Modern Engineering Thermodynamics

12.9 Mixtures of Real Gases 435
Then, Eq. (12.38) gives the Amagat compressibility factor for the mixture as
Z Am = ∑ 3
i=1
w i M m
M i
Z Ai
= w
ammoniaM m
ðZ A Þ
M ammonia
+
w
chlorineM m
ammonia
M chlorine
=
ð0:333Þð31:4 kg/kgmole mixtureÞ
ð0:64Þ
17:030 kg/kgmole ammonia
ð0:333Þð31:4kg/kgmole mixtureÞ
+ ð0:55Þ
70:906 kg/kgmole chlorinee
ðZ A Þ chlorine
+
ð0:333Þð31:4 kg/kgmole mixtureÞ
+ ð0:86Þ = 0:68
44:013 kg/kgmole nitrous oxide
The mixture gas constant can now be calculated from
w nitrous oxideM m
M nitrous oxide
ðZ A Þ nitrous oxide
R m =
R M m
= 8:3143 kJ/ðkgmole .KÞ
31:4 kg/kgmole
= 0:265 kJ
kg .K
Then, Eq. (12.37) gives the total volume of the mixture as
V m = Z Am m m R m T m
p m
= ð0:68Þð3:00 kgÞð0:265 kJ/ðkg .KÞÞð500: KÞ
ð20:0 MPaÞð1000: kPa/MPaÞ
= 0:0135 m 3
Exercises
39. Determine the volume in Example 12.15 if the composition is changed to 1.00 kg of ammonia and chlorine but 5.00 kg
of nitrous oxide. Answer: V = 0:0297 m 3 .
40. If the mixture temperature in Example 12.15 is increased from 500. K to 1000. K, what volume would then be required
to hold the mixture if all the other variables remain unchanged? Answer: V = 0:0401 m 3 .
41. If the nitrous oxide gas is eliminated from the mixture in Example 12.15 and the masses of ammonia and chlorine are
each increased to 1.50 kg, what volume would then be required to hold this new mixture if all the other variables
remain unchanged? Answer: V = 0:0141 m 3 .
It should be clear from the preceding formulae that Z Di ≠ Z Ai ; therefore, the resultant Dalton and Amagat mixture
compressibility factors also in general are not equal, or Z Dm ≠ Z Am .
Dalton’s law for mixtures of real gases (Eq. (12.35)) is based on the premise that each gas in the mixture acts as
though it alone occupies the entire volume of the mixture at the temperature of the mixture. Therefore, the
gases are assumed not to interact in any manner. We do not find this to be true experimentally except at very
low pressures or very high temperatures.
Amagat’s law for mixtures of real gases (Eqs. (12.37)), on the other hand, incorporates the resultant mixture
pressure and, therefore, automatically takes gas molecular interactions into account. Consequently, it tends to be
more accurate than Dalton’s law at high pressures and low temperatures.
A third method of incorporating the compressibility factor charts into predicting the behavior of real gas mixtures
involves defining a pseudocritical pressure and a pseudocritical temperature for the mixture as
and
Kay’s law
P cm = ∑ N
x i P ci (12.39)
i=1
T cm = ∑ N
i=1
x i T ci (12.40)