In this paper we present a two-fluid model for the heating of the solar cor
ona and acceleration of the solar wind, based on the dissipation of Alfven
waves by gravity damping. This mechanism was proposed by Khabibrakhmanov &
Mullan but has not previously been applied in modeling efforts. After exten
ding the Khabibrakhmanov & Mullan theory to give an expression for the evol
ution of the Alfven wave amplitude as a function of the local parameters of
the atmosphere, we show how gravity damping compares with other mechanisms
that have been proposed for the dissipation of Alfven waves. Then we intro
duce the system of equations that we use for the wind model: this includes,
in the energy equation, a gravity dissipation term and, in the momentum eq
uation, a different wave acceleration term from that which is usually adopt
ed. Initial conditions for the integration of the equations are compatible
with recent Ulysses measurements, and the integration proceeds from 1 AU to
ward the base of the solar corona and into the transition region [where T =
(1-2) x 10(5) K]. Our results show that the gravity damping of Alfven wave
s heats protons in the solar plasma to several million degrees and accelera
tes the solar wind to 600-700 km s(-1). Model predictions at low heliocentr
ic distances compare favorably with recently acquired data. One prediction
of our model is that the damping process is most effective in regions where
the Alfven speed is low. Another prediction is that although the energy is
deposited mainly into protons, the deposition occurs close enough to the S
un that collisional coupling also leads to effective heating of the electro
ns (to T-e approximate to 10(6) K). We compare and contrast the present mod
el with models based on ion-cyclotron resonant processes.