The free energy of the hydrophobic hydration and the strength of the solvent-mediated attraction between hydrophobic solute molecules are calculated in the pressure-temperature plane. This is done in the framework of an exactly soluble model that is an extension of the lattice model proposed by Kolomeisky and Widom [A. B. Kolomeisky and B. Widom, Faraday Discuss. 112, 81 (1999)]. The model takes into account both the mechanism of the hydrophobic effect dominant at low temperatures and the opposite mechanism of solvation appearing at high temperatures and has the pressure as a second thermodynamic variable. With this model, two boundaries are identified in the pressure-temperature plane: the first one within which the solubility, or the Ostwald absorption coefficient, decreases with increasing temperature at fixed pressure and the second one within which the strength of solvent-mediated attraction increases with increasing temperature. The two are nearly linear and parallel to each other, and the second boundary lies in the low-temperature and low-pressure side of the first boundary. It is found that a single, near-linear relation between the hydration free energy and the strength of the hydrophobic attraction holds over the entire area within the second boundary in the pressure-temperature plane. (C) 2004 American Institute of Physics.