N indistinguishable, non-interacting, monoatomic gas particles are placed into a container of size V and temperature T. Each of these particles has a dipole moment of magnitude d, which contributes to an overall polarization P. Each dipole can only point in one of six directions - +x, y, z. (need to consider molecules that point in the z-direction too) You apply an electric field E that points in the x- y plane with an angle 0. Remember that the work term for electric field/polarization systems is given by SW = E. dp (1) What is the characteristic potential for this system? (2) Write down the appropriate partition function for this ensemble and express the characteristic potential in terms of this partition function. (3) Write the analytical form of the partition function (remember to include both the effect of the applied field and the translation of the gas). (4) Express the entropy S as a function of the temperature (7), 0, IE\, d, and N.