Prepared by Pr. Noureddine
Ait Messaoudene
University of Hail
Based on
Yunus A. Cengel and Michael
A. Boles
Thermodynamics: An
Engineering Approach
6th Edition, McGraw Hill,
2007.
Faculty of Enginering
DEPARTMENT OF MECHANICAL ENGINEERING
Chapter 13
GAS MIXTURES
Lecture 16
13–1 COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS
13–2 P-v-T BEHAVIOR OF GAS MIXTURES: IDEAL GASES
13–3 PROPERTIES OF GAS MIXTURES: IDEAL GASES
Up to this point
systems that involve a single pure substance.
Many important thermodynamic systems involve mixtures of pure substances.
Objectives
•Develop rules for determining nonreacting gas mixture properties from knowledge of
mixture composition and the 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.
•Predict the P-v-T behavior of gas mixtures based on Dalton’s law of additive pressures
and Amagat’s law of additive volumes.
13–1 COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS
Two ways to describe the composition of a mixture:
by specifying the number of moles of each component, called molar analysis,
by specifying the mass of each component, called gravimetric analysis.
Deviding by
mm and Nm
mass of the
mixture
the mole number
of the mixture
Dividing by mm and by Nm
mass fraction of
component i
mole fraction of
component i
The mass of a substance can be expressed as m = NM
the apparent (or average) molar mass and the gas constant of a mixture can be
expressed as
Universal gas cte
The molar mass of a mixture can also be expressed as
Mass and mole fractions of a mixture are related by
13–2 P-v-T BEHAVIOR OF GAS MIXTURES: IDEAL GASES
When two or more ideal gases are
mixed,
the behavior of a molecule normally is
not influenced by the presence of other
similar or dissimilar molecules
a nonreacting
mixture of
ideal gases
also behaves
as an ideal gas
Example: Air can be
treated as an ideal gas in
the range where nitrogen
and oxygen behave as
ideal gases.
When a gas mixture consists of real (nonideal) gases, however, the prediction of the P-v-T
behavior of the mixture becomes rather involved
The prediction of the P-v-T behavior of gas mixtures is usually based on two models:
Dalton’s law of additive pressures and Amagat’s law of additive volumes.
And the two
laws are
identical and
give identical
results
component
pressure
component
volume
the volume a
component would
occupy if it existed
alone at Tm and Pm
The ratio Pi /Pm is called the pressure fraction of component i.
The ratio Vi /Vm is called the volume fraction of component i.
(actually, the volume of
each component is equal
to the whole volume of
the vessel)
Ideal-Gas Mixtures
using the ideal-gas relation for both the components and the gas mixture (Pv = NRuT)
The quantity yiPm is called the partial pressure (identical to the component pressure
for ideal gases),
the quantity yiVm is called the partial volume (identical to the component volume for
ideal gases).
For an ideal-gas mixture, the mole fraction, the pressure fraction, and the volume
fraction of a component are identical.
13–3 PROPERTIES OF GAS MIXTURES: IDEAL GASES
The extensive properties of a nonreacting ideal or real-gas mixture are obtained by adding
the contributions of each component of the mixture
But for intensive properties of a mixture, some kind of averaging scheme must be used.
dividing the equations above by the mass or the mole number of the mixture (mm or Nm)
Similarly, the specific heats of a gas mixture can be expressed as
The relations given above are exact for ideal-gas mixtures, and approximate for real-gas
mixtures.
Major difficulty the determination of properties for each individual gas
first approach : treat the individual gases as ideal gases.
Ideal-Gas Mixtures
In practice, mixtures are often at a high temperature and low pressure relative to the
critical-point values of individual gases.
the gas mixture and its components can be treated as ideal gases with negligible error.
the Gibbs–Dalton law, which is an extension of Dalton’s law, is applicable
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 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 Pm is
the mixture pressure.
We should treat Δs more carefully since the entropy of an ideal gas depends on the
pressure 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
(kJ/kg.K)
or
(kJ/kmol.K)
where Pi,2 = yi,2Pm,2 and Pi,1 = yi,1Pm,1.
Notice that the partial pressure Pi of each component is used in the evaluation of the
entropy change, not the mixture pressure Pm.