Thermodynamics

ors 2 s 1 1s 2 s 1 2 ideal R 1Z s2 Z s12(12–64)where the values of Z s are determined from the generalized entropy departurechart and the entropy change (s 2 s 1 ) ideal is determined from the idealgasrelations for entropy change. Notice that the last terms on the right-handside are zero for an ideal gas.Chapter 12 | 673EXAMPLE 12–11The h and s of Oxygen at High PressuresDetermine the enthalpy change and the entropy change of oxygen per unitmole as it undergoes a change of state from 220 K and 5 MPa to 300 K and10 MPa (a) by assuming ideal-gas behavior and (b) by accounting for thedeviation from ideal-gas behavior.Solution Oxygen undergoes a process between two specified states. Theenthalpy and entropy changes are to be determined by assuming ideal-gasbehavior and by accounting for the deviation from ideal-gas behavior.Analysis The critical temperature and pressure of oxygen are T cr 154.8 Kand P cr 5.08 MPa (Table A–1), respectively. The oxygen remains above itscritical temperature; therefore, it is in the gas phase, but its pressure isquite high. Therefore, the oxygen will deviate from ideal-gas behavior andshould be treated as a real gas.(a) If the O 2 is assumed to behave as an ideal gas, its enthalpy will dependon temperature only, and the enthalpy values at the initial and the final temperaturescan be determined from the ideal-gas table of O 2 (Table A–19) atthe specified temperatures:1h 2 h 1 2 ideal h 2,ideal h 1,ideal 18736 64042 kJ>kmol 2332 kJ/kmolThe entropy depends on both temperature and pressure even for ideal gases.Under the ideal-gas assumption, the entropy change of oxygen is determinedfrom1 s 2 s 12 ideal s ° 2 s ° 1 R u ln P 2P 1 1205.213 196.1712 kJ>kmol # K 18.314 kJ>kmol #10 MPaK 2ln5 MPa 3.28 kJ/kmol # K(b) The deviation from the ideal-gas behavior can be accounted for by determiningthe enthalpy and entropy departures from the generalized charts ateach state:T R1 T 1 220 KT cr 154.8 K 1.42P R1 P 15 MPa ∂ Z h1 0.53, Z s1 0.25P cr 5.08 MPa 0.98