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cen84959_ch13

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Chapter 13 GAS MIXTURES | 701 U p to this point, we have limited our consideration to thermodynamic systems that involve a single pure substance such as water. Many important thermody- namic applications, however, involve mixtures of several pure substances rather than a single pure substance. Therefore, it is important to develop an understanding of mixtures and learn how to handle them. In this chapter, we deal with nonreacting gas mixtures. A nonreacting gas mixture can be treated as a pure sub- stance since it is usually a homogeneous mixture of different gases. The properties of a gas mixture obviously depend on the properties of the individual gases (called components or constituents ) as well as on the amount of each gas in the mixture. Therefore, it is possible to prepare tables of proper- ties for mixtures. This has been done for common mixtures such as air. It is not practical to prepare property tables for every conceivable mixture composition, however, since the number of possible compositions is endless. Therefore, we need to develop rules for determining mixture properties from a knowledge of mixture composition and the properties of the individual components. We do this first for ideal-gas mixtures and then for real-gas mixtures. The basic principles involved are also applicable to liquid or solid mixtures, called solutions . Objectives The objectives of Chapter 13 are to: 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 and real-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. Perform energy and exergy analysis of mixing processes.

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13–1 COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS 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: either by specifying the number of moles of each component, called molar analysis , or by spec- ifying the mass of each component, called gravimetric analysis . Consider a gas mixture composed of k components. The mass of the mix- ture m m is the sum of the masses of the individual components, and the mole number of the mixture N m is the sum of the mole numbers of the indi- vidual components* (Figs. 13–1 and 13–2). That is, (13–1 a, b ) The ratio of the mass of a component to the mass of the mixture is called the mass fraction mf, and the ratio of the mole number of a component to the mole number of the mixture is called the mole fraction y : (13–2 a, b ) Dividing Eq. 13–1 a by m m or Eq. 13–1 b by N m , we can easily show that the sum of the mass fractions or mole fractions for a mixture is equal to 1 (Fig. 13–3):
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