Consider the following simplified model of a DNA molecule
resembling a molecular zipper: a long chain consisting of two
separate parallel strands, each strand being a linear chain of four
basic molecular units, namely, bases called A, T, G, and C. A base
in each strand is pairwise connected with a base in the other by a
hydrogen bond, either A-T or G-C with binding energies
W₁ and W₂ respectively. Each bond can have
two states, broken and unbroken. The chain consists of N base
pairs, the fraction of A-T and G-C pairs being a and b with a+b =
1

i) What is the probability of a bond being in broken state at
temperature T?

ii) Write down the canonical partition function for a single DNA
molecule

iii) Derive an expression for the entropy per molecule