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 pasco.com 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?