Homework 4

Q1: Explain the following physical variables, in the style of the lecture of 22 March. In other words, for each variable,
(i) write out the formula for the variable of interest,
(ii) say what phenomenon this variable embodies,
(iii) explain how you would maximise the variable in an experimental situation,
(iii) show that the dimensions work out,
(v) guess the formula for this variable if we were in two (space) dimensions, by using ONLY dimensional analysis.
Be concise (so you don't drive the TA crazy with long answers!).
1A: Quantum concentration (hint: when is a gas classical and when is it quantum? Think about the de Broglie wavelength and the size of the box).
1B: Fermi temperature.
1C: Einstein condensation temperature.

Q2: KK6.10 Isentropic relations of ideal gas.

Q3: KK6.13 Gibbs sum for ideal gas.

Q4: KK7.1 Density of orbitals in one and two dimensions.
Also comment on how you might have guessed these formulas by using only dimensional analysis.

Q5: KK7.3 Pressure and entropy of degenerate Fermi gas.

Q6: KK7.8: Energy, heat capacity, and entropy of a degenerate boson gas.
Note: This is a relatively hard problem, let me know if you need hints to solve this! Or I'll just make it worth fewer points... but I can only do this if you give me feedback.

Also, just for education purposes, take a look at the text of question 14 (don't do it though), and enjoy! BEC is a really cool thing experimentally...