Modern Engineering Thermodynamics

74 CHAPTER 3: Thermodynamic Properties
Pressure, p
x = 0
v g − v f
Critical point
Actual
state
x = 1
Equation (3.21) is just a simple mass-based lever rule equation
relating a mixture thermodynamic property (v) tothethermodynamic
properties of the components of the mixture (v f and
v g ). We now define the quality x of a liquid plus vapor mixture
as the relative amount of vapor present, or
Quality = x =
Mass of vapor
Mass of vapor
=
Mass of vapor + Mass of liquid Total mass
v − v f
or
v f
v v g
Specific volume, v
FIGURE 3.16
The lever rule for calculating quality.
m g
x =
m f + m g
Therefore, Eq. (3.21) can be written as
which can be rearranged as
where we define the magnitude of the liquid to vapor property change as
From Figure 3.16, we see that another definition of quality is
= m g
m
(3.22)
v = ð1 − xÞv f + xv g (3.23)
v = v f + xðv g − v f Þ = v f + xv fg (3.24)
v fg = v g − v f (3.25)
x = v − v f
v fg
(3.26)
It should be clear from the definition of quality that its value has the following bounds
Saturated liquid : x = 0
Saturated vapor : x = 1
Wet ðliquid plus vaporÞ region : 0 < x < 1
WHY DO THEY CALL IT QUALITY?
In the 19th century, there were a lot of steam engines.
Railroads, factories, ships, and so on all used steam engines
as their source of power. The people responsible for keeping
these engines running noticed that they worked better if the
steam contained more vapor than liquid. So, a mixture that
contained a lot of vapor and little liquid was said to be of
high quality. Theydefinedthisquality to be the ratio of the
mass of vapor to total mass of liquid plus vapor (Figure
3.17), or quality = x = m g /(m f + m g )=m g /m. Ontheother
hand, the amount of liquid present in a mixture is called
the moisture of the mixture, defined as moisture = m f /m =
1 − x. Since these definitions apply only to mixtures of
liquid plus vapor, they do not extend outside of the vapor
dome. The condition where the quality x =1.0isreserved
for saturated vapor and does not apply to superheated
vapor. Similarly, the condition where quality x =0 is
reserved for saturated liquid and does not apply to compressed
liquid. Note that the quality x of a liquid-vapor mixture
can never be less than 0 or greater than 1.0. That is, x
always falls in the range 0 < x < 1.0.
Vapor
Liquid
High quality,
low moisture
Vapor
Liquid
Low quality,
high moisture
FIGURE 3.17
Why do they call it quality? In all other single-phase regions
(compressed liquid, superheated vapor, gaseous), x is not defined,
because these are single-phase homogeneous regions. Note that,
since the numerical value of quality is restricted to lie in the range
from 0 to 1, no correct calculation can ever give a value of x less
than 0 or greater than 1.0.