We present specific heat experiments on CF2Cl2 monolayers physisorbed on gr
aphite and determine the entropy changes at the structural and melting phas
e transitions. The results confirm previously reported x-ray studies where
a phase sequence from a low-temperature commensurate hexagonal phase to an
incommensurate triangular mesophase and finally the liquid phase was observ
ed. The temperature dependence of the excess entropy reveals that the low t
emperature phase is orientationally ordered. Angular disorder with respect
to reorientation around the surface normal evolves in the mesophase, and is
fully developed just below the melting transition where the molecule start
s to rotate around an axis parallel to the surface. We observe strong evide
nce for two-dimensional random exchange or random field behavior at the mel
ting transition of the mesophase due to the bond; disorder produced by the
rotation about an axis parallel to the surface.