Fundamentals of STATISTICAL AND THERMAL PHYSICS
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There are some formulae to be used to answer all the questions.
I hope you can find all of them in the books you have available.
In the following, k is the Boltzmann constant. If your teacher measures temperature in units of energy, (s)he takes k = 1. Otherwise k = 1.3806503 à? 10-23 m^2 kg s^{-2} K^{-1}.
It may be easier for understanding, if I answer the questions in the order 3-1-2
Question 3:
Find (a) the average energy and (b) the equation of state of a system with partition function Z = Vf(T)
(a)
There is the formula for the internal energy of the system in terms of the partition function:
U = N k T^2 (d ln Z / dT)_{V=const}
After substitution, we get
U = N k T^2 f'/f
This is the internal energy averaged over statistical fluctuations - so it can perhaps be called "average energy".
However, if your teacher means the average energy per particle (it is a bit difficult to guess what the teacher means from the text), ...
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