  We discuss the generalized second law (GSL) and the constraints imposed by it
for two types of Friedmann universes. The first one is the Friedmann universe
with radiation and a positive cosmological constant, and the second one
consists of non-relativistic matter and a positive cosmological constant. The
time evolution of the event horizon entropy and the entropy of the contents
within the horizon are analyses in an analytical way by obtaining the Hubble
parameter. It is shown that the GSL constraint the temperature of both the
radiation and matter of the Friedmann universe. It is also shown that, even
though the net entropy of the radiation (or matter) is decreasing at
sufficiently large times as the universe expand, it exhibit an increase during
the early times when universe is decelerating. That is the entropy of the
radiation within the comoving volume is decreasing only when the universe has
got an event horizon.
