We report measurements of tensile strength and average free volume for a set of cohesive powders as a function of consolidation stress. Powders with average particle size between 7.8 and 19.2 mum were made from a styrene/butadiene copolymer, and were subsequently surface-treated with different concentrations of a submicron fumed silica. This silica acts as a flow control additive by controlling interparticle forces. The measurement technique consists of initialization of the sample by fluidization and subsequent consolidation by compression under a given gas flow while continuously monitoring the sample volume. By reversing the gas flow, a tensile stress is applied to the sample. For each consolidation state, we determine the tensile strength and the average free volume of the powder. We find that the relation between the free volume and the consolidation stress follows a logarithmic form. The magnitude of the interparticle forces is estimated from bulk measurements. At high consolidation stresses, the average tensile force per contact increases proportionally to the square root of the consolidation force per contact. Physical implications of these results are discussed.