Transformations In Phase Space Research Articles

On Phase Changes of Bose-Einstein Fluid Models

It is shown that all Bose-Einstein (B.E.) fluid models investigated thus far undergo first-order transformations in phase space. The ideal fluid condenses smoothly, e.g., without any possibility of supersaturation, insofar as its thermodynamic characteristic functions and their first derivatives, with respect to the independent variables, are continuous along the transition or saturation curve. The non-ideal B.E. fluids considered, in which attractive interatomic forces averaged over the volume of the fluid are assumed to operate, undergo sudden condensation strictly similar to that exhibited by ordinary fluids in coordinate space. This process is accompanied by the occurrence of discontinuities of the first derivatives of the characteristic functions. By introducing a suitable repulsive interatomic force, smeared over the volume of the fluid, the smooth condensation of the ideal fluid is changed to a phase transformation of the third order. Here the second derivatives of the characteristic functions exhibit discontinuities along the transformation curve. The same interatomic force lifts the order of the sudden first-order transformation by changing it to a second-order one. This is accompanied by the appearance of the lambda-point type discontinuity of the constant pressure heat capacity along the transition or lambda line. The interplay of forces of parallel and opposing tendencies in modifying the nature of a phase transformation without changing its order and in lifting or lowering their order is thus brought out in these studies over B.E. fluid models. The bearing of these results on the problems connected with the thermal properties of liquid helium is touched upon briefly.