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?

Stars x and y are both bluish main sequence stars. star x has a higher absolute brightness than star y. how do the two stars compare? explain

A248-g piece of copper is dropped into 390 ml of water at 22.6 °c. the final temperature of the water was measured as 39.9 °c. calculate the initial temperature of the piece of copper. assume that all heat transfer occurs between the copper and the water. remember, the density of water is 1.0 g/m

How do the measurements of charge at the different locations on the sphere compare to each other? the charge measurements are different at all locations on the sphere. the charge measurements are virtually not the same at all locations on the sphere except for the charge at the very top and at the very bottom that are equal. the charge measurements are virtually the same at all locations on the sphere except for the charge at the very top. at the top, the conductive sphere has a small disk that is made of different material. the charge measurements are the same at all locations on the sphere. what happens to the charge on the conductive sphere when it is connected to a source of charge such as the electrostatic voltage source? nothing will happen because no charge goes around the surface of the sphere. the charge on the conductive sphere spreads out over the surface of the sphere; being greater in some specific locations on the sphere. the charge on the conductive sphere spreads out uniformly over the surface of the sphere. the charge on the conductive sphere spreads out non-uniformly over the surface of the sphere.