Statistical Mechanics. Carefully explain. Consider a perfect crystal with N atoms and the same number N of interstitial

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Statistical Mechanics. Carefully explain.
Consider a perfect crystal with N atoms and the same number N of interstitial sites, which they are the intermediate points between the sites of its crystal lattice. Let U0 be the internal energy of atoms and E is the energy needed to move an atom from one lattice site to a position interstitial. If n is the number of atoms occupying interstitial sites in a state of equilibrium of the crystal, we are interested in calculating:

a) The internal energy of all the atoms.
b) The entropy S of the atoms.
c) An expression of S as a function of n assuming that N and N-n are large numbers.
d) If T and volume V are fixed, we are interested in calculating the (average) value n as a function of E and T, and examine its behavior for low (T→0) and high temperatures (T→∞)