Possible ideas/thoughts/questions for discussion in supervisions, roughly grouped by example sheet and including points raised in lectures that could be followed up.

- Important scales of the world worth knowing: size of the earth, orbital radius, solar flux (F) at the earth (and from the flux and orbital radius, the luminosity of the sun), why the flux averaged over the earth's surface is F/4.
- Why estimate at all? How it's a good first way to approach any problem to get understanding, then you can analyze more exactly.
- Other examples of deriving formulas by dimensions (we did Stefan-Boltzmann in lecture). For example, form drag as a function of density, velocity, and cross section.
- Honest explanations for results arrived at by dimensions, e.g. why physically is radiated flux proportional to T to the fourth rather than say T cubed?
- As many methods as possible for estimating the heat of vaporization of water. Which are more reliable? What makes one more reliable than another? One is tumble-drying clothes from the power of a dryer and the mass of water evaporated. Hmm, it should also work with drying clothes on a line using the solar flux.
- How does the greenhouse effect work? We only began this topic in lecture.
- Where does the sun gets its power, if gravitational power would not last long enough? How was it discovered? (If you know how, let me know, I'm sure it's sly.)
- Why is gravitational energy negative? Some of the consequences of this sign, for example that satellites speed up as they lose energy to air friction.
- For students who like mathematics, calculating the gravitational energy of a uniform-density sphere (and why the sun is not of uniform density), including getting the dimensionless constant. Then: Given that the sun is denser on the inside than the outside, would that increase or decrease the constant (in absolute value)?

- In an ideal gas, how do thermal diffusivity, which is roughly the kinematic viscosity, and (dynamic) viscosity depend on pressure?
- Percentage changes as the best way to quickly do numerical calculations. For example, if you change the area of a square by 0.1 (10 percent), by what fraction do you change its side length? Can do sqrt(1.05) and sqrt(50) that way.
- Related to the last point, the idea of
**scaling**, so whenever possible calculating quantities as ratios to similar quantities. For example, thermal conductivity of ice compared to water, as in lecture (instead of calculating it from scratch as conductivity=density*specific heat*thermal diffusivity). - In the cooling-by-a-sheet problem, should the specific heat matter or only the latent heat? Many students argue that to evaporate water, one first must raise it to 'boiling temperature'. What is boiling?
- Anything about random walks. For the mathematically inclined students, compute the return probability in a two-dimensional random walk.
- What is the temperature profile
*within*the ice layer? - What would happen to lakes if ice were denser than water?

- Scaling again. Don't compute quantities directly; instead compute them relative to similar quantities (as in comparing K for diamond with K for water).
- How do carbon dioxide and water vapor block infrared radiation? Estimate the vibration frequency of these molecules and convert it to an energy with h-bar and to a wavelength. Also estimate quantized rotational energy. All good reviews of IA material in preparation for IB quantum physics.
- What makes an expansion or contraction adiabatic rather than isothermal? In problem B1 (adiabatic atmosphere), what is a typical speed at which parcels rise? How big is a parcel? Hence why is the expansion adiabatic?
- Are sound waves adiabatic or isothermal (we might also do this in lecture)? Good example of reasoning from curve sketching, nicely treated in Tabor, Gases, Liquids, and Solids (3rd ed.), p. 79.
- For B1, again the general principle of counting knowns and unknowns: two unknowns hence look for two equations.

- What 'the boiling of water' means. Examples of vapor pressure changing with temperature, e.g. seeing breath on a cold day, rain shadows past mountains, fogged glasses when you walk in from a cold day.
- Why the isothermal atmosphere is convectively unstable and therefore how it becomes an adiabatic atmosphere.
- Temperature inversion in an atmosphere producing smog.
- Which, if any, of these laws apply in a quick expansion, and why?
- pV^gamma = constant
- p=nkT

What makes an expansion quick?

- Why semilog and log-log plots are useful. Other examples of their use, for example in linear circuit analysis (Bode plots).
- Boltzmann factors. Why do they have T in the denominator of the exponent? How RT (or kT) set an energy scale.
- What temperature change produces an e-fold change in vapor pressure, and how to work that out using fractional changes in the exponent -Lvap/RT (which is roughly 17 at room temperature).
- Why (1+0.01)^100 =
*e*, and the more general result used to derive as a limit the isothermal p(z) from the adiabatic. - The four steps of a Carnot cycle. Why it is bad to connect the gas (or whatever working substance) to the reservoir before temperatures are matched, hence the need for the adiabatic steps in between the isothermal ones. Why you don't need to compute the work done by the adiabatic steps (i.e. how you know they add to zero).
- Connection between different forms of the second law: e.g. entropy never decreases, heat flows from hot to cold.
- The microscopic-macroscopic puzzle given at the end of the Carnot notes (lecture 10)!

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