***Please show all work and explain answers thoroughly. Consider a polymer like
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***Please show all work and explain answers thoroughly.
Consider a polymer like DNA. One very simple model of such a polymer is to assume that the polymer forms a one-dimensional chain consisting of N >> 1 links, each having a particular length a. Each of the links in the chain may be freely oriented to the right or left, with no energy difference between these two orientations. The likelihood that each link in the chain orients to the left or the right is precisely 50/50, just like a coin toss. Suppose that Hr is the number of elements oriented to the right and is the number of elements oriented to the left, such that N = n_L + n_R. Refer to the figure at the right, in which one possible conformation of polymer links is illustrated (but where the individual links have been distributed vertically for clarity). For the example drawn, what are the values of N, n_R, and n_L? For the example drawn, what is the value of L in terms of the link length a? Write down a general expression for the end-to-end extension of such a chain, L, in terms of the parameters and a. Of course, for the particular configuration drawn, your general expression must reduce to L = 6a. Write down an expression for the number of arrangements Was a function of the total number of links N and the number of links pointing left or right, ni and hr. Explain your reasoning. (Refer back to your analysis in part 1.) What would the state of minimum and maximum entropy of this polymer look like? Can you use your results from parts A-D of this problem (and the second law of thermodynamics) to predict what you think the natural state of such a polymer would most likely look like?Explanation / Answer
A. We need to count the number of links oriented to right we have total 10 links oriented to right.
hence value of nR=10
We need to count the number of links oriented to left we have total 4 links oriented to left.
hence value of nL= 4
Each link length is a , hence length of 10 links oriented to right is 10*a= 10a
Length of 4 links oriented to left is 4*a = 4a .
TOTAL L= 10a-4a = 6a.
As length due to left oriented will be neagative to that of right oriented.
B. General expresssion will be
L = Nr*Lr - NL * LL
where Nr =link oriented to right.
Lr= length of link oriented to right
NL = Link orieneted tol left.
LL=Length of Link orinted to Left.
Put all values in general expresson you will get the values of L.
C. The no. of arrengements of will be left or right i.e. 2 for each .
total 14 links have 28 arranngements.
right oriented have 20 , and left oriented have total 4 arrangements .
D. The left oriented have max entropy as they are less in no. while the right oriented have min entropy.
E. According to overall entropy of the system will be increasing in nature as right oriented are more than left oriented.
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