​​Please provide a full solution to the attached "Question 5" (a second year course: Thermal Physics)

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Please provide a full solution to the attached question (a second year course: Thermal Physics, subjects: statistical mechanics, entropy, multiplicity).

Please write solutions on paper and send photos. Thank you very much.

I am preparing for an exam and don't have time for this, however, I have a high mark in this class and can't afford to let it drop. Please complete it perfectly, you'll have money and my immense gratitude! Thank you!

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Question 5. On Assignment 3, you showed that the multiplicity of a polymer with N links, each of length b, and an end-to-end distance L is, approximately, 2(N, L) = S(N, L = 0) e-L2/2N6? (a) [1 point] What is the formula for the entropy of this polymer, S(N, L)? (b) [4 points] For a one-dimensional system such as this, the length L is analogous to the volume V of a three-dimensional system. Similarly, the pressure P is replaced by the tension force F. Taking F to be positive when the polymer is pulling inward, write down the ther- modynamic identity (involving du, ds, and dL) for this system. Provide the relationship between F and S for this system. () [2 points] Use your result from (b) to show that the tension force in the polymer is directly proportional to L (Hooke's law). (d) [3 points] Discuss the dependence of the tension force on temperature. If you increase the temperature of a rubber band (which is composed of polymers), does it tend to expand or contract? Does this behaviour make sense?
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