We show that the pressure of the Bogoliubov weakly imperfect Bose gas (WIBG) can be calculated exactly in the thermodynamic limit. We point out the sufficient and necessary conditions for it not to equate with the pressure of the ideal Bose gas (IBG). We prove that they differ only in that part of the phase diagram where the WIBG has a Bose condensate. We show that in contast to the conventional Bose condensate (e.g. in the IBG) the condensate in the WIBG is due to an effective attraction between bosons in the zero-mode.
It is shown that the condensation in the Bogoliubov Weakly Imperfect Bose{Gas (WIBG) may appear in two stages.If the interaction is such that the pressure of the WIBG does not coincide with the pressure of the Perfect Bose{Gas (PBG), then the WIBG may manifest two kinds of condensations: a non{conventional condensation in the zero{mode due to the interaction (the rst stage) and a conventional (generalized of type I) Bose{Einstein condensation in modes next to the zero{mode due to the particle density saturation (the second stage).