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

In the van der Waals equation, for example, the two constants for the mixture

are determined from

(13–12a, b)

where expressions for aiand biare given in Chapter 3.

am
aa

k

i
 1

yia^1 i>^2 b

2

¬and¬bm
a

k

i
 1

yibi

Chapter 13 | 687

EXAMPLE 13–2 P-v-TBehavior of Nonideal Gas Mixtures

A rigid tank contains 2 kmol of N 2 and 6 kmol of CO 2 gases at 300 K and

15 MPa (Fig. 13–10). Estimate the volume of the tank on the basis of

(a) the ideal-gas equation of state, (b) Kay’s rule, (c) compressibility factors

and Amagat’s law, and (d) compressibility factors and Dalton’s law.

Solution The composition of a mixture in a rigid tank is given. The volume

of the tank is to be determined using four different approaches.

Assumptions Stated in each section.

Analysis (a) When the mixture is assumed to behave as an ideal gas, the

volume of the mixture is easily determined from the ideal-gas relation for the

mixture:

since

(b) To use Kay’s rule, we need to determine the pseudocritical temperature

and pseudocritical pressure of the mixture by using the critical-point proper-

ties of N 2 and CO 2 from Table A–1. However, first we need to determine the

mole fraction of each component:

Then,

Thus,

Vm

Zm Nm Ru Tm

Pm

ZmVideal
 1 0.49 21 1.330 m^32 
0.652 m^3

TR 

Tm

Tcr,¿m

300 K

259.7 K

1.16

PR

Pm

P¿cr,m

15 MPa

6.39 MPa

2.35

∂Zm
0.49¬¬ 1 Fig. A–15b 2

 1 0.25 21 3.39 MPa 2  1 0.75 21 7.39 MPa 2 
6.39 MPa

P¿cr,m 
ayi Pcr,i
yN 2 Pcr,N 2 yCO 2 Pcr,CO 2

 1 0.25 21 126.2 K 2  1 0.75 21 304.2 K 2 
259.7 K

Tcr,¿m 
ayi Tcr,i
yN 2 Tcr,N 2 yCO 2 Tcr,CO 2

yN 2 

NN 2

Nm

2 kmol

8 kmol

0.25¬and¬yCO 2

NCO 2

Nm

6 kmol

8 kmol

0.75

Nm
NN 2 NCO 2 
 2  6 
8 kmol

Vm

NmRuTm

Pm

1 8 kmol 21 8.314 kPa#m^3 >kmol#K 21 300 K 2

15,000 kPa

1.330 m^3

2 kmol N 2

6 kmol CO 2

300 K

15 MPa

Vm =?

FIGURE 13–10

Schematic for Example 13–2.

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