Thermodynamics

y i b ikka m a a y i a 1>2i b2andb m a (13–12a, b)Chapter 13 | 687In the van der Waals equation, for example, the two constants for the mixtureare determined fromi1i1where expressions for a i and b i are given in Chapter 3.EXAMPLE 13–2P-v-T Behavior of Nonideal Gas Mixtures2 kmol NA rigid tank contains 2 kmol of N 2 and 6 kmol of CO 2 gases at 300 K and26 kmol CO 215 MPa (Fig. 13–10). Estimate the volume of the tank on the basis of300 K(a) the ideal-gas equation of state, (b) Kay’s rule, (c) compressibility factors15 MPaand Amagat’s law, and (d ) compressibility factors and Dalton’s law.V m = ?Solution The composition of a mixture in a rigid tank is given. The volumeof the tank is to be determined using four different approaches.FIGURE 13–10Assumptions Stated in each section.Schematic for Example 13–2.Analysis (a) When the mixture is assumed to behave as an ideal gas, thevolume of the mixture is easily determined from the ideal-gas relation for themixture:V m N mR u T m 18 kmol218.314 kPa # m 3 >kmol # K21300 K2 1.330 m 3P m15,000 kPasinceN m N N2 N CO2 2 6 8 kmol(b) To use Kay’s rule, we need to determine the pseudocritical temperatureand pseudocritical pressure of the mixture by using the critical-point propertiesof N 2 and CO 2 from Table A–1. However, first we need to determine themole fraction of each component:y N2 N N 2 2 kmolN m 8 kmol 0.25andy CO 2 N CO 2 6 kmolN m 8 kmol 0.75T ¿ cr,m a y i T cr,i y N2T cr,N2 y CO2 T cr,CO2 10.252 1126.2 K2 10.7521304.2 K2 259.7 KThen,Thus,P ¿ cr,m a y i P cr,i y N2P cr,N2 y CO2 P cr,CO2 10.252 13.39 MPa2 10.75217.39 MPa2 6.39 MPaT R T mT cr,m ¿P R P mP ¿ cr,m 300 K259.7 K 1.16∂ Z m 0.491Fig. A–15b215 MPa6.39 MPa 2.35V m Z m N m R u T mP m Z m V ideal 10.49211.330 m 3 2 0.652 m 3