Modern Engineering Thermodynamics

438 CHAPTER 12: Mixtures of Gases and Vapors
EXAMPLE 12.17 (Continued )
c. Using the Amagat compressibility factor method, we have
ðp R Þ N2
= p m / ðp c Þ N2
= 1500:
492 = 3:05
ðT R Þ N2
= T m / ðT c Þ N2
= ð−100: + 459:67Þ/227:1 = 1:58
ðp R Þ CH4 = 1500:
673 = 2:23
ðT R Þ CH4
= ð−100: + 459:67Þ/343:9 = 1:05
Using these values in Figure 7.6 of Chapter 7, we find that
and
Then, Eq. (12.38) gives
and
v m = Z Am RT m /p m =
ðZ A Þ N2
= 0:84
ðZ A Þ CH4
= 0:35
Z Am = 0:300ð0:84Þ + 0:700ð0:35Þ
= 0:50
0:50ð1545:35Þð−100: + 459:67Þ
1500: ð144Þ
= 1:29 ft 3 /lbmole
or an error of
1:29 − 1:315
ð100Þ = −1:90% low
1:315
d. Using Kay’s law, Eqs. (12.39) and (12.40), we get
and
Then,
and
p cm = 0:300ð492Þ + 0:700ð673Þ = 619 psia
T cm = 0:300ð227:1Þ + 0:700ð343:9Þ = 309 R
p Rm = 1500:/619 = 2:42
T Rm = ð−100: + 459:67Þ/309 = 1:17
For these reduced values, Figure 7.6 of Chapter 7 gives Z Km = 0.51. Then, the mixture molar specific volume is
v m = Z Km RT m /p m =
0:51ð1545:35Þð − 100: + 459:67Þ
1500: ð144Þ
which has a negligible error from the measured value of 1.315 ft 3 /lbmole.
= 1:31 ft 3 /lbmole
SUMMARY
In this chapter, we deal with the problem of generating thermodynamic properties for homogeneous, nonreacting
mixtures. Because of their engineering value, we focus our analysis on gases and vapors, but the theory
extending beyond Eq. (12.15) can be easily modified to cover mixtures of liquids and solids.
We find that, if the mixture components and ultimately the mixture itself behave as an ideal gas, then all extensive
properties are additive and the partial specific properties reduce to the component specific properties. This
produces simple working equations for all the intensive properties (v, u, h, and s) of the mixture.