  We report measurements and analysis of the specific heat and magnetocaloric
effect at the phase boundary into the single magnetic field-induced phase
(phase II) of U(Ru{0.96}Rh{0.04})2Si2, which yield striking similarities to the
valence transition of Yb{1-x}YxInCu4. To explain these similarities, we propose
a bootstrap mechanism by which a structural distortion causes an electric
quadrupolar order parameter within phase II to become coupled to the
5f-electron hybridization, giving rise to a valence change at the transition.
