Answer to Question #242063 in Physics for Amey

Question

A one dimensional chain is made up of N identical elements, each of length l. The angle between
successive elements can be either 0◦ or 180◦
, but there is no difference in internal energy between
these two possibilities. For the sake of counting, one can think of each element as either pointing
to the right (+) or to the left (-). Then one has N = n+ + n− and the length of the chain
L = l(n+ − n−), where n+ is the number of elements pointing to right and n− is the number of
elements pointing to left.
(i) Use the microcanonical ensemble to find the entropy S as a function of N and n+
(ii) Find an expression for the tension F in the chain as a function of T, N, and n+
(iii) Rearrange the expression from (ii) to give the length L as a function of N, T, and F
(iv) Use the result for the high temperature behavior from (iii) to find an expression for the
thermal expansion coefficient α ≡
1
L

Answer 1

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