We were forced to move the course online due to COVID-19. This APS backpage article (from the monthly newsletter) was useful.
Interesting “Masterclass” by Neil DeGrasse Tyson. SCIENTIFIC THINKING AND COMMUNICATION. Has some of the same learning goals as PH315.
The mid-term exam had two examples of conservation of energy applied using the idea of balanced rates. A major theme of this class is the conservation of energy. It's easy for students to see when it's simply a counting exercise. It should also be easy to see when there are constant rates in balance with each other. They need a little more push in the right direction to recognize this.
Quoting Moore (C6.1) “The law of conservation of energy is one of the richest and most productive ideas in all of physics… while Newton himself understood that interactions conserve momentum, it was not until the 1800s that the physics community realized fully that energy was universally conserved.” A pioneer responsible for early realizations is Emilie du Chatelet. One way this fits into PH315: for a classical object traveling in a straight line, F = ma is a specific application of conservation of energy. Students should realized that the idea of conservation of energy is much broader and more useful than the very specific statement F = ma.
Karen Daniels has a great way of introducing the idea of “Modern physics”. It marked the end of absolutism in physics. A realization that we can make progress without knowing the movement and co-ordinates of every sub-atomic particle. There is more to figure out than treating the world like a perfectly predictable clockwork mechanism. The modern-art movement realized that art could explore places without an absolute representation of real shapes.
Elmer Imes (his molecular spectrum plot is uncredited in the Krane book) https://physicstoday.scitation.org/doi/10.1063/PT.3.4042
Emilie du Chatelet (conservation of energy, pairs well with Emmy Noether).
In the final exam I notice reliance on a technique students have invented for themselves to circumvent physical reasoning. I've heard students call it “unit analysis”. The basic idea: The problem gives some numbers to solve the problem. Mash these numbers together in a way that gives the desired units. Here is a cautionary tale of how badly this approach can fail.
Estimate the lifetime of the Sun in unit of seconds: First, piece together some facts about the Sun. The fusion of hydrogen atoms produces 1.3 x 10^12 kg.m²/s² of energy per atom. The surface area of the Sun is 4πR². The mass of the hydrogen fuel is 2 x 10^29 kg. Put these three quantities together and take the square root. Then I have something with dimensions of time (t = 2 x 10^30 seconds). Is this the lifetime of the Sun?
What is the magnitude of the things around us? Length scales, energy scales, times scales, mass scales (and the rates constructed from these dimensions (velocities, momentum, powers). Can the answers be figured out from a handful of principles? How do the answers inform technology? How do the answers inform humanity's biggest challenges?
Physics students are expected to take 231, 232 and 233 in the first year.
During the 211 sequence, students learn the following vocabulary and math:
|ph211||Acceleration, Force, Momentum, Energy, Work||Vectors, Trig, Derivatives, Line Integrals|
|ph212||Angular Momentum, Torque, Wave, Interference, Density||Wectors, Trig, Differential Equations|
|ph213||Charge, Field, Voltage, Induction, Current||Vectors, Surface and Volume Integrals, Gradients|
Many of the vocabulary words are used differently in everyday language compared to physics language. Students must learn to new definitions in the context of physics. Student must self-check their interpretation of the definition to make sure there is no ambiguity or inconsistency.
I've been integrating the MODTRAN climate simulation into the class. I want to strengthen the connection between the 1-layer atmosphere, 2-layer atmosphere, N-layer atmosphere and the MODTRAN atmosphere. All three models can be set up to find upward IR-flux (energy leaving the top layer and going into outer space) as a function of ground temperature. Later, of course, we must balance upward IR-flux with P_Sun. But this balance act can be done after we create the models.
Acknowledge the work of both Hedwig Kohn and Max Planck. When talking about multiple layers of thermal shielding, discuss other contexts where the same physical phenomena is used. Show photo of the inside of a milliKelvin fridge (from google or D-wave).
I enjoy epistomology of physics knowledge very much - “how do we know what we know?”. I hope to give you many examples during the class.
Example of epistemology from mathematics. How do we “know” the Pythagoras theorem? Mathematicians formulate a proof:
Once you've seen the mathematical proof, you know that the Pythagoras theorem is true. It's beautiful. It feels good to know.
In contrast to mathematics, the only way we “know” the physical laws of Nature is by empirical testing (experiment). Small white board question: Write down a physical law of Nature. None of these laws explain all experiments. In physics, you learn approximations that work with various levels of precision. Experiments will always have the final say. This is a huge cultural difference between mathematics and other sciences.
These ideas should also shape your idea of what scientists do. Scientists are not here to assert facts, but rather to gather evidence and give humanity tools to evaluate the evidence.
We always strive to be accurate. But the appropriate level of precision requires consideration of the cost/benefit of the precision.
When someone asks “what time is it?” You reply “almost quarter past one” When someone asks “how long does the superglue take to set?” You reply “30 seconds” You've adjusted to an appropriate level of precision.
There is value in adjusting precision. The first stages of building a house are done with 1/2“ precision. The finishing touches are done with 1/16” precision. What would happen if the whole process was attempted with 1/16“ precision?
Learning objective - recognize the appropriate precision for answering a physics question:
This class will focus one questions that can be answered using accurate but low-precision calculations.
Some physics classes say: “Writing down how you would solve the question is almost as good as solving the question”
Example… “For the take-home exam, show me that you can build a house” An answer that I would get no credit: “I would buy 1000 pieces of wood of appropriate dimension. I would cut them to the right length and nail them together.”
A real example from a physics exam:
Energy cannot be created or destroyed. It is transferred from one place to another. It is changed from one form to another. The course is largely about these two processes (moving energy through space, changing energy from one form to another). “If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.” - Nikola Tesla
More illustration of why a simplified model is useful. Comparison of bikes, trains and cars.
The course could emphasize three simplified models: Air resistance, Bohr model (be very careful about this one), and Climate model from 6 Ideas. However, I have serious concerns about teaching the Bohr model and the 6-Ideas Climate model. If this is the first time students see these topics, they are forming their ideas about how the world works. The Bohr model and 6-Ideas Climate model are qualitatively incorrect in order to be quantitatively correct. I'd like students to work in the other direction… first qualitatively correct, then quantitatively correct.
Fermi's observation during the Trinity test. Maybe turn this into a homework problem? Fermi's classified report
Order of magnitude estimates come in different flavors. There is pure “accounting-flavored” order of magnitude, such as “how many ping pong balls would fit in a Corvallis bus” (the whole problem deals with numbers that have dimension length cubed). Then there are “physics-flavored” order of magnitude problems, where the problem involves numbers that have a variety of dimensions, like the Trinity test example. This difference may be helpful to point out.
It's incorrect/misleading to say total internal energy equal to kT/2 for each degree of freedom. It is better to say that we use U = (DoF)*kT/2 to calculate total internal energy to within a constant. This constant takes into account that different degrees of freedom get unfrozen at different temperatures.
Find a simpler way to explain the inefficiency of power plants, car engines etc (see below):
Start with a 10 cc cylinder of ideal monatomic gas at 5 atmosphere (temperature is ___), then let it expand to 50 cc, while adding enough heat to keep the pressure at 5 atmosphere. What is the final temperature of the gas? How much work could be harnessed from this expansion process? How much heat was put into the gas during the expansion process?
This gives the basic idea… any engine that uses gas processes, cannot be 100% efficient.
When talking about the Carnot cycle - it's important to point out that the transfer of heat is across a negligible temperature gradient, hence there is no change of entropy when the heat transfer happens. Important prelude to using entropy concepts later.
CO2 vibrational mode coupling to IR light is probably a great kick-off point for this section (rather than 2-slit interference). CO2 light absorption hits many important points:
The term absorption cross-section might be misleading. Maybe better to call it scattering cross-section?
A really nice calculation regarding photovoltaics is to find optimal band gap for various different spectra. Use top-hat shaped spectra in a photon flux vs. photon energy graph. This gives students some experience setting up an interesting integral and optimizing.
How light bulbs work (Minute physics): https://www.youtube.com/watch?v=oCEKMEeZXug
Examples of why uncertainty is relevant and important. Gravity wave detection (maybe a homework question on this). Temperature of earth, looking back into the past. Show some graphs in class. Discuss.
Set up the motivation/purpose, testing a scientific hypothesis as rigorously as you can with the equipment provided. Make clear the final product will look like, a graph with 3 points and error bars.
Practice uncertainty analysis earlier in the term by doing a warm up lab. e.g. Hg lamp.
Practice uncertainty analysis earlier in the term as part of order of magnitude estimation. For example, the bath tub questions.
Make sure students realize big triangles are better than small triangles to determine angles using rulers.
Need to assign roles, driver and navigator. Need to call out the switching times. Groups of 2 will be more effective.
Call it an experiment, not a lab (avoids attitude “tell me what to do so I can leave faster). Experiments test a hypothesis.
Call it uncertainty and not an error.
Plot data right away to make sense of it. Don't leave without instructor signing off.
Uncertainty analysis approached in multiple ways
Discussion of experimental issues
Rewrite the rubric
|Introduction, explain the hypothesis that is being tested||10|
|Procedure, descriptive text and diagrams so that I can repeat the experiment, key equations||10|
|Data, numbers presented in tables, descriptive text accompanying tables||10|
|Uncertainty analysis, compare the s.d. of measurements with expected uncertainty (include correct propagation of error) discuss||10|
|Key graph, well-labeled, showing Eph, 1/wavelength, and linear fit, together with descriptive text||10|
|Discussion, what can you conclude from your experiment, what would you recommend scientist do next to improve the experiment?||10|
The majority of students (perhaps even 100%) have zero skepticism about human induced global warming. I was surprised by this. Even the IPCC 2013 report hedges there bets with a 95% confidence that human influence has been in the dominant factor.
The percentage confidence has steadily be going up in each IPCC report. This is a good story to tell when introducing error analysis.
I didn't get to teach fusion. However, it would fit nicely with the course. The kinetic energy of an electron needed to overcome Coulomb repulsion (the strong force kicks in at 3 fm separation). Therefore need 0.5 MeV of kinetic energy. 4.5 MeV of energy is released. Then, for thermonuclear fusion, what temperature is required? T ~ 10^9 K. In 1938, Bethe worked out the basic process inside the Sun. (Ask students to think about temperature difference between core of sun and surface of sun.) Good perspective that haven't had that much time to put the sun in a box.
A good article about the issue of nuclear waste: https://www.scientificamerican.com/article/nuclear-waste-lethal-trash-or-renewable-energy-source/
Need to read Megatons and Megawatts
Phet has simulations of alpha decay, beta decay and fission: http://physicstoday.scitation.org/doi/10.1063/PT.3.3680
See page 122 of “Back of the Envelop Physics” by Swartz. Is it conceivable for the Sun to be fueled by a chemical reaction (like burning hydrocarbons)?
Can we “see” all the mass in the galaxy? Estimate how much mass remains unseen.
Average density of cold gas in the galaxy? Could neutrinos account for the unseen mass of the galaxy? Mass about 0.1 eV. Relic background neutrinos are estimated to have density of 56 of each type per cubic centimeter (3 types).
Quantum communication between ground and satellites. Interesting topic for term papers.
Good way to represent wavefunctions: https://www.youtube.com/watch?v=imdFhDbWDyM