Download - Lec 21 22_Ch 13
-
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