Abstract: Using the free energy and the equation of state for an imperfect Bose gas, the analytical expression between the critical temperature and the length of dispersion wave and the pressure for the imperfect Bose gas is derived. The unusual properties of the specific heat at constant pressure and the expansion coefficient at constant pressure and isothermal compressibility by the attractive force for the imperfect Bose gas are revealed. The instability arising from the attractive force is pointed out, and the temperature criterion and particle density criterion of instability is given for the imperfect Bose gas under the action of attraction.

Keywords: 
• interaction /
• Bose gas /
• thermodynamical properties /
• criterion of instability