Modern Engineering Thermodynamics

406 CHAPTER 12: Mixtures of Gases and Vapors
CRITICAL THINKING
Whereas the volumes of insoluble solids and liquids seem easily defined, because their molecules do not intermingle, the
same is not true for gases and vapors, where their molecules do intermingle. But, what happens when you mix two soluble
liquids? Is the mixture volume in this case just the sum of the volumes of the mixture components before they were
mixed? Can you find an example of soluble liquids where the final mixture volume is not equal to the sum of their
premixed component volumes?
internal energy U m , mixture total enthalpy H m , and mixture total entropy S m ) of a mixture are not generally equal
to the sum of the extensive thermodynamic properties of the components. It turns out that the value of any
thermodynamic property of a mixture is just the mass weighted sum of the partial specific properties of the mixture’s
components. Therefore, to determine the numeric value of a thermodynamic property of a mixture we need to
know (a) the exact composition of the mixture and (b) the values of the partial specific properties of all the
components in the mixture. This is what the first half of this chapter is all about.
The second half of this chapter deals with the application of this material to a very special mixture of gases and
vapors, air and water vapor (atmospheric air). This is normally the domain of heating, ventilating, and air conditioning
(HVAC) engineers, but since the atmosphere affects all of us in our daily life, it provides a good textbook
application of gas and vapor mixture theory. The basic elements of HVAC involve applying the first and second
laws to systems designed to cool and dehumidify or heat and humidify atmospheric and building air. To carry out
this analysis we need the numerical values for specific internal energy, specific enthalpy, and specific entropy for
various mixtures of air and water vapor. Since atmospheric air is a fairly complex mixture, it is more convenient to
refer to industry prepared tables and charts for accurate thermodynamic property values for this mixture.
12.2 THERMODYNAMIC PROPERTIES OF GAS MIXTURES
Unfortunately, there is no single measure of mixture composition. A mixture composition often is given simply in
percent, but the percent is calculated on a mass (or weight) basis, 1 a molar basis, a volume basis,orapressure
basis; and the numerical values depend on which basis is used in the calculation. This ambiguity leads us to define
four composition percentages or fraction measures for mixtures of gases.
Consider a homogeneous mixture made up of N distinct gases, each of which has a unique molecular mass, M i . Let
the mass of each gas present in the mixture be m i . Then the mass balance gives the total mass of the mixture m m as
m m = m 1 + m 2 + + m N = ∑ N
i=1
m i (12.1)
The corresponding number of moles n i of gas i with molecular mass M i can be determined from Eq. (1.9) as
n i = m i /M i (1.12)
and because the mole unit is just another measure of mass, the total number of moles of mixture n m is simply
n m = n 1 + n 2 + + n N = ∑ N
i=1
n i (12.2)
With these two mass measures, we can define two different mass-based composition measures or fractions as
and
The mass fraction w i of chemical species i in the mixture is
w i = m (12.3)
i
m m
The mole fraction χ i of chemical species i in the mixture is
χ i = n (12.4)
i
n m
1 This is also called a gravimetric basis.