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

(13–19)

(13–20)

(13–21)

Similarly, the specific heats of a gas mixture can be expressed as

(13–22)

(13–23)

Notice that properties per unit mass involve mass fractions(mfi) and prop-

erties per unit mole involve mole fractions(yi).

The relations given above are exact for ideal-gas mixtures, and approxi-

mate for real-gas mixtures. (In fact, they are also applicable to nonreacting

liquid and solid solutions especially when they form an “ideal solution.”)

The only major difficulty associated with these relations is the determina-

tion of properties for each individual gas in the mixture. The analysis can be

simplified greatly, however, by treating the individual gases as ideal gases,

if doing so does not introduce a significant error.

Ideal-Gas Mixtures

The gases that comprise a mixture are often at a high temperature and low

pressure relative to the critical-point values of individual gases. In such cases,

the gas mixture and its components can be treated as ideal gases with negligi-

ble error. Under the ideal-gas approximation, the properties of a gas are not

influenced by the presence of other gases, and each gas component in the

mixture behaves as if it exists alone at the mixture temperature Tmand mix-

ture volume Vm. This principle is known as the Gibbs–Dalton law,which is

an extension of Dalton’s law of additive pressures. Also, the h,u,cv, and cpof

an ideal gas depend on temperature only and are independent of the pressure

or the volume of the ideal-gas mixture. The partial pressure of a component in

an ideal-gas mixture is simply Pi
yiPm, where Pmis the mixture pressure.

Evaluation of uor hof the components of an ideal-gas mixture during

a process is relatively easy since it requires only a knowledge of the initial

and final temperatures. Care should be exercised, however, in evaluating the

sof the components since the entropy of an ideal gas depends on the pres-

sure or volume of the component as well as on its temperature. The entropy

change of individual gases in an ideal-gas mixture during a process can be

determined from

(13–24)

or

¢si
s°i,2 s°i,1Ru ln (13–25)

Pi,2

Pi,1

cp,i ln

Ti,2

Ti,1

Ru ln

Pi,2

Pi,1

¢si
s°i,2 s°i,1Ri ln

Pi,2

Pi,1

cp,i ln

Ti,2

Ti,1

Ri ln

Pi,2

Pi,1

cp,m
a

k

i
 1

mfi cp,i¬ 1 kJ>kg#K 2 and¬cp,m
a

k

i
 1

yi cp,i¬ 1 kJ>kmol#K 2

cv,m
a

k

i
 1

mfi cv,i¬ 1 kJ>kg#K 2 and¬cv,m
a

k

i
 1

yi cv,i¬ 1 kJ>kmol#K 2

sm
a

k

i
 1

mfi si¬ 1 kJ>kg#K 2 and¬sm
a

k

i
 1

yi si¬ 1 kJ>kmol#K 2

hm
a

k

i
 1

mfi hi¬ 1 kJ>kg 2 and¬hm
a

k

i
 1

yi hi¬ 1 kJ>kmol 2

um
a

k

i
 1

mfi ui 1 kJ>kg 2 ¬ and¬um
a

k

i
 1

yiui 1 kJ>kmol 2

690 | Thermodynamics

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