Modern Engineering Thermodynamics

12.9 Mixtures of Real Gases 433
and Eq. (12.35) gives the mixture pressure as
p m = Z Dm m m R m T m
V m
= ð0:892Þð7:00 lbmÞð61:3ft .lbf/lbm.RÞð240: + 459:67 RÞ
1:00 ft 3
= ð268 × 10 3 lbf=ft 2 Þ ÷ ð144 in: 2 /ft 2 Þ = 1860 psia
Exercises
36. Determine the total pressure in the tank in Example 12.14 when the mixture is changed to 2.00 lbm of methane and
5.00 lbm of propane with all of the other variables remaining unchanged. Answer: p total = 1470 psia.
37. Determine the total pressure in the tank in Example 12.14 if the tank volume is reduced from 1.00 ft 3 to 0.500 ft 3 with
all the other variables remaining unchanged. Answer: p total = 3400 psia.
38. Determine the total pressure in the tank in Example 12.14 when the propane is replaced by the same mass of ethane
(C 2 H 6 ). Answer: p total = 2200 psia.
Alternatively, we could use Amagat’s law and incorporate a real gas compressibility factor as
V m = ∑ N
where V Ai is the Amagat compressibility factor partial volume defined by
i=1
V Ai = Z Amm m R m T m
p m
(12.37)
V Ai = Z Ai m i R i T m /p m
and Z Ai and Z Am are Amagat species i and mixture compressibility factors, respectively. Substituting the latter
equation into the former gives
Amagat compressibility factor
Z Am = ∑ N
ðw i M m /M i ÞZ Ai = ∑ N
x i Z Ai (12.38)
i=1
In this case, for each gas i, the Amagat Z Ai compressibility factor is determined from the compressibility charts using
the reduced temperature T Ri and reduced pressure p Ri for gas i at the temperature and pressure of the mixture, or
and
p Ri = p m /p ci
T Ri = T m /T ci
Note that we cannot use the reduced pseudospecific volume v′ Ri = v Ai p m / ðR i T m Þ in this case because the Amagat
specific volume is given by v Ai = V Ai /m i = Z Ai R i T m /p m ,andZ Ai is not usually known in advance.
i=1
EXAMPLE 12.15
The test chamber atmosphere for a new electrical device requires a mixture of 1.00 kg of each of the following gases:
ammonia (NH 3 ), chlorine (Cl 2 ), and nitrous oxide (N 2 O). Use the Amagat compressibility factor to determine the volume
occupied by this mixture at a total pressure of 20.0 MPa and a mixture temperature of 500. K.
Solution
Here, we use Eq. (12.37) to determine the mixture total volume as
V m = Z Am m m R m T m
p m
where Z Am is the Amagat compressibility factor, determined from Eq. (12.38) as
Z Am = ∑ N
w i M m
Z Ai
i=1
M i
(Continued )