A long polymer like a rubber band can be modelled as a sequence of freely hinged sub-units called monomers (length l).

A long polymer like a rubber band can be modelled as a sequence of freely hinged sub-units called monomers (length l). For simplicity, we can treat the band as one dimensional, and assume that monomers can only point to the left of right. The total length L is the net displacement from the beginning of the first monomer to the end of the last.a) Write down an expression for L in terms of the number of monomers pointing right (NR) and left (NL): this is easy, and not a trick question!b) What is the statistical weight and entropy of a polymer of length L? Express your final answers in terms of L, N and l only.c) For a 1-dimensional system like this, the length L is analogous to the volume V of a 3-D system. Similarly, the pressure P is replaced by the tensile force f. Taking f to be positive when the rubber band is pulling inward, write down the appropriate form of the first law of thermodynamics (ie the “thermodynamic identity”) for this system.(again this is straightforward: don’t think too hard!