Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

to imagine that the two phases are mixed well, forming a homogeneous

mixture (Fig. 3–35). Then the properties of this “mixture” will simply be

the average properties of the saturated liquid–vapor mixture under consider-

ation. Here is how it is done.

Consider a tank that contains a saturated liquid–vapor mixture. The vol-

ume occupied by saturated liquid is Vf, and the volume occupied by satu-

rated vapor is Vg. The total volume Vis the sum of the two:

Dividing by mtyields

since x
mg/mt. This relation can also be expressed as

(3–4)

where vfg
vgvf. Solving for quality, we obtain

(3–5)

Based on this equation, quality can be related to the horizontal distances

on a P-vor T-vdiagram (Fig. 3–36). At a given temperature or pressure, the

numerator of Eq. 3–5 is the distance between the actual state and the satu-

rated liquid state, and the denominator is the length of the entire horizontal

line that connects the saturated liquid and saturated vapor states. A state of

50 percent quality lies in the middle of this horizontal line.

The analysis given above can be repeated for internal energy and enthalpy

with the following results:

(3–6)

(3–7)

All the results are of the same format, and they can be summarized in a sin-

gle equation as

where yis v,u, or h. The subscript “avg” (for “average”) is usually dropped

for simplicity. The values of the average properties of the mixtures are

always betweenthe values of the saturated liquid and the saturated vapor

properties (Fig. 3–37). That is,

Finally, all the saturated-mixture states are located under the saturation

curve, and to analyze saturated mixtures, all we need are saturated liquid

and saturated vapor data (Tables A–4 and A–5 in the case of water).

yfyavgyg

yavg
yfxyfg

havg
hfxhfg¬¬ 1 kJ>kg 2

uavg
ufxufg¬¬ 1 kJ>kg 2

x

vavgvf

vfg

vavg
vfxvfg¬¬ 1 m^3 >kg 2

vavg
 11 x 2 vfxvg

mf
mtmg¡mtvavg
 1 mtmg 2 vfmgvg

V
mv¡mtvavg
mfvfmgvg

V
VfVg

130 | Thermodynamics

vg

v f

Saturated liquid

Saturated vapor

Saturated

liquid–vapor

mixture

≡

vavg

FIGURE 3–35

A two-phase system can be treated as a
homogeneous mixture for convenience.

P or T

v avg – v f

AB

AB

AC

x =

C

vfg

vf vavg vg v

FIGURE 3–36

Quality is related to the horizontal
distances on P-vand T-vdiagrams.