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This work tests the statistical mechanical theory of hydrophobic interactions, isolates consequences of excluded volume interactions, and obtains B2 for those purposes. Cavity methods that are particularly appropriate for study of hydrophobic interactions between atomic-size hard spheres in liquid water are developed and applied to test aspects of the Pratt-Chandler (PC) theory that have not been tested. Contact hydrophobic interactions between Ar-size hard-spheres in water are significantly more attractive than predicted by the PC theory. The corresponding results for the osmotic second virial coefficient are attractive (B2 <0), and more attractive with increasing temperature (Delta B2/Delta T < 0) in the temperature range 300K < T < 360K. This information has not been available previously, but is essential for development of the molecular-scale statistical mechanical theory of hydrophobic interactions, particularly for better definition of the role of attractive intermolecular interactions associated with the solutes., Comment: five pages, four figures