Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

708 | Thermodynamics

A mixture of two or more gases of fixed chemical composi-

tion is called a nonreacting gas mixtureThe composition of a

gas mixture is described by specifying either the mole frac-

tionor the mass fractionof each component, defined as

where

The apparent(or average) molar massand gas constantof a

mixture are expressed as

Also,

Dalton’s law of additive pressuresstates that the pressure

of a gas mixture is equal to the sum of the pressures each gas

would exert if it existed alone at the mixture temperature and

volume. Amagat’s law of additive volumesstates that the vol-

ume of a gas mixture is equal to the sum of the volumes each

gas would occupy if it existed alone at the mixture tempera-

ture and pressure. Dalton’s and Amagat’s laws hold exactly

for ideal-gas mixtures, but only approximately for real-gas

mixtures. They can be expressed as

Dalton’s law:

Amagat’s law:

Here Piis called the component pressureand Viis called

the component volume. Also, the ratio Pi/Pmis called the

pressure fractionand the ratio Vi/Vmis called the volume

fractionof component i. For ideal gases,Piand Vican be

related to yiby

The quantity yiPmis called the partial pressureand the quan-

tity yiVmis called the partial volume. The P-v-Tbehavior

of real-gas mixtures can be predicted by using generalized

Pi

Pm

Vi

Vm

Ni

Nm

yi

Vm
a

k

i
 1

Vi 1 Tm, Pm 2

Pm
a

k

i
 1

Pi 1 Tm, Vm 2

mfi
yi

Mi

Mm

¬and¬Mm

1

a

k

i
 1

mfi

Mi

Mm

mm

Nm

a

k

i
 1

yiMi¬and¬Rm

Ru

Mm

mm
a

k

i
 1

mi¬and¬Nm
a

k

i
 1

Ni

mfi

mi

mm

¬and¬yi

Ni

Nm

SUMMARY

compressibility charts. The compressibility factor of the mix-

ture can be expressed in terms of the compressibility factors

of the individual gases as

where Ziis determined either at Tmand Vm(Dalton’s law) or at

Tmand Pm(Amagat’s law) for each individual gas. The P-v-T

behavior of a gas mixture can also be predicted approximately

by Kay’s rule,which involves treating a gas mixture as a pure

substance with pseudocritical properties determined from

The extensive propertiesof a gas mixture, in general, can

be determined by summing the contributions of each compo-

nent of the mixture. The evaluation of intensive propertiesof

a gas mixture, however, involves averaging in terms of mass

or mole fractions:

and

These relations are exact for ideal-gas mixtures and approxi-

mate for real-gas mixtures. The properties or property changes

of individual components can be determined by using ideal-

gas or real-gas relations developed in earlier chapters.

cp,m
a

k

i
 1

mficp,i¬and¬cp,m
a

k

i
 1

yicp,i

cv,m
a

k

i
 1

mficv,i¬and¬cv,m
a

k

i
 1

yicv,i

sm
a

k

i
 1

mfisi¬and¬sm
a

k

i
 1

yisi

hm
a

k

i
 1

mfihi¬and¬hm
a

k

i
 1

yihi

um
a

k

i
 1

mfiui¬and¬um
a

k

i
 1

yiui

Sm
a

k

i
 1

Si
a

k

i
 1

mi si
a

k

i
 1

Nisi

Hm
a

k

i
 1

Hi
a

k

i
 1

mihi
a

k

i
 1

Nihi

Um
a

k

i
 1

Ui
a

k

i
 1

miui
a

k

i
 1

Niui

P¿cr,m
a

k

i
 1

yi Pcr,i¬and¬T¿cr,m
(^) a
k
i
1
yi Tcr,i
Zm
a
k
i
1
yi Zi
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