Infrared spectroscopy takes advantage of the ability of covalentbonds in a molecule to absorb light of certain energy. To assignparticular peaks in an IR spectrum to a certain type of bond,covalent bonds are modeled as springs between two atoms. Hooke’sLaw tells us that the energy (U) of the bond is a function oftemperature and the distance between the atoms, so U = U(T,x). Thechange in volume upon stretching a bond is negligible, so the workdone on the bond is given by w = F dx.
a. Write out an expression for the differential change inentropy, starting with the first/second laws of thermodynamics andthe total derivative of U(T,x). Assume the stretching of a bondthrough infrared light exposure is reversible.
b. If the process occurs at constant temperature T and Hooke’sLaw says that U = ½ kx2  (where k is referredto as the spring constant) and F = 4x, give the expression for DSwhen stretching a bond from x1 to x2.
