Thermodynamics

688 | Thermodynamics(c) When Amagat’s law is used in conjunction with compressibility factors, Z mis determined from Eq. 13–10. But first we need to determine the Z of eachcomponent on the basis of Amagat’s law:N 2 :T R,N2 T mP R,N2 T cr,N2P mP cr,N2 300 K126.2 K 2.38∂ Z15 MPaN2 1.021Fig. A–15b23.39 MPa 4.42CO 2 :T R,CO2 T mP R,CO2 T cr,CO2P mP cr,CO2 300 K304.2 K 0.99∂ Z15 MPaCO2 0.301Fig. A–15b27.39 MPa 2.03Mixture:Thus,Z m a y i Z i y N2Z N2 y CO2 Z CO2 10.25211.022 10.752 10.302 0.48The compressibility factor in this case turned out to be almost the same asthe one determined by using Kay’s rule.(d) When Dalton’s law is used in conjunction with compressibility factors, Z mis again determined from Eq. 13–10. However, this time the Z of each componentis to be determined at the mixture temperature and volume, which isnot known. Therefore, an iterative solution is required. We start the calculationsby assuming that the volume of the gas mixture is 1.330 m 3 , the valuedetermined by assuming ideal-gas behavior.The T R values in this case are identical to those obtained in part (c) andremain constant. The pseudoreduced volume is determined from its definitionin Chap. 3:Similarly,From Fig. A–15, we read Z N 2 0.99 and Z CO 2 0.56. Thus,andV m Z m N m R u T mP m Z m V ideal 10.48211.330 m 3 2 0.638 m 3v R,N2 v R,CO2 vN2R u T cr,N2 >P cr,N2 V m >N N 2R u T cr,N2 >P cr,N211.33 m 3 2>12 kmol218.314 kPa # m 3 >kmol # K21126.2 K2>13390 kPa2 2.1511.33 m 3 2>16 kmol218.314 kPa # m 3 >kmol # K21304.2 K2>17390 kPa2 0.648Z m y N2Z N2 y CO2 Z CO2 10.252 10.992 10.75210.562 0.67V m Z m N m RT mP m Z m V ideal 10.672 11.330 m 3 2 0.891 m 3