Suppose we have a gas in a closed fixed container, each molecule of which has a permanent dipole moment \"3 Permanent means that the orientation of the dipole moment can change, but its magnitude cannot. The gas is E affected by a homogeneous electric field (ie the strength of the field does not depend on the location), which polarizes the gas by interacting with the dipole moments of the gas molecules. It is assumed that the mutual interactions between gas molecules, including dipoledipole interactions, are vanishingly small The interaction energy of one molecule with an electric field is 8 : i\" ' E, We now consider the case of the weak interaction Hg : (XE, _} where 0 is the angle between the molecule's dipole moment u' and the electric eld E . 1) .Write the partition function ZE related to the dipole momentelectric eld interaction of one molecule 2) .Write an expression for the probability that the orientation angle of the molecule's dipole 9, 9+d9. moment is between 3) Based on the results of the previous sections, determine the expression for the molecular polarizability (I