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Homework #12: Do not turn this in since there is a test next week. I will post my solutions so that you can check your work.
That's all for homework #12.
- problem 6.38. Use Mathematica to solve this since the integral can't be done by hand due to the limits.
- Background: Read problem 6.39--but do not work this problem. It's really the temperature of the upper atmosphere of a planet that determines the rms speed of a gas that might escape from a planet. This is the "exobase" temperature, Tex. For Earth, Tex≈1,000K as stated in problem 6.39.
Actual problem: The criterion for a gas escaping a planet over a long time period is 6vrms≥vescape. For Mars, Tex≈220K. Determine whether the following gases will or will not escape from Mars: CO2, H2O, N2.
Reference: "Outgassing History and Escape of the Martian Atmosphere and Water Inventory" Space Sci Rev (2013) 174:113–154
- problem A.15 (yes, the appendices in this book have problems!)
- Treat the CO molecule of problem A.15 as a simple harmonic oscillator. Find the temperature at which you would expect there to be one molecule in the 4th excited state (E4) for every 5 in the 3rd excited state.
- For the CO molecule in the previous two problems, find (a) the helmholtz free energy A and (b) the entropy S for one mole (NA particles) of CO. Note that this will be in 1 dimension since these are not 3-d kinetic particles in a solid/liquid "crystalline" form.
- (a) Compute the quantum volume for an O2 molecule at room temperature, and argue (i.e. thoughtfully explain) that a gas of such molecules at atmospheric pressure can be treated classically. (b) At about what temperature would quantum statistics become important if the pressure were held constant? (c) Now assuming the temperature remains at room temperature, at what pressure would quantum statistics become important?