Chapman's conductive model of the solar corona is characterized by a temperature varying as r-2/7 with heliocentric distance r. The density distribution in this non-isothermal hydrostatic model has a minimum value at 123RS, and increases with r above that altitude. It is shown that this hydrostatic model becomes convectively unstable above r=35R S, where the temperature lapse rate becomes superadiabatic. Beyond this radial distance heat conduction fails to be efficient enough to keep the temperature gradient smaller than the adiabatic lapse rate. We report the results obtained by Lemaire who showed that an additional mechanism is then required to transport the energy flux away from the Sun into interplanetary space. He pointed out that this additional mechanism is advection: i.e. the stationary hydrodynamic expansion of the corona. In other words the corona is unable to stay in hydrostatic equilibrium. The hydrodynamic solar wind expansion is thus a physical consequence of the too steep (superadiabatic) temperature gradient beyond the peak of coronal temperature that can be determined from white light brightness distributions observed during solar eclipses. The thermodynamic argument for the existence of a continuous solar wind expansion which is presented here, complements Parker's classical argument based on boundary conditions imposed to the solutions of the hydrodynamic equations for the coronal expansion: i.e. the inability of the mechanical forces to hold the corona in hydrostatic equilibrium. The thermodynamic argument presented here is based on the energy transport equation. It relies on the temperature distribution which becomes super-adiabatic above a certain altitude in the inner corona.