The phase transition of the first order in the critical region of the gas-liquid system

Abstract

This is a summarising investigation of the events of the phase transition of the first order that occur in the critical region below the liquid-gas critical point. The grand partition function has been completely integrated in the phase-space of the collective variables. The basic density measure is the quartic one. It has the form of the exponent function with the first, second, third and fourth degree of the collective variables. The problem has been reduced to the Ising model in an external field, the role of which is played by the generalised chemical potential μ*. The line μ*(η) =0, where η is the density, is the line of the phase transition. We consider the isothermal compression of the gas till the point where the phase transition on the line μ*(η) =0 is reached. When the path of the pressing reaches the line μ* =0 in the gas medium, a droplet of liquid springs up. The work for its formation is obtained, the surface-tension energy is calculated. On the line μ* =0 we have a two-phase system: the gas and the liquid (the droplet) one. The equality of the gas and of the liquid chemical potentials is proved. The process of pressing is going on. But the pressure inside the system has stopped, two fixed densities have arisen: one for the gas-phase ηG=ηc(1-d/2) and the other for the liquid-phase ηL=ηc(1+d/2) (symmetrically to the rectlinear diameter), where ηc=0.13044 is the critical density. Starting from that moment the external pressure works as a latent work of pressure. Its value is obtained. As a result, the gas-phase disappears and the whole system turns into liquid. The jump of the density is equal to ηc d, where d=√D/2G ~ τν/². D and G are coefficients of the Hamiltonian in the last cell connected with the renormalisation-group symmetry. The equation of state is written.

Розглядається поведiнка системи взаємодiючих частинок в областi температур нижче критичної точки T É Tc. Завершується розрахунок великої статистичної суми, початий у попереднiх роботах у методi колективних змiнних. За базову густину мiри береться четвiрний (а не Гаусовий) розподiл. Описанi подiї пов’язанi з фазовим переходом 1-го роду, що вiдбуваються в результатi iзотермiчного квазiстатичного стиснення газу. Видiлена лiнiя µ ∗(η) = 0, на якiй у газовiй фазi пiд дiєю тиску виникає крапля рiдини. Має мiсце рiвнiсть хiмiчних потенцiалiв газової i рiдкої (у краплi) фаз; знайдено величину поверхневої енергiї краплi, розраховано скриту роботу конденсацiї, визначено скачок густини, написано рiвняння стану. Робота становить певну кiнцеву стадiю дослiджень в областi температур i густин, що включає у собi критичну точку рiдина–газ.