(a) Consider a gaseous system of \(N\) noninteracting, diatomic molecules, each having an electric dipole moment \(\mu\), placed in an external electric field of strength \(E\). The energy of such a molecule will be given by the kinetic energy of rotation as well as translation plus the potential energy of orientation in the applied field:

\[
\varepsilon=\frac{p^{2}}{2 m}+\left\{\frac{p_{\theta}^{2}}{2 I}+\frac{p_{\phi}^{2}}{2 I \sin ^{2} \theta}ight\}-\mu E \cos \theta
\]
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) \(|\mu E| \ll k T\). \({ }^{16}\)

(b) The molecule \(\mathrm{H}_{2} \mathrm{O}\) has an electric dipole moment of \(1.85 \times 10^{-18}\) e.s.u. Calculate, on the basis of the preceding theory, the dielectric constant of steam at \(100^{\circ} \mathrm{C}\) and at atmospheric pressure.