  The basic continuum model for polar fluids is deceptively simple. The free
energy integral consists of four terms: The coupling of polarization to an
external field, the electrostatic energy of the induced electric field
interacting with itself and the stored polarization energy quadratic in the
polarization. A local function of density accounts for the mechanical state of
the fluid. Viewed as a non-equilibrium free energy functional of number density
and polarization, minimization in these two densities under constraints of the
Maxwell field equations should lead the correct equilibrium state. The
alternative is a continuum mechanics approach in which the mechanical degree of
freedom is extended to full deformation. We show that the continuum
electromechanics method leads to a force balance equation which is consistent
with the density functional equilibrium equation. The continuum mechanics
procedure is significantly more demanding. The gain is a well defined pressure
tensor derived from deformation of total energy. This resolves the issue of the
uncertainty in the pressure tensor obtained from integration of the force
density, which is the conventional method in density based thermomechanics. Our
derivation is based on the variational electrostatics approach developed by
Ericksen (Arch. Rational Mech. Anal. {\bf 183} 299 (2007)).
