(a) Consider a gaseous system of N non-interacting, diatomic molecules, each having an electric dipole moment μ, placed in an external electric field of strength E. The energy of a molecule will be given by the kinetic energy of rotation as well as of translation plus the potential energy of orientation in the applied field:
ε=2mp2+{2Ipθ2+2Isin2θpϕ2}−μEcosθ,
where I is the moment of inertia of the molecule. Study the thermodynamics of this system, including the electric polarization and the dielectric constant. Assume that (i) the system is a classical one and (ii) ∣μE∣≪kT.
(b) The molecule H2O has an electric dipole moment of 1.85×10−18 e.s.u. Calculate, on the basis of the preceding theory, the dielectric constant of steam at 100∘C and at atmospheric pressure.