Lerner Physics

We started today talking through questions about the pressure under the surface of the fluid. The problems started easy, with some simple computations. But then the questions got more conceptual. How does the pressure vary if the container isn't just a cylinder or a rectangle but has angled or curved walls? How does the pressure change if you submerge something in the water? So we ran some experiments:

We finished up talking about microstates and entropy which finished the ideal gas model. The class applauded. Then I asked the question, "how could we add gravity to our ideal gas model." Groans.

So many models build on the next. I'm telling a story. I'm trying to show logical connections between one idea and the next. And what a better way to extend the ideal gas model than to add gravity? How does the pressure relate to the depth of the fluid? And, since we can't really see differences in pressure that well with gases, why not look to liquids? Hence the lab.

We got very similar results, with slopes of 9200 pascals per meter. One group decided the slope would be negative, since we kept going deeper (and lower) to measure higher pressures. We figured out what the 9200 pascals per meter meant, and why it was smaller than theory would predict. We had a few minutes at the end of class to practice this new mathematical relationship. 

Today was 100 minutes of pure whiteboard speed dating. I only changed the groups about every 7 or 8 minutes, but the problems were long and complex enough that we still got through two or three "dates" per problem. All the problems were old AP Physics B ideal gas problems, which worked out really well. These problems really helped students talk about how the internal energy, the work done, and the heat exchanged, the temperature change, and the volume change are interrelated.

We quantified the work done by a gas by looking at the pressure-volume graph, which was easy. We quantified the internal kinetic energy of the gas, which was much harder. The metaphor we used was that of the Koopa Troopa, the Mario turtle that, if you step on it, can bounce back and forth from wall to wall at the same speed forever. It's a good model of many, many elastic collisions even if it isn't realistic. It does require some handwaving to get the derivation, but we know have an expression for the kinetic energy of one molecule of a gas. It also allowed us to explain why there's not much hydrogen gas in our atmosphere.

We then previewed the heat engine lab. We have a lot of practice to do before we get to that lab.

We practicing tracking the energy going into and out of an ideal gas. We practiced the four types of transitions that can happen: isobaric, isovolumetric, isothermal, and adiabatic. Adiabatic is my favorite. We also did Super LOL diagrams, which, if you don't know about, you should read this blog post. 

We also talked about the first law of thermodynamics, which is pretty obvious if you understand the LOL diagrams. We know that work in and out is related to volume, but we're not sure exactly how, and we know internal energy is related to temperature, but we're not sure how, but I guess that's what tomorrow is for.

We practiced the ideal gas model today by whiteboarding a few problems that were more difficult than they first appeared. We had to take a little detour over to air pressure and how it is everywhere. It's always fun to play with suction cups. We practiced drawing pressure-volume graphs to describe what's happening to the gas, and started drawing energy bar charts (LOL diagrams) for ideal gases.

It turns out there's only two ways to put energy into a gas: compression and heating the gas. And there's only two ways to take energy out of a gas: expansion and heating the environment. The energy of the gas, for our monatomic ideal gas model, is only translational kinetic energy, so we only need bars in the L's of the LOL for kinetic energy. Now it's time to classify all the different changes a gas can undergo.

We talked about differentiated instruction today in the morning, then had lunch at Jack's Deli, then listened to the lawyer for an hour, and then went to three mini-sessions. I led one on Standards-Based Grading. I don't feel like I'm an expert on it, but I have lived it for more than a year now, and I could talk about it for a while and help other teachers think about how they could implement it in the future.

After the rotational motion test, we whiteboarded problems on the kinetic theory of gases. It was impressive watching them integrate knowledge of physics with knowledge from chemistry. Energy bar charts were drawn with no input from me. Awesome!

How can we extend mechanics? Well, the ideal gas model seems to make sense. According to the kinetic theory of gases, we can model it as a whole lot of particles that collide elastically, and we know about elastic collisions. Everyone takes chemistry before this class, so everyone has seen the ideal gas model, but we still played with the PHeT simulation of gas properties to have that visual of our model. We also talked about the transfer of internal energy, or heating, that can happen, through conduction, convection, and radiation.