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On your last assignment, HW#2, you figured out energy fluctuations in the canonical ensemble.
Now, figure out KK 5.10 about number fluctuations. Remember to focus on the grand partition function Z. .
[This is a derivational problem.]
Do KK 5.12 about "Ascent of Sap in Trees".
[This does require thinking hard about setting up the mathematical representation of the problem.]
Does dimensional analysis help?
(a) Suppose that our universe is spherical, and that the only matter in the universe is a bunch of photons. Find the work done by the system if it adiabatically expands until its diameter grows to M times its initial diameter.
(b) Now suppose instead that our universe is spherical, but this time made of non-relativistic ideal gas particles. Figure out what you can about the work done by this system if it adiabatically grows to M times its initial diameter.
(c*) How do both your results above depend on the dimensionality of space?
[Note: for an adiabatic process there is no heat transfer. Therefore, there is no entropy transfer, because dQ=TdS.]
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