8/10/2019 Lec 21 22_Ch 13

1/21

Lecture 21 & 22

Gas Mixtures (Ch-13)

Thermodynamics - II

Zia Ud Din

8/10/2019 Lec 21 22_Ch 13

2/21

2

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 composition

of 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 on

Daltons law of additive pressures and Amagats law ofadditive volumes.

8/10/2019 Lec 21 22_Ch 13

3/21

3

COMPOSITION OF A GAS MIXTURE:

MASS AND MOLE FRACTIONS

The mass of a mixture is equal to the

sum of the masses of its components.

The number of moles of a nonreacting mixture

is equal to the sum of the number of moles of

its components.

To determine the properties of a mixture, we need to know the composition of

the mixture as well as the properties of the individual components. There are

two ways to describe the composition of a mixture:

Massfraction

Mole

fraction

Molar analysis: specifying

the number of moles of

each component

Gravimetric analysis:

specifying the mass of eachcomponent

8/10/2019 Lec 21 22_Ch 13

4/21

4

The sum of the mole

fractions of a mixture is

equal to 1.

Average molar mass

Gas constant

The molar mass of a mixture

Mass and mole fractions of a

mixture are related by

The sum of the mass and

mole fractions of a mixture

is equal to 1.

8/10/2019 Lec 21 22_Ch 13

5/21

5

Constituent Chemical

Symbol

Analysis Molar Mass

By Volume % By Mass % (Kg/kmol)

Oxygen O2 20.95 23.14 31.999

Nitrogen N2 78.09 75.53 28.013

ArgonAr 0.93 1.28 39.948

Carbon

Diaoxide CO2 0.03 0.05 44.010

Properties of Air

8/10/2019 Lec 21 22_Ch 13

6/21

6

Constituent Chemical

Symbol

Analysis Molar Mass

By Volume % By Mass % (Kg/kmol)

Oxygen O2 21 23.3 32

Nitrogen N2 79.0 76.7 28

Volumetric analysis is the analysis by volume

Gravimetric analysis is the analysis by mass

Approximate Analysis of Air

8/10/2019 Lec 21 22_Ch 13

7/21

Example 13-1: Mass and Mole Fractions of a

Gas Mixtures

8/10/2019 Lec 21 22_Ch 13

8/21

Example 13-1: Mass and Mole Fractions of a

Gas Mixtures

8/10/2019 Lec 21 22_Ch 13

9/21

Example 13-1: Mass and Mole Fractions of a

Gas Mixtures

8/10/2019 Lec 21 22_Ch 13

10/21

10

pT V= volume

of the container

Mixture of two

Ideal gasesA+B

Consider a closed vessel of volume V at temperature T, which contains a mixture

of ideal gases at a known pressure.

pA

T

Gas A

Mass= mA

pB

T

Gas B

Mass= mB

Mixture A+B

Mass= m = mA + mB

When the individual gas is kept at the same Temperature and Volume as

that of the mixture then the pressure will be lowered.

The partial pressure of each constituent is that pressure which the gas

would exert if it occupied alone that volume occupied by the mixture at the

same temperature.

Daltons Law of Partial Pressures

8/10/2019 Lec 21 22_Ch 13

11/21

11

Daltons Law of Partial Pressures states that The pressure of a mixture of

gasses is equal to the sum of partial pressures of the constituents

TV

Mixture of two

perfect gassesA+B

T

Gas A

Mass= mA

T

Gas B

Mass= mBMixture A+B

A Bp p p Ap

Bp

A Bp p pBy Daltons Law: By Conservation of mass:

A Bm m m

Daltons Law of Partial Pressures

A B C

i

p p p p etc

p p

A B C

i

m m m m etc

m m

8/10/2019 Lec 21 22_Ch 13

12/21

12

P-v-T BEHAVIOR OF GAS

MIXTURES: IDEAL AND

REAL GASES

Daltons law of additive pressures for a mixture

of two ideal gases.

Amagats law of additive volumes for a mixture

of two ideal gases.

The prediction of the P-v-T

behavior of gas mixtures

is usually based on two

models:Daltons law of additive

pressures: The pressure

of a gas mixture is equal

to the sum of the

pressures each gas would

exert if it existed alone atthe mixture temperature

and volume.

Amagats law of additive

volumes: The volume of a

gas mixture is equal to the

sum of the volumes each

gas would occupy if it

existed alone at the

mixture temperature and

pressure.

8/10/2019 Lec 21 22_Ch 13

13/21

13

The volume a component would occupy if it existed alone

at the mixture T and P is called the component volume (for

ideal gases, it is equal to the partial volume yiVm).

For ideal gases, Daltons and Amagats

laws are identical and give identical results.

Pi

component pressure Vi

component volume

Pi/P

mpressure fraction V

i/V

mvolume fraction

8/10/2019 Lec 21 22_Ch 13

14/21

14

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 yiPm is called the partial pressure (identical to the component

pressure for ideal gases), and the quantity yiVm 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 leaving

a combustion chamber) is frequently determined by a volumetric analysis

(Orsat Analysis)

8/10/2019 Lec 21 22_Ch 13

15/21

15

Real-Gas

Mixtures

One way of predicting the P-v-T

behavior of a real-gas mixture is to

use compressibility factor.

Zi is determined either at Tm and VmDaltons law) or at Tm and Pm (Amagats

law) for each individual gas. Using

Daltons law gives more accurate

results.

Another way of predicting theP-v-T behavior of a real-gas

mixture is to treat it as a

pseudopure substance with

critical properties.

Zm is determined by using thesepseudocritical properties.

The result by Kays rule is

accurate to within about 10%

over a wide range of

temperatures and pressures.

Kays ruleCompressibility factor

8/10/2019 Lec 21 22_Ch 13

16/21

16

PROPERTIES OF GAS MIXTURES:

IDEAL AND REAL GASES

The extensive

properties of a

mixture are

determined by

simply adding the

properties of thecomponents.

Extensive properties of a gas mixture

Changes in properties of a gas mixture

8/10/2019 Lec 21 22_Ch 13

17/21

17

The intensive

properties of a

mixture are

determined by

weighted

averaging.

Extensive properties of a gas mixture

Properties per unit mass involve

mass fractions (mfi) andproperties per unit mole involve

mole fractions (yi).

The relations are exact for ideal-

gas mixtures, and approximate for

real-gas mixtures.

8/10/2019 Lec 21 22_Ch 13

18/21

18

Ideal-Gas Mixtures

Partial pressures (not

the mixture pressure)

are used in the

evaluation of entropychanges of ideal-gas

mixtures.

GibbsDalton law: Under the ideal-gas

approximation, the properties of a gas are

not influenced by the presence of othergases, and each gas component in the

mixture behaves as if it exists alone at

the mixture temperature Tm and mixture

volume Vm.

Also, the h, u, cv, and cp of an ideal gas

depend on temperature only and areindependent of the pressure or the

volume of the ideal-gas mixture.

8/10/2019 Lec 21 22_Ch 13

19/21

Expansion of an Ideal Gas Mixture in a

Turbine

A mixture of oxygen (O2), carbon dioxide (CO2) andhelium (He) gases with mass fractions of 0.0625, 0.625

and 0.3125 respectively, enter an adiabatic turbine at

1000 kPa and 600 K steadily and expand to 100 kPa

pressure. The isentropic efficiency of the turbine is 90 %.

For gas components assuming constant specific heats atroom temperature, determine

(a) The work output per unit mass of mixture

8/10/2019 Lec 21 22_Ch 13

20/21

20

Real-Gas Mixtures

It is difficult to predict the

behavior of nonideal-gas

mixtures because of the

influence of dissimilar

molecules on each other.

This equation suggests that the generalized property

relations and charts for real gases developed inChap. 12 can also be used for the components of

real-gas mixtures. But TRand PRfor each

component should be evaluated using Tm and Pm.

If the Vm and Tm are specified instead of Pm and Tm,

evaluate Pm using Daltons law of additive pressures.Another way is to treat the mixture as a pseudopure

substance having pseudocritical properties,

determined in terms of the critical properties of the

component gases by using Kays rule.

T ds relation for a gas mixture

8/10/2019 Lec 21 22_Ch 13

21/21

21

Summary

Composition of a gas mixture: Mass and mole

fractions

P-v-Tbehavior of gas mixtures

Ideal-gas mixtures

Real-gas mixtures

Properties of gas mixtures

Ideal-gas mixtures

Real-gas mixtures