WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition 12 CHAPTER Gas Mixtures

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition © The McGraw-Hill Companies, Inc.,1998 Dalton’s Law of Additive Pressures for the Mixture of Two Ideal Gases 12-1

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Amagat’s Law of Additive Volumes for the Mixture of Two Ideal Gases 12-2

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Compressibility Factors: One Way of Predicting Real-Gas Mixture P-v-T (Fig. 12-8) 12-3

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Another Way of Predicting the P-v- T Behavior of a Real-Gas Mixture (Fig. 12-9) 12-4 Treat a real-gas mixture as a pseudopure substance with critical properties P´ cr and T´ cr

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Use of Partial Pressures for Entropy Evaluation (Fig ) 12-5 Partial pressures (not the mixture pressure) are used in the evaluation of entropy changes of ideal-gas mixtures

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary A mixture of two or more gases of fixed chemical composition is called a nonreacting gas mixture. The composition of a gas mixture is described by specifying either the mole fraction or the mass fraction of each component, defined as where 12-6

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The apparent (or average) molar mass and gas constant of a mixture are expressed as and 12-7

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary Dalton's law of additive pressures states that the pressure of a gas mix-ture is equal to the sum of the pressures each gas would exert if it existed alone at the mixture temperature and volume. 12-8

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary Amagat's law of additive volumes states that 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. 12-9

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary Dalton's and Amagat's laws hold exactly for ideal- gas mixtures, but only approximately for real-gas mixtures. They can be expressed as Dalton's law: Amagat's law: 12-10

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary Here P i is called the component pressure and V i is called the component volume. Also, the ratio P i /P m is called the pressure fraction and the ratio V i /V m is called the volume fraction of component i. For ideal gases, P i and V i can be related to y i by 12-11

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The quantity y i P m is called the partial pressure and the quantity y i V m, is called the partial volume

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The P-v-T behavior of real-gas mixtures can be predicted by using generalized compressibility charts. The compressibility factor of the mixture can be expressed in terms of the compressibility factors of the individual gases as where Z is determined either at T m and V m, (Dalton's law) or at T m and P m (Amagat's law) for each individual gas. Chapter Summary 12-13

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The P-v-T behavior of a gas mixture can also be predicted approximately by Kay's rule, which involves treating a gas mixture as a pure substance with pseudocritical properties determined from and 12-14

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The extensive properties of a gas mixture, in general, can be determined by summing the contributions of each component of the mixture. The evaluation of intensive properties of a gas mixture, however, involves averaging in terms of mass or mole fractions: 12-15

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary and 12-16

WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary These relations are applicable to both ideal- and real-gas mixtures. The properties or property changes of individual components can be determined by using ideal-gas or real-gas relations developed in earlier chapters