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

13–3
PROPERTIES OF GAS MIXTURES:

IDEAL AND REAL GASES

Consider a gas mixture that consists of 2 kg of N 2 and 3 kg of CO 2. The
total mass (an extensive property) of this mixture is 5 kg. How did we do it?
Well, we simply added the mass of each component. This example suggests
a simple way of evaluating the extensive propertiesof a nonreacting ideal-
or real-gas mixture:Just add the contributions of each component of the
mixture(Fig. 13–11). Then the total internal energy, enthalpy, and entropy
of a gas mixture can be expressed, respectively, as

(13–13)

(13–14)

(13–15)

By following a similar logic, the changes in internal energy, enthalpy, and
entropy of a gas mixture during a process can be expressed, respectively, as

(13–16)

(13–17)

(13–18)

Now reconsider the same mixture, and assume that both N 2 and CO 2 are at
25°C. The temperature (an intensiveproperty) of the mixture is, as you would
expect, also 25°C. Notice that we did not add the component temperatures to
determine the mixture temperature. Instead, we used some kind of averaging
scheme, a characteristic approach for determining the intensive propertiesof
a mixture. The internal energy, enthalpy, and entropy of a mixture per unit

massor per unit moleof the mixture can be determined by dividing the equa-
tions above by the mass or the mole number of the mixture (mmor Nm). We
obtain (Fig. 13–12)

¢Sm
a

k

i
 1

¢Si
a

k

i
 1

mi ¢si
a

k

i
 1

Ni ¢si¬¬ 1 kJ>K 2

¢Hm
a

k

i
 1

¢Hi
a

k

i
 1

mi ¢hi
a

k

i
 1

Ni ¢hi¬¬ 1 kJ 2

¢Um
a

k

i
 1

¢Ui
a

k

i
 1

mi ¢ui
a

k

i
 1

Ni ¢ui¬¬ 1 kJ 2

Sm
a

k

i
 1

Si
a

k

i
 1

misi
a

k

i
 1

Nisi¬¬ 1 kJ>K 2

Hm
a

k

i
 1

Hi
a

k

i
 1

mihi
a

k

i
 1

Nihi¬¬ 1 kJ 2

Um
a

k

i
 1

Ui
a

k

i
 1

miui
a

k

i
 1

Niui¬¬ 1 kJ 2

Chapter 13 | 689

This is 33 percent lower than the assumed value. Therefore, we should

repeat the calculations, using the new value of Vm. When the calculations

are repeated we obtain 0.738 m^3 after the second iteration, 0.678 m^3 after

the third iteration, and 0.648 m^3 after the fourth iteration. This value does

not change with more iterations. Therefore,

Discussion Notice that the results obtained in parts (b), (c), and (d) are

very close. But they are very different from the ideal-gas values. Therefore,

treating a mixture of gases as an ideal gas may yield unacceptable errors at

high pressures.

Vm
0.648 m^3

2 kmol A

6 kmol B

UA=1000 kJ

UB=1800 kJ

Um=2800 kJ

FIGURE 13–11

The extensive properties of a mixture

are determined by simply adding the

properties of the components.

2 kmol A

3 kmol B

u-A=500 kJ/kmol

u-B=600 kJ/kmol

u-m=560 kJ/kmol

FIGURE 13–12

The intensive properties of a mixture

are determined by weighted averaging.