Thermodynamics and Chemistry

CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES

8.2 PHASEDIAGRAMS OFPURESUBSTANCES 207

rs rs

rs

rs

rs

rs

rs

ut

ut

ut

ut

ut

ut

bc bc bc bc ut

bc rs

0

200

400

600

800

1000

270 280 290 300 310

T=K

=

kg m

^3

(a)

ut

ut ut

ut ut

utut

utut

utut

ut

rs

rs rs

rs rs

rsrs

rsrs

rsrs

rs

bc bc bc bc bcbcbcbcbcbcbcbcrs

450

500

550

600

650

700

750

800

850

900

950

1000

1050

315 316 317 318 319

T=K

=

kg m

^3

(b)

Figure 8.8 Densities of coexisting gas and liquid phases close to the critical point

as functions of temperature for (a) CO 2 ;a(b) SF 6 .b Experimental gas densities are

shown by open squares and experimental liquid densities by open triangles. The mean

density at each experimental temperature is shown by an open circle. The open dia-

mond is at the critical temperature and critical density.

aBased on data in Ref. [ 116 ].

bData of Ref. [ 127 ], Table VII.

Tandp, the system point moves to point B at the right end of the tie line.V=nat this point
must be the same as the molar volume of the gas,Vmg. We can see this because the system
point could have moved from within the one-phase gas area to this position on the boundary
without undergoing a phase transition.
When, on the other hand, enough heat is transferred out of the system to condense all
of the gas, the system point moves to point A at the left end of the tie line.V=nat this point
is the molar volume of the liquid,Vml.
When the system point is at position S on the tie line, both liquid and gas are present.
Their amounts must be such that the total volume is the sum of the volumes of the individual
phases, and the total amount is the sum of the amounts in the two phases:

V DVlCVgDnlVmlCngVmg (8.2.1)

nDnlCng (8.2.2)

The value ofV=nat the system point is then given by the equation

V

n

D

nlVmlCngVmg

nlCng

(8.2.3)