Thermodynamics

dh m T m ds m v m dP m each other.Chapter 13 | 693the mole fraction of the gases in the mixture. What is not so obvious is thatif the same gas in two different chambers is mixed at constant temperatureand pressure, the entropy change is zero.Substituting the known values, the entropy change becomesN m N O2 N CO2 13 52 kmol 8 kmoly O2 N O 2 3 kmolN m 8 kmol 0.375y CO2 N CO 2 5 kmolN m 8 kmol 0.625¢S m R u 1N O2ln y O2 N CO2 ln y CO2 218.314 kJ>kmol # K2313 kmol21ln 0.3752 15 kmol2 1ln 0.62524 44.0 kJ/KThe exergy destruction associated with this mixing process is determinedfromX destroyed T 0 S gen T 0 ¢S sys 1298 K2144.0 kJ>K2 13.1 MJDiscussion This large value of exergy destruction shows that mixing processesare highly irreversible.Real gasA25°C0.4 m 3100 kPaReal gasB25°C0.6 m 3100 kPaReal gasmixtureA + B25°C1 m 3102 kPa ?FIGURE 13–16It is difficult to predict the behavior ofnonideal-gas mixtures because of theReal-Gas MixturesWhen the components of a gas mixture do not behave as ideal gases, theanalysis becomes more complex because the properties of real (nonideal)gases such as u, h, c v , and c p depend on the pressure (or specific volume) aswell as on the temperature. In such cases, the effects of deviation fromideal-gas behavior on the mixture properties should be accounted for.Consider two nonideal gases contained in two separate compartments ofan adiabatic rigid tank at 100 kPa and 25°C. The partition separating thetwo gases is removed, and the two gases are allowed to mix. What do youthink the final pressure in the tank will be? You are probably tempted to say100 kPa, which would be true for ideal gases. However, this is not true fornonideal gases because of the influence of the molecules of different gaseson each other (deviation from Dalton’s law, Fig. 13–16).When real-gas mixtures are involved, it may be necessary to account for theeffect of nonideal behavior on the mixture properties such as enthalpy andentropy. One way of doing that is to use compressibility factors in conjunctionwith generalized equations and charts developed in Chapter 12 for real gases.Consider the following T ds relation for a gas mixture:It can also be expressed asd a a mf i h i b T m d a a mf i s i b a a mf i v i b dP m