Modern Engineering Thermodynamics

412 CHAPTER 12: Mixtures of Gases and Vapors
EXAMPLE 12.2 (Continued )
2. Oops, Research discovered still another error; it turns out that the composition given in Example 12.1 was correct except
that it is 50.0% propane and 50.0% air on a molar basis. Now , Research wants you to determine the corresponding
mass based composition. Answer: w propane = 0.603 and w air = 0.397.
3. A more detailed composition for air than that given in Example 12.2 is
Component Molar % (Answer: Mass %)
Nitrogen (N 2 ) 78.084 75.519
Oxygen (O 2 ) 20.948 23.143
Argon (Ar) 0.934 1.288
Carbon dioxide (CO 2 ) 0.0314 0.0477
Neon (Ne) 0.00182 0.00127
Helium (He) 0.000520 0.0000720
Methane (CH 4 ) 0.000200 0.000110
Krypton (Kr) 0.000110 0.000320
Hydrogen (H 2 ) 0.0000500 0.00000350
Dinitrogen monoxide (N 2 O) 0.0000500 0.0000620
Xenon (Xe) 0.00000800 0.0000360
Total = 100.000% 100.000%
Determine the equivalent molecular mass and the corresponding composition on a mass (or weight) basis. Answer:
M m = 28.97 kg/kgmole = 28.97 lbm/lbmole, and see the table.
12.3 MIXTURES OF IDEAL GASES
A mixture of ideal gases behaves as a unique ideal gas with an equivalent molecular mass M m and gas
constant R m given by Eqs. (12.11) or (12.12) and (12.15). Ideal gas mixtures obey all of the ideal gas
equations of state:
p m V m = m m R m T m
u m2 − u m1 =
Z Tm2
T m1
c vm dT m
and
h m2 − h m1 =
Z Tm2
T m1
c pm dT m
s m2 − s m1 =
=
Z Tm2
T m1
Z Tm2
T m1
ðc vm /T m Þ dT m + R m lnðv m2 /v m1 Þ
c pm /T m dTm − R m lnðp m2 /p m1 Þ
where p m and T m are the mixture pressure and temperature, respectively. If the mixture can be considered to
have constant specific heats, then these equations reduce to
u m2 − u m1 = c vm ðT m2 − T m1 Þ
h m2 − h m1 = c pm ðT m2 − T m1 Þ
s m2 − s m1 = c vm lnðT m2 /T m1
= c pm lnðT m2 /T m1
i=1
Þ+ R m lnðv m2 /v m1 Þ
Þ− R m lnðp m2 /p m1 Þ
From p m V m = m m R m T m and Eqs. (12.3), (12.12), and (12.15), we find that, for a mixture of ideal gases,
V m = m
mR m T m
= m
R T m
m
p m M m p m
= m m R ∑ N !
w i T m
= RT N
m
M i p m p ∑
m i
m M i
i=1