Model Of Imperfect Gas Research Articles

Temperley’s model of gas condensation

Temperley’s imperfect gas model is discussed. The stability of the pressure-volume isotherm is considered in the light of Van Hove’s theorem.

On the Surface Tension of Liquid Helium II

The intrinsic surface tension of liquid He II, arising from the structural energy of the free surface, is calculated on the basis of Gross and Pitaevski's imperfect-gas model. The resulting expression, when supplemented by the contribution arising from the presence of quantized surface modes of vibration, gives a value of 0.28 erg ${\mathrm{cm}}^{\ensuremath{-}2}$ for the surface tension of liquid helium in the limit T \ensuremath{\rightarrow} 0\ifmmode^\circ\else\textdegree\fi{}K. This value compares well with the experimental estimate of 0.37 erg ${\mathrm{cm}}^{\ensuremath{-}2}$. It is also demonstrated that the so-called boundary effects, which arise from a better enumeration of the density of states in a bounded statistical system, do not make a significant contribution to the temperature dependence of the surface tension. The dominant contribution is again the one due to the quantized surface modes.

A soluble model of a classical imperfect gas in a vessel

A natural extension of the `Gaussian' model of an imperfect gas permits an exact description of such a gas in a vessel. The conclusion of a former paper that the virial curve extends smoothly to infinite density is confirmed, but it is shown that this fact does not rule out the possibility of a phase transition. A preliminary study suggests that this model would have a transition to an ordered arrangement of molecules, similar to that of the rigid sphere model. Although continuous, this model shares several analytic properties with models of `lattice' type.