Polymers, like rubber, are made of very long molecules that tangle into a configuration that has lots of S. A crude model of a rubber band contains N links, all of equal length L, which can only point either left or right (2 possible states). The total length of the band is thus the net displacement from the first to the final link. Let us to solve it step by step, and derive Hooke’s law and find “elastic entropy”. (a) Find an expression for the entropy of the rubber band in terms of the total number of links, N, and of the number that point ‘right’, Nright. (The multiplicity is as straight as u hope and use Stirling.) (b)What is L in terms of N and Nright.( In other words, eliminate Nleft from this expression).
For a 1- dim system like this, we can make an analogy with P and V for a 3-dim system : V becomes L, and P becomes F. Take F, or the tension force, if u will, to be positive when the rubber band is pulling ‘back'(inwards).What is the thermodynamic identity of this system-in other words, what is the re-written version of the 1st law? Comment on this. Using this identity, you can now find an expression for F in terms of a derivative involving S(dU=0). Now expand this partial derivative by putting in the following term,
∂Nright./∂Nright which is obviously unity and does not change the value of the derivative. Using your result from (b), you should now have a (1/2L) term. Use part (a) and apply the derivative w.r.t Nright now and not L, to find the tension force = f(L, T, N, Nright). Show that when L<<NL, F has a very familiar form. What is the value of the spring constant, K ? Discuss the dependence of the tension force on T. If you increase the T of a rubber band, does it (tend to) expand or contract? Comment! We did not find the total S above ; we ignored the vibrational entropy, which depends on E but not L. Stretch and contract a good rubber band, and use your lips as a probe. Comment !
The last part of your posting was missing: ”Show that when L<…”. But I think that part is probably trivial once you understand how to deal with this problem.
To avoid confusion I will call the length of one link a, and use the symbol L for the length of a chain. Also, N_r = N_right, N_l = N_left. You can write the length as:
L = a|N_r – N_l|.
Since N = N_r + N_l you can rewrite this as:
L = a|2 N_r – N|.
The entropy is related to the number of ways you can arrange the links to get the same length. This is just the number of ways you choose N_r links from …
A detailed solution is given..To continue with the answer check on mycoursewriter.com/
Why Choose Us
Quality Homework Writing
Do you need to ace your test? We have qualified writers to assist you in writing 100% quality homework writing. Mycoursewriter offers students unique and personalized custom papers that help them in getting good grades. Our academic experts will assist you with your dissertation papers, thesis writing, research papers, term papers, and case study homework help. Our writers are experienced and have perfected the art of crafting the best essay writing papers regardless of your academic level. Order now and get our superb homework writing services.
Expert Academic Writers
A student needs professional assistance outside class time. Before hiring our writers, they undergo thorough tests and strict educational backgrounds. After passing a test, our writers undergo training to ensure they deliver expert professional papers to our customers. We ensure they meet the timely delivery of papers and follow our customers' provided instructions. Every writer is an ENL writer and is from the USA, Canada, UK, or Australia. Our experts approach papers effectively depending on their area of specialization.
Affordable Price Guarantees
Is the deal too good to be true? Mycoursewriter is the most affordable assignment help website on the market. We consider students' daily needs for academic help. Our paper costs are reasonably priced to approximately 90% of students around the globe. Our main aim is to ensure students achieve academic excellence, and we believe inconsiderable prices should not hinder students from getting quality homework writing help. In case of any dissatisfaction, we offer unlimited revisions and rewrites without extra charges.
Timely delivery of papers
Tight deadline? Is your paper due in the next few hours? Worry no more. Our writers are here for your rescue. Many college students find it hard to balance their social and academic life and get caught up with academic deadlines. Drafting your paper at the last minute does not allow you to conduct extensive research and craft the correct answers. We have expert writers ready to work on your assignment writing. Urgent writing services are the ultimate solutions you need. We guarantee you timely delivery of papers at your convenience and specified time delivery of the customer.
100% Original Tasks
The ultimate deal-breaker in achieving good grades is submitting imitative papers. Plagiarism is a breach of examination standards and has serious consequences. Students need to deliver papers written in their understanding by paraphrasing their research findings and relevant citations. Our expert's primary consideration is providing free plagiarized papers that meet the lecturers' requirements. Our editors will proofread your paper before delivery ad ensure your papers will not be substandard. We guarantee extreme originality, and in case of any customer concerns, we offer a plagiarism report.
All Round the clock Customer Support
Our website is user-friendly and super useful! Mycoursewriter is the most trusted online writing website always available to provide you with assignment writing services that you need. Our primary concern is meeting customer need specifications by our friendly customer support team that Is available all the time. Our website usability is self-learnable but in case of any problem, feel free to contact us directly through our website email: email@example.com. We have diligently satisfied thousands of students, and you can witness this on our sites' review page.
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
Advantages of Using Our Assignment writing Services
Mycoursewriter welcomes you for superb essay writing services. We are a legit site offering help with your most challenging homework writing assignments at affordable prices. Your essay paper will be assigned to a professional writer who will craft the paper from scratch according to your provided instructions.
Essay writing is a common assignment writing for most college students. It takes a lot of time to craft a complete perfect essay. Mycourserwiter offers the best essay writing and proofreading services for most college students. Your paper is assigned to an expert writer who does thorough research on fresh ideas and personalizes your essay paper according to your assignment writing guidelines. Our essays are entirely exceptional and undergo a strict procedure that includes papers free from plagiarism and thorough proofreading.
Admission and Business Papers
Writing an admission paper is not every student's desire, and this should not hinder any student from earning an admission. Writing a perfect personal statement to earn a position in a dream school or job can be stressful. Personal statements should display a high level of confidence and uniqueness. Admission essays require you to have a vast knowledge of the current happenings in the world and knowhow of the business world. We have qualified writers with skills who will write your admission paper through comprehensive research. All you have to do is provide us with little details about yourself, instructions and our writers will craft a perfect paper for you.
Editing and Proofreading
Mycoursewriter offers you assignment writing services free from grammatical and formatting mistakes. An error-free paper is significant in scoring the desired maximum grades. We have a team of editors who will go through your paper after our expert writers have delivered their fully crafted papers. Our writers will cover all the aspects of your paper instructions, such as fonts, spacing, and educational formats. Our team of editors will check through your paper to make sure it meets the formatting style provided in the paper instructions. Under no circumstances will a poorly formatted paper will be forwarded to you as our team of editors will ensure careful proofreading.
Assignment writing is part of a learning process, and one may not have the knowledge to answer all questions correctly. This should not be a stress to you as we have qualified essay writing experts to help you. Our qualified writers are holders of PhDs, Degrees, and Masters in different areas of study and can handle any papers regardless of the complexity. Multiple assignments may be challenging to finish on time. Our skilled professional writers are here to assist you in crafting all the correct answers for your assignment. Stop stressing about your homework writing and place an order with us, and our expert writers will provide you with the best assignment help.