Modern Engineering Thermodynamics

Summary 439
Last, we combine Dalton’s and Amagat’s laws with the compressibility factor technique to produce methods for
dealing with the p-v-T mixture properties of real gases and vapors.
Some of the more important equations introduced in this chapter follow. Do not attempt to use them blindly
without understanding their limitations. Please refer to the text material where they are introduced to gain an
understanding of their use and limitations.
1. Mass, mole, volume, and pressure fractions of gas mixtures are defined as follows:
a. w i is the mass fraction of gas i in a mixture of N gases whose total mass is m m = ∑m i
w i = m i
m m
b. χ i is the mole fraction of gas i in a mixture of N gases whose total molar mass is n m = ∑n i
χ i = n i
n m
c. ψ i is the volume fraction of gas i in a mixture of N ideal gases that occupy a total volume of V m = ∑ N
(where V i is the partial volume of ideal gas i in the mixture)
ψ i = V i
V m
d. π i is the pressure fraction of gas i in a mixture of N ideal gases that are subjected to a total pressure of
p m = p i (where p i is the partial pressure of ideal gas i in the mixture)
π i = p i
p m
and the mass, mole, volume, and pressure fractions always sum to unity, or
∑ N
w i = ∑ N
χ i = ∑ N
ψ i = ∑ N
π i = 1:0
i=1 i=1 i=1 i=1
2. The effective molecular mass of a mixture of N gases is given by
M m = ∑ N
i=1
M i and M m =
1
∑ N
w i
i=1
M i
3. The equivalent gas constant of a mixture of N gases is then given by
V i
i=1
R m =
R M m
where R = 8:3143 kJ/ ðkgmole.KÞ = 1545:35 ft .lbf/ ðlbm.RÞ is the universal gas constant.
4. If all the gases in the mixture are ideal gases, then the composition measures are related as follows:
χ i = n i
= ψ
n i = V i
= π i = p
i M
= w m
i
m V m p m M i
5. The changes in specific internal energy, specific enthalpy, and specific entropy for mixtures of ideal gases are
given by
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
Þ+ R m lnðv m2 /v m1 Þ
Þ− R m lnðp m2 /p m1 Þ