  For a deeply supercooled liquid just above its glass transition temperature,
we present a simple thermodynamic model, where the deeply supercooled liquid is
assumed to be a mixture of solid-like and liquid-like micro regions. The mole
fraction of the liquid-like regions controls the thermodynamic properties of
the supercooled liquid while that of the solid-like regions controls its
relaxation time or viscosity. From the universal temperature dependence of the
molar excess entropy for the deeply supercooled liquids, we derive the
temperature dependence of the mole fraction of the liquid-like regions to
obtain the universal temperature dependence of the relaxation time or the
viscosity for the deeply supercooled liquids. A central parameter of our model
is then shown to be a measure for the fragility of a supercooled liquid. We
also suggest a way to test our physical picture of deeply supercooled liquids
by means of molecular dynamics simulations of model liquids.
