General Physics by L.D. Landau A.I. Akhiezer & E.M. Lifshitz

Author:L.D. Landau, A.I. Akhiezer & E.M. Lifshitz
Language: eng
Format: epub
Tags: Physics; Particle Mechanics; Fields; Motion; Oscillations; Matter; Symmetry; Heat; Viscosity; Phase Transitions; Chemical Reactions; Solutions; Surface Phenomena; Diffusion; Solids

The specific volumes of the gas and the liquid which are formed from each other (V g and V t ) are functions of the temperature at which the transition occurs. When these two functions are represented by appropriate curves, we obtain a phase diagram of the kind shown in Fig. 82. The regions of the diagram to the right and left of the hatched area correspond to the gaseous and liquid phases. The hatched area between the two curves is the region of separation into two phases. The horizontal hatching is significant: the points A and B at which a horizontal line through a point C in this region meets the boundaries of the region give the specific volumes of the liquid and vapour coexisting at that point.

The different points on AB evidently correspond to equilibrium of the same liquid and vapour in different relative amounts. Let the fractions of vapour and liquid at some point C be x and 1 — x. Then the total volume of the system per unit mass is

V = xV a +(l-x)V h

whence

_ V-Vi t _ x yr l x

The ratio of these quantities is

x ^ V-V l = BC

\-x V g -V AC "

We see that the quantities of vapour and liquid are inversely proportional to the lengths of AC and BC, i.e. the distances of C from the points A and B which correspond to the pure vapour and pure liquid. This relation is called the lever rule.

The phase diagram with pressure instead of temperature as ordinate is exactly similar in appearance. We see that these diagrams do not resemble the diagrams in the pT plane. The region of separation into two phases, which in the pT diagram is only a line, occupies a whole area in the VT and Vp diagrams. This difference arises because phases in equilibrium necessarily have the same temperature and pressure by the general conditions of thermal equilibrium, but their specific volumes are different.

Table 1 shows the melting and boiling points of a number of substances (at atmospheric pressure).

Table 1

Helium liquefies at a lower temperature than any other substance existing in Nature; the solidification of helium will be discussed in §72. Tungsten has higher melting and boiling points than those of any other chemical element.

§67]

THE CLAUSIUS-CLAPEYRON EQUATION

201

§67. The Clausius-Clapeyron equation

The transition of matter from one phase to another always involves the gain or loss of a certain quantity of heat called the latent heat or heat of transition. When a liquid becomes a gas this is the heat of evaporation; when a solid becomes a liquid, it is the heat of fusion.

Since a phase transition occurs at constant pressure, the heat of transition q 12 from phase 1 to phase 2 is equal to the difference of the enthalpies W x and W 2 of the substance in the two phases (see §56):

Qt2=W 2 -W l .

It is clear that q 12 = — q 21 , i.e. if heat is absorbed in a given phase transition, the reverse transition is accompanied by the evolution of heat.

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