Problems 13-15
Problem #13
To reduce heat absorption from the sun, it is wise to paint the exterior of the house a light color with a low value of emissivity. What about the inside of the house? As long as there is little direct sunshine on the walls, does the color make any difference?
Problem #14
A zipper contains a large number of links. The energy associated with opening a link is ε > 0. The zipper can only unzip from one end while the bulk of the interior remains closed. Find the mean and the variance of the number of open links at temperature T. (This is an oversimplified model of the opening of a double stranded DNA molecule when it replicates or synthesizes mRNA).
Problem #15
Suppose that a system has a ground state with degeneracy W and that there are no accessible higher-energy states. Show that the entropy of this system is just k ln W . (This is the Boltzmann formula for the entropy. In addition to the simple system described here, the Boltzmann formula gives the entropy of a system of known total energy and volume. In that case, W is the number of different ways of rearranging the system without changing the energy or volume.)1.Consider a two-level system in which neither energy level is degenerate. Let the upper level have an energy ∈ relative to the lower level. At what temperature does the population in the upper level become significant relative to that of the lower level?
2.Work out the internal energy and entropy of this system.