For a id system like a linear polymer, we write d sigma = du-fdl, where is the "natural" temperature r = k_b t, f is the external force on the line, and l is the extension of the line. from this, we get f= - . consider a polymer chain in id with n links of length a, where each link can be oriented to the left or the right with equal probability. the total end-to-end extension of the polymer is given by l = 2|s|a, where. v is the excess oflengths pointing to the right. show that for |s| n, we can write the entropy as sigma(l) = ln[2g(n, 0)] -l^2/(2na^2) where g(n, s) - n! /(1/2 n+s)! {1/2n-s)! ] analogously to the spin system studied in class. show that the force at extension l is given by f = l/(na^2). what does this mean physically will happen to the polymer as the temperature is increased?