Chap 13 Lecture Poo

8/11/2019 Chap 13 Lecture Poo

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Objectives Develop rules for determining nonreacting gas mixture

properties from knowledge of mixture composition andthe properties of the individual components.

Define the quantities used to describe the compositionof a mixture, such as mass fraction, mole fraction, and

volume fraction. Apply the rules for determining mixture properties to

ideal-gas mixtures and real-gas mixtures.

Predict the P -v -T behavior of gas mixtures based onDaltons law of additive pressures and Amagats law ofadditive volumes.

Perform energy and exergy analysis of mixingprocesses.


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COMPOSITION OF A GAS MIXTURE:MASS AND MOLE FRACTIONS

The mass of a mixture is equal to thesum of the masses of its components.

The number of moles of a nonreactingmixture is equal to the sum of thenumber of moles of its components.

To determine the properties of a mixture, we need to know the composition ofthe mixture as well as the properties of the individual components. There aretwo ways to describe the composition of a mixture:

Massfraction

Mole

fraction

Molar analysis: specifyingthe number of moles ofeach componentGravimetric analysis: specifying the mass of eachcomponent


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The sum of the molefractions of a mixtureis equal to 1.

Apparent (or average) molar mass

Gas constant

The molar mass of a mixture

Mass and mole fractions of amixture are related by

The sum of the mass andmole fractions of a mixtureis equal to 1.


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P -v -T BEHAVIOR OF GAS MIXTURES:IDEAL AND REAL GASES

The prediction of the P-v-T behaviorof gas mixtures is usually based ontwo models:

Daltons law of additivepressures: The pressure of a gas

mixture is equal to the sum of thepressures each gas would exert if itexisted alone at the mixturetemperature and volume.

Amagats law of additivevolumes: The volume of a gasmixture is equal to the sum of thevolumes each gas would occupy if itexisted alone at the mixturetemperature and pressure.

Daltons law of additive pressures fora mixture of two ideal gases.

Amagats law of additive volumesfor a mixture of two ideal gases.


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The volume a component would occupy if it existed aloneat the mixture T and P is called the component volume (for

ideal gases, it is equal to the partial volume y i V m).

For ideal gases, Daltons and Amagatslaws are identical and give identical results.

P i component pressure V i component volume

P i /P m pressure fraction V i /V m volume fraction


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Ideal-Gas Mixtures

This equation is only valid for ideal-gas mixtures as it is derived by assumingideal-gas behavior for the gas mixture and each of its components.

The quantity y i P m is called the partial pressure (identical to the component pressure for ideal gases), and the quantity y i V m is called the partial volume (identical to the component volume for ideal gases).

Note that for an ideal-gas mixture, the mole fraction, the pressure fraction,and the volume fraction of a component are identical.

The composition of an ideal-gas mixture (such as the exhaust gases leavinga combustion chamber) is frequently determined by a volumetric analysis(Orsat Analysis ).


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Real-Gas Mixtures

One way of predicting the P -v -Tbehavior of a real-gas mixture is to

use compressibility factor.

Z m is determined by using thesepseudocritical properties.The result by Kays rule isaccurate to within about 10%over a wide range oftemperatures and pressures.

Kays rule

Z i is determined either at T m and V m Daltons law) or at T m and P m (Amagatslaw) for each individual gas. UsingDaltons law gives more accurate

results.

Compressibility factor


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PROPERTIES OF GAS MIXTURES:IDEAL AND REAL GASES

The extensiveproperties of amixture aredetermined bysimply adding theproperties of thecomponents.

Extensive properties of a gas mixture

Changes in properties of a gas mixture


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The intensiveproperties of amixture aredetermined byweighted

averaging.

Extensive properties of a gas mixture

Properties per unit mass involvemass fractions (mf i ) and

properties per unit mole involvemole fractions (y i ).

The relations are exact for ideal-gas mixtures, and approximate for

real-gas mixtures.


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Ideal-Gas Mixtures

Partial pressures (notthe mixture pressure)

are used in theevaluation of entropychanges of ideal-gas

mixtures.

Gibbs Dalton law: Under the ideal-gasapproximation, the properties of a gas are

not influenced by the presence of othergases, and each gas component in themixture behaves as if it exists alone atthe mixture temperature T m and mixturevolume V m.

Also, the h, u, c v , and c p of an ideal gasdepend on temperature only and areindependent of the pressure or thevolume of the ideal-gas mixture.


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Real-Gas Mixtures

It is difficult to predict thebehavior of nonideal-gasmixtures because of theinfluence of dissimilarmolecules on each other.

This equation suggests that the generalized propertyrelations and charts for real gases developed inChap. 12 can also be used for the components ofreal-gas mixtures. But T R and P R for eachcomponent should be evaluated using T m and P m.

If the V m and T m are specified instead of P m and T m,

evaluate P m using Daltons law of additive pressures. Another way is to treat the mixture as a pseudopuresubstance having pseudocritical properties,determined in terms of the critical properties of thecomponent gases by using Kays rule.

T ds relation for a gas mixture


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Summary Composition of a gas mixture: Mass and

mole fractions P-v-T behavior of gas mixtures

Ideal-gas mixtures

Real-gas mixtures Properties of gas mixtures

Ideal-gas mixtures

Real-gas mixtures

Chap 13 Lecture Poo

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