Thermodynamics

684 | ThermodynamicsorAlso,M m a y i M i y O2M O2 y N2M N2 y CH4 M CH4 10.09221322 10.1752 1282 10.73321162 19.6 kg>kmolR m R u 8.314 kJ>1kmol # K2 0.424 kJ/kg # KM m 19.6 kg>kmolDiscussion When mass fractions are available, the molar mass and molefractions could also be determined directly from Eqs. 13–4 and 13–5.Gas AV, TP A+Gas BV, TP BGasmixtureA + BV, TP A + P BFIGURE 13–5Dalton’s law of additive pressures fora mixture of two ideal gases.Gas AP, TV A+Gas BP, TV BGas mixtureA + BP , TV A + V BFIGURE 13–6Amagat’s law of additive volumes fora mixture of two ideal gases.13–2 P-v-T BEHAVIOR OF GAS MIXTURES:IDEAL AND REAL GASESAn ideal gas is defined as a gas whose molecules are spaced far apart sothat the behavior of a molecule is not influenced by the presence of othermolecules—a situation encountered at low densities. We also mentionedthat real gases approximate this behavior closely when they are at a lowpressure or high temperature relative to their critical-point values. The P-v-Tbehavior of an ideal gas is expressed by the simple relation Pv RT, whichis called the ideal-gas equation of state. The P-v-T behavior of real gases isexpressed by more complex equations of state or by Pv ZRT, where Z isthe compressibility factor.When two or more ideal gases are mixed, the behavior of a molecule normallyis not influenced by the presence of other similar or dissimilar molecules,and therefore a nonreacting mixture of ideal gases also behaves as anideal gas. Air, for example, is conveniently treated as an ideal gas in therange where nitrogen and oxygen behave as ideal gases. When a gas mixtureconsists of real (nonideal) gases, however, the prediction of the P-v-Tbehavior of the mixture becomes rather involved.The prediction of the P-v-T behavior of gas mixtures is usually based ontwo models: Dalton’s law of additive pressures and Amagat’s law of additivevolumes. Both models are described and discussed below.Dalton’s law of additive pressures: The pressure of a gas mixture is equalto the sum of the pressures each gas would exert if it existed alone at themixture temperature and volume (Fig. 13–5).Amagat’s law of additive volumes: The volume of a gas mixture is equalto the sum of the volumes each gas would occupy if it existed alone at themixture temperature and pressure (Fig. 13–6).Dalton’s and Amagat’s laws hold exactly for ideal-gas mixtures, but onlyapproximately for real-gas mixtures. This is due to intermolecular forcesthat may be significant for real gases at high densities. For ideal gases, thesetwo laws are identical and give identical results.