plunge the metal gas cylinder into boiling water while keeping the piston from expanding. The linear relationship between volume and temperature at constant pressure? Do the same thing, but instead allow the piston to rise. And the experiment I previously described shows the inverse relationship between pressure and volume at constant temperature! Cool, eh?

18 November 2009

Mailbag -- thermodynamics sign convention?

From Jonathan Kirby, an Atlantan:

"I have a quick question for you. We are just getting into thermodynamics, and I was wondering if I should teach "ΔU = Q-W" where W is the work done BY the system, or if I should teach "ΔU = Q+W" where W is the work done ON the system. Which way would be better (if either) for the AP Test?"

The AP test changed to the ΔU = Q+W route in about 2002. Don't even mention the other way, unless your textbook does, in which case, good luck. :-)

(When I've used such a textbook, I've just repeated the correct definition over and over, and prayed.)


13 November 2009

Follow-up to multiple choice test corrections

Those of you who have attended my workshops know that, in Jacobs Physics, test corrections are one of the two most important components of the course. Sometimes, though, even the test corrections need correction.

Instead of assigning another round of “correction corrections,” I tend to just give the whole class a quiz when I find consistent misunderstandings. For example, consider the two multiple choice questions below. These were originally AAPT Physics Bowl questions, I believe…

1. A 2 kg object initially moving with a constant velocity is subjected to a force of magnitude F in the direction of motion. A graph of F as a function of time t is shown. What is the increase, if any, in the velocity of the object during the time the force is applied?
(A) 0 m/s
(B) 2.0 m/s
(C) 3.0 m/s
(D) 4.0 m/s
(E) 6.0 m/s

2. A deliveryman moves 10 cartons from the sidewalk, along a 10-meter ramp to a loading dock, which is 1.5 meters above the sidewalk. If each carton has a mass of 25 kg, what is the total work done by the deliveryman on the cartons to move them to the loading dock?
(A) 2500 J
(B) 3750 J
(C) 10 000 J
(D) 25 000 J
(E) 37 500 J

Many students showed an iffy grasp of these two questions on their test corrections. So, I posted to our class folder early last night. I noted that we would take a follow-up quiz today on these problems. I wrote the quiz to address specifically the mistakes that I had repeatedly seen on the first attempt at corrections. Here’s the quiz:

1. (a) What’s wrong with the statement “Work is done both up and to the right in order to move the boxes up the incline?”

(b) What is the direction of the force necessary to carry one box up the incline at constant speed? Justify your answer. Your justification should include a free body diagram.

2. (a) Explain why the average force during the time interval t = 1 s to t = 5 s is NOT 1.0 N.

(b) How do you get impulse from this graph WITHOUT trying to find an average force?

09 November 2009

Going over a test

I know it's happened to you and it's frustrated you.  You give back a test, you discuss one of the more frequently missed questions, hoping for a teachable moment.  But half the class is rooting through the rest of the test, sitting back with a vacant expression, or simply absent mentally.  What to do?

One option, which I've discussed before, is to allow corrections for half credit.  Then there's no need for you to take too much class time to go over the test -- it's the students' job to figure out what they missed, and to convince you they understand now.  A related idea is to announce a "fundamentals quiz" over commonly missed concepts from the test.  Either way, the students are forced to think about the test beyond just "what did I get?"

Of course, test corrections are time- and manpower-intensive. You have to give time in or out of class to get the corrections done, you have to grade them as thoroughly as you would a test.  I only do corrections in my AP class -- I find the general class moves slowly enough that those who missed important points will pick them up soon. 

So how do I go over a test in general physics?  Well, keeping my comments brief and to the point helps.  But the key little trick is to HOLD THE TESTS IN MY HAND while I go over them. 

Here I'm playing with the students' minds.  They desperately want their tests back, but only so they can see the grade.  Once they see that grade, their mind is done for a while, and they don't want to think about physics.  So I use the grade as a carrot.  I dangle the papers with the grades on them right in front of the class.  Not obviously or obnoxiously, of course, but they are never sure when I'm going to shut up and hand out the tests.  And, they're nervous about what they did right or wrong.

So they listen.  And ask questions.  They want to hear what I say, so they can figure out whether they were right or wrong.  The same discussion AFTER I give the tests back would be fruitless.

How do I know this technique works?  Well, I don't for sure.  But I do note that folks occasionally note to their friends whether they did or didn't make the mistakes that I discussed... so they must have paid some attention.