Modern Engineering Thermodynamics

12.9 Mixtures of Real Gases 431
When p, v, T, andc v data on the gas mixture of interest are not available, engineering approximations can be
obtained by combining either Dalton’s orAmagat’s law with the simplified compressibility factor equation of
state pV = ZmRT. For example, using Dalton’s law,
p m = ∑ N
where p Di is the Dalton compressibility factor partial pressure, defined by
i=1
p Di = Z Dm m m R m T m /Vm (12.35)
p Di = Z Di m i R i T m /V m
and Z Di and Z Dm are the Dalton species i and mixture compressibility factors, respectively. Substituting the latter
equation into the former and solving for Z Dm gives
Dalton compressibility factor
Z Dm = ∑ N
i=1
w i M m
Z di = ∑ N
M i
i=1
χ i Z Di (12.36)
For each gas i, the Dalton Z Di compressibility factor is determined from the compressibility charts (Figures 7.5, 7.6,
and 7.9 in Chapter 7) by using the reduced temperature T Ri and reduced pseudospecific volume v′ Ri for gas i at the
temperature and volume of the mixture, or
T Ri = T m /T ci
v′ Ri = v Di p ci /ðR i T ci Þ
= ðV m /m i Þðm m /m m Þðp ci Þ/ðR i T ci Þ = ðv m /w i Þ½p ci /ðR i T ci ÞŠ
= ðV m /n i Þðn m /n m Þðp ci Þ/ðRT ci Þ = ðv m /x i Þ½p ci /ðRT ci ÞŠ
where v Di = V m /m i = v m /w i is the Dalton specific volume of gas i, and v m = V m /m m and v m = V m /n m are the mixture
mass and molar specific volumes, respectively. Notethatwecannotusethereducedpressurep Ri = p Di /p ci in this
case because p Di = Z Di m i R i T m /V m , and Z Di is not usually known in advance.
EXAMPLE 12.14
A new type of fuel for the camping stove shown in Figure 12.12 is made by mixing 3.00 lbm
of methane (CH 4 ) with 4.00 lbm of propane (C 3 H 8 ) and compressing the mixture into a
1.00 ft 3 portable storage tank. Use the Dalton compressibility factor to determine the total
pressure in the tank when it is exposed to the hot summer sun and its internal temperature
reaches 240.°F.
Solution
The unknown is the total pressure in the tank. Here, we use Eq. (12.35) to determine the
mixture pressure as
p m = Z Dmm m R m T m
V m
where Z Dm is the Dalton compressibility factor, determined from Eq. (12.36) as
Z Dm = ∑ N
i=1
w i M m
M i
First, we find the mixture composition and molecular mass. The mass of the entire mixture
is m m = m methane + m propane = 3.00 + 4.00 = 7.00 lbm. The mass fractions are
Z Di
w methane = 3:00=7:00 = 0:429
w propane = 4:00=7:00 = 0:571
FIGURE 12.12
Example 12.14.
(Continued )