Thermodynamics

Chapter 13 | 695critical temperatures, but they are also above their critical pressures. Therefore,air will probably deviate from ideal-gas behavior, and thus it should betreated as a real-gas mixture.The energy balance for this steady-flow system can be expressed on a unitmole basis ase in e out ¢e system→0 0 S e in e out S h 1 h 2 qoutqout h 1 h 2 y N21h 1 h 2 2 N2 y O21h 1 h 2 2 O2where the enthalpy change for either component can be determined from thegeneralized enthalpy departure chart (Fig. A–29) and Eq. 12–58:h 1 h 2 h 1,ideal h 2,ideal R u T cr 1Z h1 Z h2 2The first two terms on the right-hand side of this equation represent theideal-gas enthalpy change of the component. The terms in parentheses representthe deviation from the ideal-gas behavior, and their evaluation requires aknowledge of reduced pressure P R and reduced temperature T R , which arecalculated at the mixture temperature T m and mixture pressure P m .(a) If the N 2 and O 2 mixture is assumed to behave as an ideal gas, theenthalpy of the mixture will depend on temperature only, and the enthalpyvalues at the initial and the final temperatures can be determined from theideal-gas tables of N 2 and O 2 (Tables A–18 and A–19):T 1 220 K S h 1,ideal,N2 6391 kJ>kmolh 1,ideal,O2 6404 kJ>kmolT 2 160 K S h 2,ideal,N2 4648 kJ>kmolh 2,ideal,O2 4657 kJ>kmolqout y N21h 1 h 2 2 N2 y O21h 1 h 2 2 O2 10.79216391 46482 kJ>kmol 10.212 16404 46572 kJ>kmol 1744 kJ/kmol(b) Kay’s rule is based on treating a gas mixture as a pseudopure substancewhose critical temperature and pressure areandT ¿ cr,m a y i T cr,i y N2T cr,N2 y O2T cr,O2 10.792 1126.2 K2 10.2121154.8 K2 132.2 KThen,P ¿ cr,m a y i P cr,i y N2P cr,N2 y O2P cr,O2 10.79213.39 MPa2 10.21215.08 MPa2 3.74 MPaT R,1 T m,1T cr,m 220 K132.2 K 1.66P R P m 10 MPa f ZP cr,m 3.74 MPa 2.67h1 ,m 1.0T R,2 T m,2T cr,m 160 K132.2 K 1.21f Z h2 ,m 2.6