Question

Polar rods: consider rod-shaped molecules with moment of inertia i and a dipole moment . The contribution of the rotational degrees of freedom to the hamiltonian is given by hrot = 1 2i p2 + p2 sin2 ! e cos ; (4) where e is an external electric eld. ( 2 [0; 2]; 2 [0; ] are the azimuthal and polar angles, and p, p are the conjugate momenta.) (a) calculate the contribution of the rotational degrees of freedom of each dipole to the classical partition function. (b) obtain the mean polarization p = h cosi > of each dipole. (c) find the zero eld polarizability. t = @p @e je=0: (5) (d) calculate the rotational energy per particle (at nite e), and comment on its high and low-temperature limits. (e) sketch the rotational heat capacity per dipole.

Answer 1

Answer:

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